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1. xpression elevation Dry initial condition Setup boundary conditions an a i Bi anuga Dirichlet_boundary 0 4 0 0 Inflow Br anuga Reflective_boundary domain Solid reflective wall Bo anuga Dirichlet_boundary 5 0 0 Outflow domain set_boundary left Bi right Br top Br bottom Br Evolve system through time for t in domain evolve yieldstep 0 2 finaltime 40 0 print domain timestepping_statistics if domain get_quantity stage get_values interpolation_points 10 2 5 gt 0 print Stage gt 0 Changing to outflow boundary domain set_boundary right Bo This example differs from the first version in that a constant outflow boundary condition has been defined Bo anuga Dirichlet_boundary 5 0 0 Outflow and that it is applied to the right hand side boundary when the water level there exceeds 0m for t in domain evolve yieldstep 0 2 finaltime 40 0 domain write_time if domain get_quantity stage get_values interpolation_points 10 2 5 gt print Stage gt 0 Changing to outflow boundary domain set_boundary right Bo The if statement in the timestepping loop evolve gets the quantity stage and obtains the interpolated value at the point 10m 2 5m which is on the right boundary If the stage exceeds Om a message is printed and the old boundary con
2. 76 Chapter 8 Basic ANUGA Assumptions APPENDIX A Supporting Tools This section describes a number of supporting tools supplied with ANUGA that offer a variety of types of function ality and can enhance the basic capabilities of ANUGA A 1 caching The cache function is used to provide supervised caching of function results A Python function call of the form result func argl argn can be replaced by from caching import cache result cache func argl argn which returns the same output but reuses cached results if the function has been computed previously in the same context result and the arguments can be simple types tuples list dictionaries or objects but not unhashable types such as functions or open file objects The function func may be a member function of an object or a module This type of caching is particularly useful for computationally intensive functions with few frequently used combina tions of input arguments Note that if the inputs or output are very large caching may not save time because disc access may dominate the execution time If the function definition changes after a result has been cached this will be detected by examining the functions bytecode and the function will be recomputed However caching will not detect changes in modules used by func In this case the cache must be cleared manually Options are set by means of the function set_option key value where key
3. pmesh mesh_interface py Rather than using either of these forms in this chapter we specify the location simply as anuga pmesh mesh_ interface in keeping with the usage in the Python statement for importing the function namely from anuga pmesh mesh_interface import create_mesh_from_regions The following parameters are common to many functions and classes and are omitted from the descriptions given below use_cache Specifies whether caching is to be used for improved performance See Section for details on the underlying caching functionality verbose If True provides detailed terminal output to the user 5 3 Mesh Generation Before discussing the part of the interface relating to mesh generation we begin with a description of a simple example of a mesh and use it to describe how mesh data is stored Figure 5 I represents a very simple mesh comprising just 11 points and 10 triangles 40 Chapter 5 ANUGA Public Interface Figure 5 1 A simple mesh 11 5 3 Mesh Generation 41 The variables points triangles and boundary represent the data displayed in Figure as follows The list points stores the coordinates of the points and may be displayed schematically as in Table index x y 0 1 1 1 4 2 2 8 1 3 1 3 4 5 5 5 8 6 6 11 5 7 3 6 8 1 8 9 4 9 10 10 7 Table 5 1 Point coordinates for mesh in Figure 5 1 The list triangles specifies the triangles that make up the mesh It does this
4. A 6 Graphical Mesh Generator GUI 87 A 7 class Alpha_Shape Alpha shapes are used to generate close fitting boundaries around sets of points The alpha shape algorithm produces a shape that approximates to the shape formed by the points or the shape that would be seen by viewing the points from a coarse enough resolution For the simplest types of point sets the alpha shape reduces to the more precise notion of the convex hull However for many sets of points the convex hull does not provide a close fit and the alpha shape usually fits more closely to the original point set offering a better approximation to the shape being sought In ANUGA an alpha shape is used to generate a polygonal boundary around a set of points before mesh generation The algorithm uses a parameter a that can be adjusted to make the resultant shape resemble the shape suggested by intuition more closely An alpha shape can serve as an initial boundary approximation that the user can adjust as needed The following paragraphs describe the class used to model an alpha shape and some of the important methods and attributes associated with instances of this class class Alpha_Shape points alpha None Module alpha_shape Instantiate an instance of the Alpha_Shape class points isan N x 2 list of points x1 y1 x2 y2 alpha is the fitting parameter alpha_shape via files point file boundary file alpha None Module alpha_shape This func
5. H 2 v 7 2 h4 ho h hF ho h 72 i 7 4 Flux limiting 71 where hy is a regularisation parameter that controls the minimal magnitude of the denominator Taking the limits we have for i lim 4 lim _ 0 h 0 h gt 0 h ho h and lim 4 lim A aby h 00 h 00 h ho h h with similar results for 0 The maximal value of is attained when h ho h is minimal or by differentiating the denominator 1 ho h 0 or ho h ANUGA has a global parameter Ho that controls the minimal depth which is considered in the various equations This parameter is typically set to 10 Setting ho H provides a reasonable balance between accuracy and stability In fact setting h Ho will scale the predicted speed by a factor of 0 5 h ho h 4 Ho H Hol 2mo 2h 2 In general for multiples of the minimal depth N Ho one obtains ar H 1 3 h h o h nonm NHo Ho N h 1 1 N2 which converges quadratically to the true value with the multiple N Although this equation can be used for any depth we have restricted its use to depths less than 10 Ho or 1 cm to computational resources According to Equation 7 3 this cutoff affects the calculated velocity by less than 1 7 5 Slope limiting A multidimensional slope limiting technique is employed to achieve second order spatial accuracy and to prevent spurious oscillations This is using the MinMod limiter and is documented elsewhere
6. INIA Figure 7 1 Triangular mesh used in our finite volume method Conserved quantities h uh and vh are associated with the centroid of each triangular cell The equations constituting the finite volume method are obtained by integrating the differential conservation equations over each triangular cell of the mesh Introducing some notation we use to refer to the th triangular cell T and N to the set of indices referring to the cells neighbouring the ith cell Then A is the area of the ith triangular cell and l is the length of the edge between the th and jth cells By applying the divergence theorem we obtain for each volume an equation which describes the rate of change of the average of the conserved quantities within each cell in terms of the fluxes across the edges of the cells and the effect of the source terms In particular rate equations associated with each cell have the form du 1 Taare Ly Hijliy S JEN i where e U the vector of conserved quantities averaged over the ith cell e S is the source term associated with the th cell and e H is the outward normal flux of material across the ijth edge The flux H is evaluated using a numerical flux function H which is consistent with the shallow water flux in the sense that for all conservation vectors U and normal vectors n H U U n E U n G Ulna Then Hi H U mi Uj Mij niz where mi is the midpoint of the ijth edge
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8. Sets the minimum depth that will be recognised when writing to an SWW file This is useful for removing thin water layers that seems to be caused by friction creep minimum_storable_height is the new minimum storable height value lt domain gt set_maximum allowed_speed maximum_allowed_speed Module shallow_water shallow_water_domain Set the maximum particle speed that is allowed in water shallower than minimum_allowed_height This 1s useful for controlling speeds in very thin layers of water and at the same time allow some movement avoiding pooling of water maximum_allowed_speed sets the maximum allowed speed value lt domain gt set_time time 0 0 Module abstract_2d_finite_volumes domain time sets the initial time in seconds for the simulation The default is 0 0 lt domain gt set_default_order n Module abstract_2d_finite_volumes domain Sets the default spatial order to the value specified by n which must be either 1 or 2 Assigning any other value to n will cause an error lt domain gt set_store_vertices_uniquely flag reduction None Module shallow_water shallow_water_domain Decide whether vertex values should be stored uniquely as computed in the model or whether they should be reduced to one value per vertex using averaging flag may be True meaning allow surface to be discontinuous or False meaning smooth vertex values reduction defines the smoothing operation if flag is False If not supplied
9. bottom Br 8 Chapter 4 Getting Started Evolve system through time for t in domain evolve yieldstep 0 1 finaltime 10 0 print domain timestepping_statistics 4 1 4 Establishing the Mesh The first task is to set up the triangular mesh to be used for the scenario This is carried out through the statement points vertices boundary anuga rectangular_cross 10 10 The function rectangular_cross is imported from a module mesh_ factory defined elsewhere ANUGA also contains several other schemes that can be used for setting up meshes but we shall not discuss these The above assignment sets up a 10 x 10 rectangular mesh triangulated in a regular way The assignment points vertices boundary anuga rectangular_cross m n returns e alist points giving the coordinates of each mesh point e alist vertices specifying the three vertices of each triangle and e a dictionary boundary that stores the edges on the boundary and associates each with one of the symbolic tags left right top or bottom The edges are represented as pairs i j where i refers to the triangle id and j to the edge id of that triangle Edge ids are enumerated from 0 to 2 based on the id of the vertex opposite For more details on symbolic tags see page I1 An example of a general unstructured mesh and the associated data structures points vertices and boundary is given in Section 5 3 4 1
10. elevation Polygon_function B default 0 0 lt domain gt set_region tag quantity X location vertices Module abstract_2d_finite_volumes domain see also abstract_2d_finite_volumes quantity set_values This function is used to assign values to individual quantities given a regional tag It is similar to set_ quantity For example if in the mesh generator a regional tag of ditch was used set_region can be used to set elevation of this region to 10m X is the constant or function to be applied to the quantity over the tagged region location describes how the values will be applied Options are vertices the default edges unique vertices and centroids This method can also be called with a list of region objects This is useful for adding quantities in regions and having one quantity value based on another quantity See abst ract_2d_finite_volumes region for more details slump_tsunami length depth slope width None thickness None radius None dphi 0 48 x0 0 0 y0 0 0 alpha 0 0 gravity 9 8 gamma 1 85 massco 1 dragco 1 frictionco 0 dx None kappa 3 0 kappad 1 0 zsmall 0 01 scale None domain None verbose False Module shallow_water smf This function returns a callable object representing an initial water displacement generated by a submarine sediment failure These failures can take the form of a submarine slump or slide In the case of a slide use slide_tsunami
11. ocean_east if project scenario fixed _wave Save every two mins leading up to wave approaching land for t in domain evolve yieldstep 120 finaltime 5000 print domain timestepping_statistics print domain boundary_statistics tags ocean_east Save every 30 secs as wave starts inundating ashore for t in domain evolve yieldstep 10 finaltime 10000 skip_initial_step True print domain timestepping_statistics print domain boundary_statistics tags ocean_east For the fixed wave scenario the simulation is run to 10000 seconds with the first half of the simulation stored at two minute intervals and the second half of the simulation stored at ten second intervals This functionality is especially convenient as it allows the detailed parts of the simulation to be viewed at higher time resolution This also demonstrates the ability of ANUGA to dynamically override values The method add_quantity works like set_quantity except that it adds the new surface to what exists already In this case it adds the initial shape of the water displacement to the water level 4 7 Exploring the Model Output Now that the scenario has been run the user can view the output in a number of ways As described earlier the user may run anuga_ viewer to view a three dimensional representation of the simulation The user may also be interested in a maximum inundation map This simply shows the maximum water dept
12. onshore Bd top Bs if project scenario slide Boundary conditions for slide scenario domain set_boundary ocean_east Bd bottom Bd onshore Bd top Bd Note that we use different boundary conditions depending on the scenario defined in project py It is not a requirement in ANUGA to have this code structure just an example of how the script can take different actions depending on a variable 4 6 7 Evolution With the basics established the running of the evolve step is very similar to the corresponding step in runup py except we have different evolve loops for the two scenarios For the slide scenario the simulation is run for an intial 60 seconds at which time the slide occurs We use the function tsunami_source to adjust stage values We then run the simulation until 5000 seconds with the output stored every ten seconds 30 Chapter 4 Getting Started 1f project scenario slide Initial run without any event for t in domain evolve yieldstep 10 finaltime 60 print domain timestepping_statistics print domain boundary_statistics tags ocean_east Add slide to water surface if allclose t 60 domain add_quantity stage tsunami_source Continue propagating wave for t in domain evolve yieldstep 10 finaltime 5000 skip_initial_step True print domain timestepping_statistics print domain boundary_statistics tags
13. However close to the bed the limiter must ensure that no negative depths occur On the other hand in deep water the bed topography should be ignored for the purpose of the limiter Let w z h be the stage bed elevation and depth at the centroid and let w zi hi be the stage bed elevation and depth at vertex i Define the minimal depth across all vertices as Amin as Amin min hi Let w be the stage obtained from a gradient limiter limiting on stage only The corresponding depth is then defined as hi Wi Zi We would use this limiter in deep water which we will define somewhat boldly as Amin 2 72 Chapter 7 ANUGA mathematical background Similarly let w be the stage obtained from a gradient limiter limiting on depth respecting the bed slope The corre sponding depth is defined as We introduce the concept of a balanced stage w which is obtained as the linear combination Wi aw 1 o or 7 2 Wi Zi ah 1 a h where a 0 1 Since w is obtained in deep water where the bedslope is ignored we have immediately that a 1 for hmin gt If hmin lt we want to use the shallow limiter just enough that no negative depths occur Formally we will require that 7 E ahi 1 a h gt e Vi or o h hi gt E hi Vi 7 4 There are two cases 1 hy lt hi The deep water limited using stage vertex is at least as far away from the bed than the shallow water
14. See set_boundary_type page 88 See get_boundary page 88 88 Appendix A Supporting Tools A 8 Numerical Tools The following table describes some useful numerical functions that may be found in the module utilities numerical_tools angle vl v2 None normal_vector v mean x cov x y None err x y 0 n 2 relative True norm x corr x y None ensure_numeric A typecode None histogram a bins relative Fals create_bins data number_of_ bins None Angle between two dimensional vectors v1 and v2 or be tween v1 and the z axis if v2 is None Value is in range 0 to 27 Normal vector to v Mean value of a vector x Covariance of vectors x and y If y is None returns cov x x Relative error of x y to y 2 norm if n 2 or Max norm if n None If denominator evaluates to zero or if y is omitted or if relative False absolute error is returned 2 norm of x Correlation of x and y If y is None returns autocorrelation of x Returns a numeric array for any sequence A If A is already a numeric array it will be returned unaltered Otherwise an attempt is made to convert it to a numeric array Needed because array A can cause memory overflow Standard histogram If relative is True values will be normalised against the total and thus represent frequencies rather than counts Safely create bins for use with histogram If data contains only o
15. 3 3 07 volumes LZ OF 0 ily 1 12 13 A 1 20 SN m a lt xd cd am N H 2 14 3 M Ss LO s aa LO os wy Sos dst 65 File Formats 6 1 Oty O68 0 97 1 0 0 1 0 2 0 3 0 4 0 5 i 7 F r Lety Lal as Biz Dudo Lia Lin det La Li 2y 2elp Lia 23y 2sty 285p 2 O LL 229 3 Selly A 343 il 0 3267 Be oabr 3 95 Ag stage 0 025 0 02777778 0 02777778 0 02777778 0 02777778 0 02777778 0 02777778 0 02777778 0 02777778 0 02777778 0 03333334 0 01111111 5 782412e 019 5 782412e 019 5 782412e 019 5 782412e 019 5 782412e 019 5 782412e 019 5 782412e 019 5 782412e 019 0 1654055 0 1558442 0 1504084 xmomentum The SWW format is used not only for output but also serves as input for functions such as file_boundary and file function described in Chapter 5 An STS file is used for storing a set of points and associated times It contains in addition to dimension information the following variables e x and y coordinates of the points represented as numeric arrays e permutation Original indices of the points as specified by the optional ordering_file see the function urs2sts in Section 6 1 9 e elevation a numeric array storing bed elevations e time a numeric array containing times for model evaluation The only difference between the STS format and the SWW format is the former does not contain a list specifying the points at
16. Figures 4 7 and 4 8 show the maximum water depth within the defined region for the slide and fixed wave scenario respectively Note these inundation maps have been based on purely hypothetical scenarios and were designed explicitly for demonstration purposes only The user could develop a maximum absolute momentum or other expressions which can be derived from the quantities It must be noted here that depth is more meaningful when the elevation is positive depth stage elevation as it describes the water height above the available elevation When the elevation is negative depth is meauring the water height from the sea floor With this in mind maximum inundation maps are typically clipped to the coastline However the data input here did not contain a coastline 32 Chapter 4 Getting Started Speed Legend Slump Origin CI Extent Caims fu Island J shatiow Slide Maximum Depth m lt VALUE gt MN lt 02 EE 02 04 EJ 0 4 o s E 06 08 EJ o8 1 0 1 0 1 2 E 2 114 14 16 EJ 16 18 GE 18 20 B 20 40 MA 40 50 Hl gt 6 0 Figure 4 7 Maximum inundation map for the Cairns slide scenario Note this inundation map has been based on a purely hypothetical scenario which was designed explictiy for demonstration purposes only 4 7 Exploring the Model Output 33 Legend Stump Origin E cams Fixed Wave Maximum Depth m E MN lt 02 EE 02 04 A 04 05 EJ 06 08
17. Module abstract_2d_finite_volumes domain Generates output about boundary forcing at each timestep quantities names the quantities to be reported may be None a string or a list of strings tags names the tags to be reported may be either None a string or a list of strings When quantities stage and tags top bottom will return a string like Boundary values at time 0 5000 top stage in 0 25821218 0 02499998 bottom stage in 0 27098821 0 02499974 lt domain gt get_quantity name location vertices indices None Module abstract_2d_finite_volumes domain This function returns a Quantity object Q Access to its values should be done through O get_values documented on Page 59 name is the name of the quantity to retrieve location is indices is lt domain gt set_quantities_to_be_monitored quantity polygon None time_interval None Module abstract_2d_finite_volumes domain Selects quantities and derived quantities for which extrema attained at internal timesteps will be collected quantity specifies the quantity or quantities to be monitored and must be either ethe name of a quantity or derived quantity such as stage elevation ea list of quantity names or eNone polygon can be used to monitor only triangles inside the polygon Otherwise all triangles will be included time_interval will restrict monitoring to time steps in the interval Otherwise all timesteps
18. are not removed and x no compensation is received Private research and institutional x x use is free You may distribute modified versions of this code UNDER x THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE x SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR BOTH SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE AND CLEAR x NOTICE IS GIVEN OF THE MODIFICATIONS Distribution of this code a x part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT x x WITH THE AUTHOR If you are not directly supplying this code to a x customer and you are instead telling them how they can obtain it for x x free then you are not required to make any arrangement with me TKK KK RK RK KKK KK KK OK KK RR KK RK RK RARA RRA RARA RAR RARA OK OK OK OK OK OK ROK KKK RK RK RRA RAR e Pmwis a toolkit for building high level compound widgets in Python using the Tkinter module Parts of Pmw have been incorpoated into the graphical mesh generator The license for Pmw reads nou Pmw copyright Copyright 1997 1999 Telstra Corporation Limited Australia Copyright 2000 2002 Really Good Software Pty Ltd Australia Permission is hereby granted free of charge to any person obtaining a copy of this software and associated documentation files the Software to deal in the Software without restriction including without limitation the rights to use copy modify mer
19. but must be specified before a forcing term is applied i e simulation has started The default value is 0 0 i e no forcing centerand radius optionally restrict forcing to a circle with given center and radius polygon optionally restricts forcing to an area enclosed by the given polygon Note specifying center radius and polygon will cause an exception to be thrown Moreover if the specified polygon or circle does not lie fully within the mesh boundary an Exception will be thrown Example P x0 yO xl yO x1 yl x0 y1 Square polygon xmom General_forcing domain xmomentum polygon P ymom General_forcing domain ymomentum polygon P xmom rate f ymom rate domain forcing_terms append xmom domain forcing_terms append ymom 54 Chapter 5 ANUGA Public Interface Here f and g are assumed to be defined as functions of time providing a time dependent rate of change for xmomentum and ymomentum respectively P is assumed to be the polygon specified as a list of points class Inflow domain rate 0 0 center None radius None polygon None default_rate None verbose False Module shallow_water shallow_water_domain This is a general class for inflow and abstraction of water according to a given rate of change This class will always modify the st age quantity Inflow is based on the General_forcing class so the functionality is similar domain is the domain being evolved rate is the
20. file interpolation_points is a list of absolute coordinates or a geospatial object for points at which values are sought boundary_polygon is a list of coordinates specifying the vertices of the boundary This must be the same polygon as used when calling create_mesh_from_regions This argument can only be used when reading boundary data from an STS format file output_centroids set to true to sample at the centre of the triangle containing the point This may be useful for debugging new in 1 2 The model time stored within the file function can be accessed using the method lt callable_ object gt get_time The underlying algorithm used is as follows Given a time series i e a series of values associated with different times whose values are either just numbers a set of numbers defined at the vertices of a triangular mesh such as those stored in SWW files or a set of numbers defined at a number of points on the boundary such as those stored in STS files Interpolation_ function is used to create a callable object that interpolates a value for an arbitrary time t within the model limits and possibly a point x y within a mesh region The actual time series at which data is available is specified by means of an array time of monotonically increasing times The quantities containing the values to be interpolated are specified in an array or dictionary of arrays used in conjunction with the optional argument quant
21. verbose True except ImportError ANUGA does not rely on pylab to work print must have pylab installed to generate plots Here the time series for the quantities stage depth and speed will be generated for each gauge defined in the gauge file As described earlier depth is more meaningful for onshore gauges and stage is more appropriate for offshore gauges As an example output Figure 4 10 shows the time series for the quantity stage for the Elford Reef location for each scenario the elevation at this location is negative therefore stage is the more appropriate quantity to plot Note the large negative stage value when the slide was introduced This is due to the double Gaussian form of the initial surface displacement of the slide By contrast the time series for depth is shown for the onshore location of the Cairns Airport in Figure 36 Chapter 4 Getting Started stage at Elford Reef gauge Slide elevation 62 71m Fixed Wave elevation 62 71m 100 E 50 E Vv lt Uv gt 0 50 0 20 40 60 80 100 120 140 160 time minutes Figure 4 10 Time series information of the quantity stage for the Elford Reef location for the fixed wave and slide scenario 4 7 Exploring the Model Output 37 depth at Cairns Airport gauge Slide elevation 3 35m Fixed Wave elevation 3 35m water depth m 0 20 40 60 80 100 120 140 160 time
22. without mesh information tms NetCDF format for storing time series f t csv txt ASCII format for storing arbitrary points and associated attributes pts NetCDF format for storing arbitrary points and associated attributes asc ASCII format of regular DEMs as output from Arc View pry Associated ArcView file giving more metadata for asc format ers ERMapper header format of regular DEMs for ArcView dem NetCDF representation of regular DEM data tsh ASCII format for storing meshes and associated boundary and region info msh NetCDF format for storing meshes and associated boundary and region info nc Native ferret NetCDF format geo Houdinis ASCII geometry format The above table shows the file extensions used to identify the formats of files However typically in referring to a format we capitalise the extension and omit the initial full stop thus we refer to SWW files or PRJ files not sww files or prj files A typical dataflow can be described as follows SOMETHING MISSING HERE 6 1 1 Manually Created Files ASC PRJ Digital elevation models gridded NC Model outputs for use as boundary conditions e g from MOST 63 6 1 2 Automatically Created Files ASC PRJ DEM gt PTS NC SWW PTS TSH TSH with elevation TSH gt SWW TSH Boundary SWW SWW Polygonal mesh outline Convert DEMs to native pts file Convert MOST boundary files to boundary sww
23. 1 NOTE For details refer to the module utilities polygon py The maximal area of a triangular cell in a mesh Models a solid wall Returns same conserved quantities as those present in the neighbouring volume but reflected Specific to the shallow water equation as it works with the momentum quantities assumed to be the second and third conserved quantities visualisation tool used with ANUGA Returns values for the conserved quantities as a function of time The user must specify the domain to get access to the model time onshore elevation A point at which edges meet ER oOo xmomentum conserved quantity note two dimensional SWW equations say only x and y and NOT z ymomentum conserved quantity 96 Appendix D Glossary gl g2 lt Geospatial_data gt split Geospatial_data method indices count separate _points_ by_polygon in module utili ties polygon 80 time Q get_flow_through_cross_ section in module 61 x y get_maximum_inundation_ location in module 61 lt area gt polygon_area in module utili ties polygon 81 lt array gt inside _polygon in module utili ties polygon 79 lt array gt outside _polygon in module utili ties polygon 80 lt boolean gt is_inside_polygon ule utilities polygon lt boolean gt is_outside polygon in mod ule utilities polygon lt boolean gt point_on_line in module
24. 6 1 9 Basic File Conversions sww2dem basename_in basename_out None quantity None reduction None cellsize 10 number_of_decimal_ places None NODATA value 9999 easting_min None easting_max None northing_min None nor thing_max None verbose False origin None datum WGS84 format ers block_size None Module shallow_water data_manager 6 1 File Formats 67 Takes data from an SWW file basename_in and converts it to DEM format ASC or ERS of a desired grid size cel lsize in metres The user can select how many decimal places the output data is represented with by using number_of_decimal_places with the default being 3 The easting and northing values are used if the user wishes to determine the output within a specified rectan gular area The reduction input refers to a function to reduce the quantities over all time step of the SWW file e g maximum or an index referring to a time step to extract a time slice of data dem2pts basename_in basename_out None eastingmin None easting_max None northing_min None nor thing max None use_cache False verbose False Module shallow_water data_manager Takes DEM data a NetCDF file representation of data from a regular Digital Elevation Model and converts it to PTS format urs2sts basename_in basename_out None weights None verbose False origin None mean_stage 0 0 zs cale 1 0 ordering filename None Module shallow_water data_manager Takes URS data timese
25. E 08 10 E 10 12 2 14 14246 i 16 18 EJ 1 8 20 MA 20 40 MM 40 60 E gt 60 Figure 4 8 Maximum inundation map for the Cairns fixed wave scenario Note this inundation map has been based on a purely hypothetical scenario which was designed explictiy for demonstration purposes only 34 Chapter 4 Getting Started The user may also be interested in interrogating the solution at a particular spatial location to understand the behaviour of the system through time To do this the user must first define the locations of interest A number of locations have been identified for the Cairns scenario as shown in Figure 4 9 Figure 4 9 Point locations to show time series information for the Cairns scenario These locations must be stored in either a csv or txt file The corresponding csv file for the gauges shown in Figure 4 9 is gauges csv easting northing name elevation 367622 63 8128196 42 Cairns 0 360245 11 8142280 78 Trinity Beach 0 386133 51 8131751 05 Cairns Headland 0 430250 8128812 23 Elford Reef 0 367771 61 8133933 82 Cairns Airport 0 Header information has been included to identify the location in terms of eastings and northings and each gauge is given a name The elevation column can be zero here This information is then passed to the function sww2csv_ gauges shown in GetTimeseries py which generates the csv files for each point location The CSV files can then be used in csv2t imeseries
26. Least squares fit Convert TSH to sww viewable using anuga_viewer Simulation using ANUGA TSH or MSH 6 1 3 SWW STS and TMS Formats The SWW STS and TMS formats are all NetCDF formats and are of key importance for ANUGA An SWW file is used for storing ANUGA output and therefore pertains to a set of points and a set of times at which a model is evaluated It contains in addition to dimension information the following variables x and y coordinates of the points represented as numeric arrays e elevation a numeric array storing bed elevations e volumes a list specifying the points at the vertices of each of the triangles e time a numeric array containing times for model evaluation The contents of an SWW file may be viewed using the anuga viewer anuga_viewer which creates an on screen visualisation See section A 2 page 78 in Appendix A for more on anuga_viewer Alternatively there are tools such as ncdump that allow you to convert a NetCDF file into a readable format such as the Class Definition Language CDL The following is an excerpt from a CDL representation of the output file runup sww generated from running the simple example runup py of Chapter 4 netcdf bedslope dimensions number_of_volumes 200 number_of_vertices 3 number_of_points 121 number_of_timesteps variables UNLIMITED 41 currently float x number_of_points hoh h h opoh h h global attr
27. Miscellaneous Functions The functions here are not Geospatial_data object methods but are used with them X find_optimal_smoothing_parameter data file alpha_list None mesh_file None boundary_ poly None mesh_resolution 100000 north_bound ary None south_boundary None east_boundary None west_boundary None plot name all_alphas _ splitfac tor 0 1 seed_num None cache False verbose False Module geospatial_data geospatial_data Calculate the minimum covariance from a set of points in a file It does this by removing a small random sample of points from dat a_file and creating models with different alpha values from alpha_list and cross validates the predicted value to the previously removed point data Returns the alpha value which has the smallest covariance data_file is the input data file and must not contain points outside the boundaries defined and is either a PTS TXT or CSV file alpha_list is the list of alpha values to use mesh_file is the path to a mesh file to create if supplied If None a mesh file will be created named temp msh NOTE if there is a mesh_resolution defined or any boundaries are defined any input mesh_file value is ignored mesh_resolution is the maximum area size for a triangle north_boundary south_boundary east_boundary west_boundary are the boundary values to use plot_name is the path name of the plot file to write seed_num is the random number generator seed
28. The method must return a list of three floating point numbers representing values for stage xmomentum and ymoment um respectively The constructor of a particular boundary class may be used to specify particular values or flags to be used by the evaluate method Please refer to the source code for the existing boundary conditions for examples of how to implement boundary conditions 5 7 Forcing Terms ANUGA provides a number of predefined forcing functions to be used with simulations Gravity and friction are always calculated using the elevation and friction quantities but the user may additionally add forcing terms to the list domain forcing_terms and have them affect the model Currently predefined forcing terms are class General_forcing domain quantity_name rate 0 0 center None radius None polygon None default_ rate None verbose False Module shallow_water shallow_water_domain This is a general class to modify any quantity according to a given rate of change Other specific forcing terms are based on this class but it can be used by itself as well e g to modify momentum domain is the domain being evolved quant ity_name is the name of the quantity that will be affected by this forcing term rate is the rate at which the quantity should change This can be either a constant or a function of time Positive values indicate increases negative values indicate decreases The parameter rate can be None at initialisation
29. a triangle used for triangulation and a triangular mesh is created inside the polygon using a mesh generation engine On any given platform the same mesh will be returned each time the script is run Boundary tags are not restricted to left bottom right and top as in the case of runup py Instead the user specifies a list of tags appropriate to the configuration being modelled In addition the mesh generator provides a way to adapt to geographic or other features in the landscape whose presence may require an increase in resolution This is done by allowing the user to specify a number of interior polygons each with a specified resolution It is also possible to specify one or more holes that is areas bounded by polygons in which no triangulation is required 24 Chapter 4 Getting Started In its general form the mesh generator takes for its input a bounding polygon and optionally a list of interior poly gons The user specifies resolutions both for the bounding polygon and for each of the interior polygons Given this data the mesh generator first creates a triangular mesh with varying resolution The function used to implement this process is create_domain_from_regions which creates a Domain object as well as a mesh file Its arguments include the bounding polygon and its resolution a list of boundary tags and a list of pairs polygon resolution specifying the interior polygons and their reso
30. and assumes a projection into UTM with false easting of 500000 and false northing of 1000000 on the southern hemisphere 0 on the northern hemisphere All locations must consequently be specified in Cartesian coordinates eastings northings or x y where the unit is metres Alternative projections can be used but ANUGA does have the concept of a UTM zone that must be the same for all coordinates in the model 8 2 2 Internal coordinates It is important to realise that for numerical precision ANUGA uses coordinates that are relative to the lower left node of the rectangle containing the mesh min Ymin This origin is referred to internally as x11corner yllcorner following the ESRI ASCII grid notation The SWW file format also includes x11corner yllcorner and any coordinate in the file should be adjusted by adding this origin See Section 6 1 3 Throughout the ANUGA interface functions have optional boolean arguments absolute which controls whether spatial data received is using the internal representation absolute False or the user coordinate set absolute True See e g get_vertex_coordinates on 48 DEMs meshes and boundary conditions can have different origins However the internal representation in ANUGA will use the origin of the mesh 75 8 2 3 Polygons When generating a mesh it is assumed that polygons do not cross Having polygons that cross can cause bad meshes to be produced or the mesh generation itself may fail
31. argument can be None in which case nothing is stored Otherwise the argument must be a dictionary where the keys are names of quantities already defined within ANUGA and the values are either 1 or 2 If the value is 1 the quantity will be stored once at the beginning of the simulation if the value is 2 it will be stored at each timestep The ANUGA default is equivalent to the call domain set_quantities_to_be_stored elevation 1 stage 2 xmomentum 2 ymomentum 2 lt domain gt get_nodes absolute False Module abstract_2d_finite_volumes domain Return x y coordinates of all nodes in the domain mesh The nodes are ordered in an Nx2 array where N is the number of nodes This is the same format they were provided in the constructor i e without any duplication absolute is a boolean which determines whether coordinates are to be made absolute by taking georeference into account Default is False as many parts of ANUGA expect relative coordinates lt domain gt get_vertex_coordinates absolute False Module abstract_2d_finite_volumes domain Return vertex coordinates for all triangles as a 3 Mx2 array where the jth vertex of the ith triangle is located in row 3 i j and M is the number of triangles in the mesh absolute is a boolean which determines whether coordinates are to be made absolute by taking georeference into account Default is False as many parts of ANUGA expect relative coordinates l
32. available on sourceforge at http sourceforge net projects anugal A snapshot of work in progress is available through the ANUGA software repository atihttp datamining anu edu au svn anuga trunk anuga_core source anuga where the more adventurous reader might like to go This manual describes ANUGA version 1 2 1 To check for later versions of this manual go to http datamining anu edu au anuga 1 2 Scope This manual covers only what is needed to operate the software after installation and configuration It does not include instructions for installing the software or detailed API documentation both of which will be covered in separate publications and by documentation in the source code The latest installation instructions may be found at http datamining anu edu au anuga attachment wiki WikiStart anuga_installation_guide 1 2 0 pdf 1 3 Audience Readers are assumed to be familiar with the Python Programming language and its object oriented approach Python tutorials include nttp docs python org tutand http www sthurlow com python Readers also need to have a general understanding of scientific modelling as well as enough programming experience to adapt the code to different requirements CHAPTER TWO Background Modelling the effects on the built environment of natural hazards such as riverine flooding storm surges and tsunami is critical for understanding their economic and social impact on our urban comm
33. bed xpression elevation Setup boundary conditions Bi anuga Dirichlet_boundary 0 4 0 0 Inflow Br anuga Reflective_boundary domain Solid reflective wall domain set_boundary left Bi right Br top Br bottom Br Evolve system through time for t in domain evolve yieldstep 0 2 finaltime 40 0 print domain timestepping_statistics In discussing the details of this example we follow the outline given above discussing each major step of the code in turn 4 4 4 Establishing the Mesh In this example we use a similar simple structured triangular mesh as in runup py for simplicity but this time we will use a Symmetric one and also change the physical extent of the domain The assignment points vertices boundary anuga rectangular_cross m n lenl length len2 width returns an mxn mesh similar to the one used in the previous example except that now the extent in the x and y directions are given by the value of length and width respectively Defining m and n in terms of the extent as in this example provides a convenient way of controlling the resolution By defining dx and dy to be the desired size of each hypotenuse in the mesh we can write the mesh generation as follows length 10 0 width 5 0 dx dy bh Resolution Length of subdivisions on both axes points vertices boundary anuga rectangular_cross int length dx
34. by specifying for each triangle the indices the numbers shown in the first column above that correspond to the three points at the triangles vertices taken in an anti clockwise order around the triangle Thus in the example shown in Figure 5 1 the variable triangles contains the entries shown in Table 5 2 The starting point is arbitrary so triangle 0 1 3 is considered the same as 1 3 0 and 3 0 1 index points 0 0 1 3 1 1 2 4 2 2 5 4 3 2 6 5 4 4 5 9 5 4 9 7 6 3 4 7 I 7 9 8 8 1 4 3 9 5 10 9 Table 5 2 Triangles for mesh in Figure 5 1 Finally the variable boundary identifies the boundary triangles and associates a tag with each create_mesh_from_regions bounding polygon boundary tags maximum triangle_area None file name None interior_regions None interior_holes None hole_tags None poly_geo_reference None mesh_geo_reference None minimum_triangle_an gle 28 0 fail_if_polygons_outside True breaklines None use_cache False verbose True Module pmesh mesh_interface This function allows a user to initiate the automatic creation of a mesh inside a specified polygon input bounding_polygon Among the parameters that can be set are the resolution maximal area for any tri angle in the mesh and the minimal angle allowable in any triangle The user can specify a number of internal polygons within each of which the resolution of the mesh can be specified interior_regions is a paired list c
35. if a planar wave is reflected out through this boundary class Transmissive_stage_zero_momentum_boundary domain None Module shallow_water This boundary returns same stage conserved quantities as those present in its neighbour volume but sets mo mentum to zero The underlying domain must be specified when boundary is instantiated This type of boundary is useful when stage is known at the boundary as a function of time but momentum should be set to zero This is for example the case where a boundary is needed in the ocean on the two sides perpendicular to the coast to maintain the wave height of the incoming wave This class is specific to the shallow water equation as it works with the momentum quantities assumed to be the second and third conserved quantities This boundary condition should not cause the numerical instabilities seen with the transmissive momentum boundary conditions see Page 52 and Page 53 class Dirichlet_discharge_boundary domain None stageO None wh0 None Module shallow_water shallow_water_domain 5 6 Boundary Conditions 53 stageo sets the stage wh 0 sets momentum in the inward normal direction 5 6 2 User defined boundary conditions All boundary classes must inherit from the generic boundary class Boundary and have a method called evaluate which must take as inputs self vol_id and edge_id where self refers to the object itself and vol_id and edge_id are integers referring to particular edges
36. in question ea list of numbers or a numeric array ordered the same way as the mesh vertices ea function e g see the samples introduced in Chapter 2 ean expression composed of other quantities and numbers arrays lists for example a linear combination of quantities such as lt domain gt set_quantity stage elevation x ethe name of a file from which the data can be read In this case the optional argument att ribute_name will select which attribute to use from the file If left out set_quantity will pick one This is useful in cases where there is only one attribute ea geospatial dataset See Section A 5 Optional argument attribute_name applies here as with files Exactly one of the arguments numeric quantity function geospatial_data and filename must be present set_quantity will look at the type of the numeric and determine what action to take Values can also be set using the appropriate keyword arguments If x is a function for ex ample domain set_quantity name x domain set_quantity name numeric x and domain set_quantity name function x are all equivalent Other optional arguments are eindices which is a list of ids of triangles to which set_quant it y should apply its assignment of values elocation determines which part of the triangles to assign to Options are vertices the default edges unique vertices and centroids If vertices is used edge and c
37. modelling flows in areas larger than one UTM zone 6 degrees wide Fluid is assumed to be inviscid i e no kinematic viscosity included The finite volume is a very robust and flexible numerical technique but it is not the fastest method around If the geometry is sufficiently simple and if there is no need for wetting or drying a finite difference method may be able to solve the problem faster than ANUGA Frictional resistance is implemented using Manning s formula but ANUGA has not yet been fully validated in regard to bottom roughness CHAPTER FOUR Getting Started This section is designed to assist the reader to get started with ANUGA by working through some examples Two examples are discussed the first is a simple example to illustrate many of the concepts and the second is a more realistic example 4 1 A Simple Example 4 1 1 Overview What follows is a discussion of the structure and operation of a script called runup py This example carries out the solution of the shallow water wave equation in the simple case of a configuration compris ing a flat bed sloping at a fixed angle in one direction and having a constant depth across each line in the perpendicular direction The example demonstrates the basic ideas involved in setting up a complex scenario In general the user specifies the geometry bathymetry and topography the initial water level boundary conditions such as tide and any forcing terms
38. we did for runup py domain set_quantity friction 0 0 4 6 5 3 Elevation The elevation is specified by reading data from a file with a name derived from project demname with the pts extension domain set_quantity elevation filename project demname pts use_cache True verbose True alpha 0 1 The alpha parameter controls how smooth the elevation surface should be See section A 7 page 88 Setting cache True allows ANUGA to save the result in order to make subsequent runs faster Using verbose True tells the function to write diagnostics to the screen 4 6 An Example with Real Data 29 4 6 6 Boundary Conditions Setting boundaries follows a similar pattern to the one used for runup py except that in this case we need to associate a boundary type with each of the boundary tag names introduced when we established the mesh In place of the four boundary types introduced for runup py we use the reflective boundary for each of the tagged segments defined by create_domain_from_regions Bd anuga Dirichlet_boundary tide 0 0 Mean water level Bs anuga Transmissive_stage_zero_momentum_boundary domain Neutral boundary if project scenario fixed_wave Huge 50m wave starting after 60 seconds and lasting 1 hour Bw anuga Time_boundary domain domain function lambda t 60 lt t lt 3660 x50 0 0 domain set_boundary ocean_east Bw bottom Bs
39. will be included Information can be tracked in the evolve loop by printing quantity_statistics and collected data will be stored in the SWW file 58 Chapter 5 ANUGA Public Interface lt domain gt quantity_statistics precision 4f Module abstract_2d_finite_volumes domain Reports on extrema attained by selected quantities Returns a string of the following type for each timestep Monitored quantities at time 1 0000 stage elevation values since time 0 00 in 0 00000000 0 30000000 minimum attained at time 0 00000000 location 0 16666667 0 33333333 maximum attained at time 0 00000000 location 0 83333333 0 16666667 ymomentum values since time 0 00 in 0 00000000 0 06241221 minimum attained at time 0 00000000 location 0 33333333 0 16666667 maximum attained at time 0 22472667 location 0 83333333 0 66666667 xmomentum values since time 0 00 in 0 06062178 0 47886313 minimum attained at time 0 00000000 location 0 16666667 0 33333333 maximum attained at time 0 35103646 location 0 83333333 0 16666667 The quantities and derived quantities listed here must be selected at model initialisation time using the method domain set_quantities_to_be_monitored The optional keyword argument precision 4f will determine the precision used for floating point values in the output This diagnostics helps track extrema attained by the s
40. x exp t 0 0 0 0 The effect of these statements is to set up a selection of different alternative boundary conditions and store them in variables that can be assigned as needed Each boundary condition specifies the behaviour at a boundary in terms of the behaviour in neighbouring elements The boundary conditions introduced here may be briefly described as follows e Reflective boundary Returns same stage as in its neighbour volume but momentum vector reversed 180 degrees reflected Specific to the shallow water equation as it works with the momentum quantities assumed to be the second and third conserved quantities A reflective boundary condition models a solid wall e Transmissive boundary Returns same conserved quantities as those present in its neighbour volume This is one way of modelling outflow from a domain but it should be used with caution if flow is not steady state as replication of momentum at the boundary may cause numerical instabilities propagating into the domain and eventually causing ANUGA to crash If this occurs consider using e g a Dirichlet boundary condition with a stage value less than the elevation at the boundary e Dirichlet boundary Specifies constant values for stage z momentum and y momentum at the boundary e Time boundary Like a Dirichlet boundary but with behaviour varying with time Before describing how these boundary conditions are assigned we recall that a mesh is specified using three variables
41. 5 Initialising the Domain These variables are then used to set up a data structure domain through the assignment domain anuga Domain points vertices boundary This creates an instance of the Domain class which represents the domain of the simulation Specific options are set at this point including the basename for the output file and the directory to be used for data domain set_name runup domain set_datadir In addition the following statement could be used to state that quantities stage xmomentum and ymomentum are to be stored at every timestep and elevation only once at the beginning of the simulation 4 1 A Simple Example 9 domain set_quantities_to_be_stored stage 2 xmomentum 2 ymomentum 2 elevation However this is not necessary as the above is the default behaviour 4 1 6 Initial Conditions The next task is to specify a number of quantities that we wish to set for each mesh point The class Domain has a method set_quantit y used to specify these quantities It is a flexible method that allows the user to set quantities in a variety of ways using constants functions numeric arrays expressions involving other quantities or arbitrary data points with associated values all of which can be passed as arguments All quantities can be initialised using set_quantity For a conserved quantity such as stage xmomentum ymoment um this is called an initial condition How
42. 6 lt domain gt get_disconnected_triangles Domain method 48 lt domain gt get_maximum_inundation_ elevation method 60 lt domain gt get_maximum_inundation_ location method 60 lt domain gt get_name Domain method 46 lt domain gt get_nodes Domain method 48 lt domain gt get_triangles Domain method lt domain gt get_vertex_coordinates main method 48 lt domain gt get_wet_elements method 60 lt domain gt quantity_statistics method lt domain gt set_boundary method 52 lt domain gt set_datadir Domain method 46 lt domain gt set_default_order Domain method 47 lt domain gt set_maximum_allowed_speed Domain method 47 Do 97 lt domain gt set_minimum_allowed_height Domain method lt domain gt set_minimum_storable_height Domain method lt domain gt set_name Domain method 46 lt domain gt set_quantities_to_be_ monitored method 58 lt domain gt set_quantities_to_be_stored Domain method lt domain gt set_quantity method 49 lt domain gt set_region method 50 lt domain gt set_store_vertices_uniquely Domain method 47 lt domain gt set_time Domain method 47 lt domain gt statistics method 58 lt domain gt timestepping_statistics method 58 lt mesh gt add_hole Mesh method 44 lt mesh gt add_hole_from_polyg
43. ANUGA User Manual Release 1 2 1 Geoscience Australia and the Australian National University Friday 26 November 2010 Three minutes past Six in the afternoon Geoscience Australia Email anuga ga gov au Commonwealth of Australia Geoscience Australia and the Australian National University 2004 2010 Permission to use copy modify and distribute this software for any purpose without fee is hereby granted under the terms of the GNU General Public License as published by the Free Software Foundation either version 2 of the License or at your option any later version provided that this entire notice is included in all copies of any software which is or includes a copy or modification of this software and in all copies of the supporting documentation for such software This program is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the GNU General Public License http www gnu org copyleft gpl for more details You should have received a copy of the GNU General Public License along with this program if not write to the Free Software Foundation Inc 59 Temple Place Suite 330 Boston MA 02111 1307 This work was produced at Geoscience Australia and the Australian National University funded by the Commonwealth of Australia Neither the Australian Government the Australian National University Geoscience Austral
44. Conditions 51 of arrays used in conjunction with the optional argument quant it y_names called quantities The optional arguments vertex_coordinates and triangles represent the spatial mesh associated with the quantity arrays If omitted the function created by Interpolation_function will be a function of t only Since in practice values need to be computed at specified points the syntax allows the user to specify once and for all a list interpolation_points of points at which values are required In this case the function may be called using the form f t id where id is an index for the list interpolation_points 5 6 Boundary Conditions ANUGA provides a large number of predefined boundary conditions represented by objects such as Ref lective_ boundary domain and Dirichlet_boundary 0 2 0 0 0 0 described in the examples in Chap ter 2 Alternatively you may prefer to roll your own following the method explained in Section These boundary objects may be used with the function set_boundary described below to assign boundary condi tions according to the tags used to label boundary segments lt domain gt set_boundary boundary _map Module abstract_2d_finite_volumes domain This function allows you to assign a boundary object corresponding to a pre defined or user specified boundary condition to every boundary segment that has been assigned a particular tag boundary_map is a dictionary of boundary objects keye
45. M 2 3xM 1 5 5 Initial Conditions In standard usage of partial differential equations initial conditions refers to the values associated to the system variables the conserved quantities here for time 0 In setting up a scenario script as described in Sections and set_quantity is used to define the initial conditions of variables other than the conserved quantities such as friction Here we use the terminology of initial conditions to refer to initial values for variables which need prescription to solve the shallow water wave equation Further it must be noted that set_quantity does not necessarily have to be used in the initial condition setting it can be used at any time throughout the simulation lt domain gt set_quantity numeric None quantity None function None geospatial_data None file name None attribute name None alpha None location vertices poly gon None indices None smooth False verbose False use_cache False Module abstract_2d_finite_volumes domain This method passes off to abstract_2d_finite_volumes quantity set_values This function is used to assign values to individual quantities for a domain It is very flexible and can be used with many data types a statement of the form lt domain gt set_quantity name x can be used to define a quantity having the name name where the other argument x can be any of the following ea number in which case all vertices in the mesh gets that for the quantity
46. _graphs to create the timeseries plot for each desired quantity csv2timeseries_ graphs relies on pylab to be installed which is not part of the standard anuga release however it can be down loaded and installed from http matplotlib sourceforge net Generate time series of nominated gauges read from project gauge_filename This is done by first running sww2csv_gauges on two different directories to make esv files Then running csv2timeseries_graphs detailing the two directories containing the csv file and produces one set of graphs in the output_dir containing 4 7 Exploring the Model Output 35 the details at the gauges for both these sww files Note this script will only work if pylab is installed on the platform nun from os import sep import project import anuga anuga sww2csv_gauges cairns_slide sww project gauge_filename quantities stage speed depth elevation verbose True anuga sww2csv_gauges cairns_fixed_wave sww project gauge_filename quantities stage speed depth elevation verbose True try import pylab anuga csv2timeseries_graphs directories_dic slide sep Slide 0 0 fixed_wave sep Fixed Wave 0 0 output_dir fixed_wave sep base_name gauge_ plot_numbers quantities stage speed depth extra_plot_name assess_all_csv_files True create_latex False
47. _quantity stage tsunami_source Continue propagating wave for t in domain evolve yieldstep 10 finaltime 5000 skip_initial_step True print domain timestepping_statistics print domain boundary_statistics tags ocean_east if project scenario fixed_wave Save every two mins leading up to wave approaching land for t in domain evolve yieldstep 120 finaltime 5000 print domain timestepping_statistics print domain boundary_statistics tags ocean_east Save every 30 secs as wave starts inundating ashore for t in domain evolve yieldstep 10 finaltime 10000 skip_initial_step True print domain timestepping_statistics print domain boundary_statistics tags ocean_east print That took 2f seconds time time t0 In discussing the details of this example we follow the outline given above discussing each major step of the code in turn 4 6 3 Establishing the Mesh One obvious way that the present example differs from runup py is in the use of a more complex method to create the mesh Instead of imposing a mesh structure on a rectangular grid the technique used for this example involves building mesh structures inside polygons specified by the user using a mesh generator The mesh generator creates the mesh within a single polygon whose vertices are at geographical locations specified by the user The user specifies the resolution that is the maximal area of
48. all the stored times in the SWW file Q is a hydrograph of total flow across the given segments for all stored times The normal flow is computed for each triangle intersected by the polyline and added up If multiple segments at different angles are specified the normal flows may partially cancel each other Example to find flow through cross section cross_section x 0 x width time Q get_flow_through_cross_section filename cross_section 5 10 Other quantity lt domain gt create_quantity from expression string Module abst ract_2d_finite_volumes domain Create a new quantity from other quantities in the domain using an arbitrary expression string is a string containing an arbitrary quantity expression Returns the new Quantity object Handy for creating derived quantities on the fly Depth domain create_quantity_from_expression stage elevation exp xmomentum xmomentum ymomentum ymomentum 0 5 Absolute_momentum domain create_quantity_from_expression exp 62 Chapter 5 ANUGA Public Interface CHAPTER SIX ANUGA System Architecture 6 1 File Formats ANUGA makes use of a number of different file formats The following table lists all these formats which are described in more detail in the paragraphs below Extension Description SWW NetCDF format for storing model output with mesh information f t x y SES NetCDF format for storing model ouput f t x y
49. and n is the outward pointing normal with respect to the th cell on the ijth edge The function U x for x T is obtained from the vector U of conserved average values for the ith and neighbouring cells We use a second order reconstruction to produce a piece wise linear function construction of the conserved quantities for all x T for each cell see Figure 7 2 This function is allowed to be discontinuous across the edges of the cells but the slope of this function is limited to avoid artificially introduced oscillations 70 Chapter 7 ANUGA mathematical background Godunov s method see Toro1999 involves calculating the numerical flux function H by exactly solving the corresponding one dimensional Riemann problem normal to the edge We use the central upwind scheme of KurNP2001 to calculate an approximation of the flux across each edge Figure 7 2 From the values of the conserved quantities at the centroid of the cell and its neighbouring cells a discontinuous piecewise linear reconstruction of the conserved quantities is obtained In the computations presented in this paper we use an explicit Euler timestepping method with variable timestepping adapted to the observed CFL condition At min min ZE T 7 1 k i 0 1 2 Uka Uki where rx is the radius of the k th triangle and vz is the maximal velocity across edge joining triangle k and it s 2 th neighbour triangle ny as calculated by the num
50. antity None function None geospatial_data None file name None attribute name None alpha None location vertices poly gon None indices None smooth False verbose False use_cache False Module abstract_2d_finite_volumes quantity Assign values to a quantity object 5 8 Evolution 59 This method works the same way as set_quantity except that it doesn t take a quantity name as the first argument since it is applied directly to the quantity Use set_values is used to assign values to a new quantity that has been created but which is not part of the domain s predefined quantities locationis indices is The method set_values is always called by set_quant it y behind the scenes lt quantity gt get_integral Module abstract_2d_finite_volumes quantity Return the computed integral over the entire domain for the quantity lt quantity gt get_maximum_value indices None Module abstract_2d_finite_volumes quantity Return the maximum value of a quantity on centroids indices is the optional set of element ids that the operation applies to We do not seek the maximum at vertices as each vertex can have multiple values one for each triangle sharing it lt quantity gt get_maximum_location indices None Module abstract_2d_finite_volumes quantity Return the location of the maximum value of a quantity on centroids indices is the optional set of element ids that the operation applies to W
51. ations are oU S OE y OG Ot Ox Oy S T ia where U h uh vh is the vector of conserved quantities water depth h x momentum uh and y momentum vh Other quantities entering the system are bed elevation z and stage absolute water level w where the relation w z h holds true at all times The fluxes in the x and y directions E and G are given by uh vh E u2h gh 2 andG vuh uvh uh gh 2 and the source term which includes gravity and friction is given by 0 S gh zc Sfx gh zy Sty where Sy is the bed friction The friction term is modelled using Manning s resistance law un Vu v vn vu v h4 3 h4 3 in which 7 is the Manning resistance coefficient The model does not currently include consideration of kinematic viscosity or dispersion As demonstrated in our papers ZR 1999 nielsen2005 these equations and their implementation in ANUGA provide a reliable model of general flows associated with inundation such as dam breaks and tsunamis Spo and Sry 7 3 Finite Volume Method We use a finite volume method for solving the shallow water wave equations ZR1999 The study area is represented by a mesh of triangular cells as in Figure 7 1 in which the conserved quantities of water depth h and horizontal 69 momentum uh vh in each volume are to be determined The size of the triangles may be varied within the mesh to allow greater resolution in regions of particular interest
52. ave polygon lines cross or be on top of each other This can result in regions of unspecified resolutions Do not have polygon close to each other This can result in the area between the polygons having small triangles For more control over the mesh outline use the methods described below 5 3 1 Advanced mesh generation For more control over the creation of the mesh outline use the methods of the class Mesh class Mesh userSegments None userVertices None holes None regions None geo reference None Module pmesh mesh A class used to build a mesh outline and generate a two dimensional triangular mesh The mesh outline is used to describe features on the mesh such as the mesh boundary Many of this class s methods are used to build a mesh outline such as add_vertices and add_region_from_polygon userSegments and userVertices define the outline enclosing the mesh holes describes any regions inside the mesh that are not to be included in the mesh geo_reference defines the geo_reference to which all point information is relative If geo_reference is None then the default geo reference is used 5 3 1 1 Key Methods of Class Mesh lt mesh gt add_hole x y geo_reference None Module pmesh mesh This method adds a hole to the mesh outline x and y define a point on the already defined hole boundary If geo_reference is not supplied the points are assumed to be absolute lt mesh gt add_hole_from_polygon polygon segment_
53. ay be a list of points an N x 2 array or a Geospatial_data object closed determines whether points on the polygon edge are inside True or outside False the polygon Returns a new Geospatial_data object representing points inside the Compare with clip_outside page specified polygon geospatial lt Geospatial_data gt clip_outside polygon closed True verbose False Module geospatial_data geospatial_data Clip a Geospatial_data object with a polygon polygon is the polygon to clip the Geospatial_data object with This may be a list of points an N x 2 array or a Geospatial_data object closed determines whether points on the polygon edge are inside True or outside False the polygon Returns a new Geospatial_data object representing points outside the specified polygon Compare with clip page 84 84 Appendix A Supporting Tools gl g2 lt Geospatial data gt split factor 0 5 seed_num None verbose False Module geospatial_data geospatial_data Split a Geospatial_data object into two objects of predetermined ratios factor is the ratio of the size of the first returned object to the original object If 0 5 is supplied the two resulting objects will be of equal size seed_num if supplied will be the random number generator seed used for the split Points of the two new geospatial_data object are selected RANDOMLY Returns two geospatial_data objects that are disjoint sets of the original A 5 1
54. can be very time consuming The SWW files are easy and quick to read and offer information about the model results such as runup heights time histories of selected quantities flow through cross sections and much more elevation get_maximum_inundation_elevation filename polygon None time interval None verbose False Module shallow_water data_manager Return the highest elevation where depth is positive h gt 0 filename is the path to a NetCDF SWW file containing ANUGA model output polygon restricts the query to the points that lie within the polygon time_interval restricts the query to within the time interval Example to find maximum runup elevation max_runup get_maximum_inundation_elevation filename If no inundation is found within the polygon and time_interval if specified the return value is None This indicates No Runup or Everything is dry x y get_maximum_inundation_location filename polygon None time_interval None ver bose False Module shallow_water data_manager Return location x y of the highest elevation where depth is positive h gt 0 filename is the path to a NetCDF SWW file containing ANUGA model output polygon restricts the query to the points that lie within the polygon time_interval restricts the query to within the time interval Example to find maximum runup location max_runup_location get_maximum_inundation_location filename If no inundation i
55. cribes each step of the program and explains it significance Simple water flow example using ANUGA Water driven up a linear slope and time varying boundary similar to a beach environment woe Import necessary modules import anuga from math import sin pi exp Setup computational domain points vertices boundary anuga rectangular_cross 10 10 Basic mesh domain anuga Domain points vertices boundary Create domain domain set_name runup Output to file runup sww domain set_datadir Use current folder oa Setup initial conditions def topography x y return x 2 linear bed slope return xx 2 0 x x 5 curved bed slope domain set_quantity elevation topography Use function for elevation domain set_quantity friction 0 1 Constant friction domain set_quantity stage 0 4 Constant negative initial stage aus a an Setup boundary conditions H _ _ E _ Br anuga Reflective_boundary domain Solid reflective wall Bt anuga Transmissive_boundary domain Continue all values on boundary Bd anuga Dirichlet_boundary 0 2 0 0 Constant boundary values Bw anuga Time_boundary domain domain Time dependent boundary f lambda t 0 1x sin tx 2x pi 0 3 x exp t 0 0 0 0 Associate boundary tags with boundary objects domain set_boundary left Br right Bw top Br
56. cripts 4 4 2 Overview As in the case of runup py the actions carried out by the program can be organised according to this outline 1 Set up a triangular mesh 2 Set certain parameters governing the mode of operation of the model specifying for instance where to store the model output 3 Set up initial conditions for various quantities such as the elevation to be specified at each mesh point vertex 4 Set up the boundary conditions 5 Carry out the evolution of the model through a series of time steps and output the results providing a results file that can be viewed 44 3 The Code Here is the code for the first version of the channel flow channel py Simple water flow example using ANUGA Water flowing down a channel nun Import necessary modules Import standard shallow water domain and standard boundaries import anuga Setup computational domain points vertices boundary anuga rectangular_cross 10 5 len1 10 0 len2 5 0 Mesh domain anuga Domain points vertices boundary Create domain domain set_name channell Output name Setup initial conditions def topography x y return x 10 linear bed slope 4 4 Aslightly more complex example 15 domain set_quantity elevation topography Use function for elevation domain set_quantity friction 0 01 Constant friction domain set_quantity stage Dry
57. ction of time Positive values indicate rain being added or be used for general infiltration negative values indicate outflow at the specified rate presumably this could model evaporation or abstraction centerand radius optionally restrict forcing to a circle with given center and radius polygon optionally restricts forcing to an area enclosed by the given polygon Example catchmentrainfall Rainfall rate file_function Q100_2hr_Rain tms domain forcing_terms append catchment rainfall Here Q100_2hr_Rain tms is assumed to be a NetCDF file in the TMS format defining a timeseries for the rainfall class Culvert_flow domain culvert_description filename None culvert_routine None end_pointO None end_pointl None enquiry_pointO None enquiry_pointl None type box width None height None length None number_of_barrels 1 trigger_depth 0 01 manning None sum_loss None use_velocity_head False use_momentum_jet False label None de scription None update_interval None log file False discharge_hydrograph False ver bose False Module culvert_flows culvert_class 5 7 Forcing Terms 55 This is a general class for implementing flow through a culvert This class modifies the quantities stage xmomentum and ymomentum in areas at both ends of the culvert The Culvert_flow forcing term uses Inflow and General_forcing to update the quantities The flow direction is determined on the fly so openings are refer
58. d by symbolic tags lt domain gt get_boundary_ tags Module abstract_2d_finite_volumes domain Returns a list of the available boundary tags 5 6 1 Predefined boundary conditions class Reflective_boundary domain None Module shallow_water Reflective boundary returns same conserved quantities as those present in the neighbouring volume but reflected This class is specific to the shallow water equation as it works with the momentum quantities assumed to be the second and third conserved quantities class Transmissive_boundary domain None Module abstract_2d_finite_volumes generic_boundary_conditions A transmissive boundary returns the same conserved quantities as those present in the neighbouring volume The underlying domain must be specified when the boundary is instantiated class Dirichlet_boundary conserved_quantities None Module abstract_2d_finite_volumes generic_boundary_conditions A Dirichlet boundary returns constant values for each of conserved quantities In the example of Dirichlet_boundary 0 2 0 0 0 0 the stage value at the boundary is 0 2 and the xmoment um and ymoment um at the boundary are set to 0 0 The list must contain a value for each conserved quantity class Time_boundary domain None function None default_boundary None verbose False Module abstract_2d_finite_volumes generic_boundary_conditions A time dependent boundary returns values for the conserved quantities as a function of time function
59. dary Conditions 24 00 20 eS eos rar 2 Peek Sed ba wh bs 30 4 6 7 Evolution e 248 2 4 0 4 038 eh Sidon a BA be Se wd eo eS ee le da 30 4 7 Exploring the Model Qutput ee 31 5 _ANUGA Public Interface 39 D1 Documentation edo ia a A A ea a Boe SS 39 5 2 Public vs Private Interface ee 39 5 3 Mesh Generation o oie eik e da aR A a ea e a de ie ae de a 40 5 3 1 Advanced mesh generation 0 0 0 0 02 eee eee ee ee 44 5 3 1 1 Key Methods of Class Mesh o o e 44 9 4 Initralising the Domain s se s sisp ee 0 2 2 1 0 2 PE ee EER ee 46 5 4 1 Key Methods of Domain 0 0 0 0000000000 t r 46 53 Initial CONDITIONS a A era 44 OS Re ee we Ae Me A ee ee A eS 49 3 6 Boundary Conditions i aas 64 444 e a SR SES AE eA EYES Se eRe EEE Se CARES 52 5 6 1 Predefined boundary conditions 2 000000 00002 eee eee 52 5 6 2 User defined boundary conditions 2 2 2 e 54 5 7 Forcing Terms ca ak ee ko e RA Ae eS Se a 54 5 8 EVO oir eo a a ee Re A ES ee ee Ge ee ee ee a SR a 57 58 1 DIAENOSUCS eiii we ei aa a RA a G 58 5 9 Queries of SWW model output files o o o e 61 A 6 3 28 Sat Cawood eh hha ed Bee hee ees hig Bees eed 62 6 ANUGA System Architecture 63 6 1 FilesFormats ce Se gee ee eo ee BO RE ae A BM Gee ia ee ee Each Bee Se a 63 6 1 1 Manually Created Files 2 2 0 ee ee ee 63 6 1 2 Automatically C
60. ding the landscape is important in determining the location and resolution of interior polygons The supporting data is found in the ASCII grid cairns asc which has been sourced from the publically available Australian Bathymetry and Topography Grid 2005 grid250 The required resolution for inundation modelling will depend on the underlying topography and bathymetry as the terrain becomes more complex the desired resolution would decrease to the order of tens of metres 26 Chapter 4 Getting Started Figure 4 5 Landscape of the Cairns scenario The following statements are used to read in the specific polygons from project cairns and assign a defined resolution to each polygon islands_res 100000 cairns_res 100000 shallow_res 500000 interior_regions project poly_cairns project poly_islando project poly_islandl project poly_island2 project poly_island3 project poly_shallow Figure 4 6jillustrates the polygons used for the Cairns scenario cairns_res islands_res islands_res islands_res islands_res shallow_res 4 6 An Example with Real Data 27 ANUGA demo Cairns Tsunami Scenario Legend Slump Origin Cc Extent CJ Caims Cc Island CJ Shallow DEM lt VALUE gt MY 2 153 1 500 B 1 499 9 1 000 MA 999 9 500 MA 499 9 250 HM 2499 100 HM 299 0 TE MA 00000000 1 MA 10 00000001 MA 15 00000001 20 Figure 4 6 Interior and bounding pol
61. dition at tag right is replaced by the outflow boundary using the method domain set_boundary right Bo This type of dynamically varying boundary could for example be used to model the breakdown of a sluice door when water exceeds a certain level 4 5 2 Output The text output from this example looks like this 18 Chapter 4 Getting Started Time 15 4000 delta t in 0 03789902 0 03789916 steps 6 6 Time 15 6000 delta t in 0 03789896 0 03789908 steps 6 6 Time 15 8000 delta t in 0 03789891 0 03789903 steps 6 6 Stage gt 0 Changing to outflow boundary Time 16 0000 delta t in 0 02709050 0 03789898 steps 6 6 Time 16 2000 delta t in 0 03789892 0 03789904 steps 6 6 4 5 3 Flow through more complex topographies Here is the code for the third version of the channel flow channel3 py Simple water flow example using ANUGA Water flowing down a channel with more complex topography woe Import necessary modules import anuga Setup computational domain length 40 width 5 dx dy 1 Resolution Length of subdivisions on both axes points vertices boundary anuga rectangular_cross int length dx int width dy lenl length len2 width domain anuga Domain points vertices boundary domain set_name channel3 Output name print domain statistics Setup initial conditions H m E def topography x y Comple
62. dy Jack Kelly and Christopher Zoppou who contributed to this project at various times e A stand alone visualiser anuga_viewer based on Open scene graph was developed by Darran Edmundson and James Hudson e The mesh generator engine was written by Jonathan Richard Shewchuk and made freely available under the following license See source code triangle c for more details on the origins of this code The license reads KKK IKK RK KK KK KK OK RARA RARA RARA RRA RARA RARA OK OK OK OK RRA RARA RARA RK RAR x 888888888 10 888 888 880880 088880 88088880 0888880 888 0888880 x 888 888 888 88b 888 888 888 888 888 d888 88b x x 888 888 888 0880888 888 888 88888 888 888800888 x 888 888 888 C888 888 888 888 888 q888 888 888 888 8807888 888 888 Cb 888 880000 x 8008D x x A Two Dimensional Quality Mesh Generator and Delaunay Triangulator x triangle c x Version 1 6 x x July 28 2005 x Copyright 1993 1995 1997 1998 2002 2005 Jonathan Richard Shewchuk x 2360 Woolsey H x x Berkeley California 94705 1927 x x Jrsfcs berkeley edu x This program may be freely redistributed under the condition that the x x copyright notices including this entire header and the copyright notice printed when th h switch is selected
63. e do not seek the maximum at vertices as each vertex can have multiple values one for each triangle sharing it If there are multiple cells with the same maximum value the first cell encountered in the triangle array is returned lt domain gt get_wet_elements indices None Module shallow_water shallow_water_domain Returns the indices for elements where h gt minimum_allowed_height indices is the optional set of element ids that the operation applies to lt domain gt get_maximum_inundation_elevation indices None Module shallow_water shallow_water_domain Return highest elevation where h gt 0 indices is the optional set of element ids that the operation applies to Example to find maximum runup elevation z domain get_maximum_inundation_elevation lt domain gt get_maximum_inundation_location indices None Module shallow_water shallow_water_domain Return location x y of highest elevation where h gt 0 indices is the optional set of element ids that the operation applies to Example to find maximum runup location x y domain get_maximum_inundation_location 60 Chapter 5 ANUGA Public Interface 5 9 Queries of SWW model output files After a model has been run it is often useful to extract various information from the SWW output file see Section 6 1 3 This is typically more convenient than using the diagnostics described in Section 5 8 1 which rely on the model running something that
64. eate pts file for anuga dem2pts project data name_stem asc use_cache True verbose True onshore DEM name_stem dem use_cache True verbose True Create the triangular mesh and domain based on overall clipping polygon with a tagged boundary and interior regions as defined in project py domain anuga create_domain_from_regions project bounding_polygon boundary_tags top 0 ocean_east bottom 2 onshore 3 maximum_triangle_area project default_res mesh_filename project meshname interior_regions project interior_regions use_cache True verbose True 1 Print some stats about mesh and domain print Number of triangles len domain print The extent is domain get_extent print domain statistics 22 Chapter 4 Getting Started Setup parameters of computational domain domain set_name cairns_ project scenario Name of sww file domain set_datadir Store sww output here domain set_minimum_storable_height 0 01 Store only depth gt 1cm Setup initial conditions tide 0 0 domain set_quantity stage tide domain set_quantity friction 0 0 domain set_quantity elevation filename project name_stem pts use_cache True verbose True alpha 0 1 Setup information for slide scenario to be applied 1 min i
65. eed for random number generator exclude is a list of polygons inside main polygon from where points should be excluded lt point gt point_in_polygon polygon delta 1e 8 Module utilities polygon Returns a point inside the specified polygon and close to the edge The distance between the returned point and the nearest point of the polygon is less than v2 times the second argument delta which is taken as 1078 by default lt array gt inside_polygon points polygon closed True verbose False Module utilities polygon Get a set of points that lie inside a given polygon points is the list of points to test polygon is the polygon to test the points against A 3 utilities polygons 79 closed specifies if points on the polygon edge are considered to be inside or outside the polygon True means they are inside Returns a numeric array comprising the indices of the points in the list that lie inside the polygon If none of the points are inside returns zeros 0 1 ie an empty numeric array Compare with out side_polygon page 80 lt array gt outside_polygon points polygon closed True verbose False Module utilities polygon Get a set of points that lie outside a given polygon points is the list of points to test polygon is the polygon to test the points against closed specifies if points on the polygon edge are considered to be outside or inside the polygon True means they are o
66. elected quantities at every internal timestep These values are also stored in the SWW file for post processing lt quantity gt get_values interpolation_points None location vertices indices None use_cache False verbose False Module abstract_2d_finite_volumes quantity Extract values for quantity as a numeric array interpolation_points is a list of x y coordinates where the value is sought using interpolation If interpolation_points is given values for location and indices are ignored Assume either an absolute UTM coordinates or geospatial data object location specifies where values are to be stored Permissible options are vertices edges centroids or unique vertices The returned values will have the leading dimension equal to length of the indices list or N all values if indices is None If location is centroids the dimension of returned values will be a list or a numeric array of length N N being the number of elements If Location is vertices or edges the dimension of returned values will be of dimension Nx3 If location is unique vertices the average value at each vertex will be returned and the dimension of returned values will be a 1d array of length number of vertices indices is the set of element ids that the operation applies to The values will be stored in elements following their internal ordering lt quantity gt set_values numeric None qu
67. elevation get_maximum_inundation_ elevation in module 61 evolution Field_boundary class in 53 File_boundary class in 53 finite volume method 95 flux forcing ee Forcing terms General_forcing class in 54 geospatial lt Geospatial_data gt clip Geospatial _data method geospatial lt Geospatial_data gt clip_ outside Geospatial_data method 84 Geospat ial_data class in 83 grid Inflow class in 55 Initial Conditions 49 Initialising the Domain 46 latitude longitude Manning friction coefficient Mesh generation Mesh class in mesh 95 mesh file mesh establishing 9 NetCDF node northing points lt Geospatial_data gt get_data_ points Geospatial_data method 83 98 Index points file polygon 96 populate_polygon in module utilities polygon public vs private interface 39 O lt domain gt get_quantity method 58 quantity lt domain gt create_quantity_ from_expression method 62 Rainfall class in 5 reflective boundary 96 Reflective_boundary class in resolution separate_point s_by_polygon 80 slump_tsunami in module 50 stage i 96 sww2dem in module 67 sww2timeseries in module 61 time boundary 96 Time_boundary class in 52 topography transmissive boundary 96 Transmissive_boundary class in 52 Trans
68. enced simple as openingO and opening with either being able to take the role as Inflow or Outflow The Culvert_f low class takes as input edomain a reference to the domain being evolved eculvert_description_filename eculvert_routine eend_point0 Coordinates of one opening eend_point1 Coordinates of other opening eenquiry_pointo eenquiry_pointl etype default is box ewidth eheight elength enumber_of_barrels Number of identical pipes in the culvert default is 1 etrigger_depth default is 0 01 emanning Mannings Roughness for Culvert esum_loss euse_velocity_head euse_momentum_jet elabel Short text naming the culvert edescription Text describing the culvert eupdate_interval elog_file edischarge_hydrograph The user can specify different culvert routines However ANUGA currently provides only one namely the boyd_generalised_culvert_model as used in the example below Chapter 5 ANUGA Public Interface from anuga culvert_flows culvert_class import Culvert_flow from anuga culvert_flows culvert_routines import boyd_generalised_culvert_model culvertl Culvert_flow domain label Culvert No 1 description This culvert is a test unit 1 2m Wide by 0 75m High end_point0 9 0 2 5 end_pointl1 13 0 2 5 width 1 20 height 0 75 culvert_routine boyd_generalised_culvert_model number_of_barrels 1 verbose True culvert2 Culvert_flow domain label C
69. entroid values are automatically com puted as the appropriate averages This option ensures continuity of the surface If on the other hand centroids is used vertex and edge values will be set to the same value effectively creating a piecewise constant surface with possible discontinuities at the edges 5 5 Initial Conditions 49 ANUGA provides a number of predefined initial conditions to be used with set_quantity See for example callable object slump_tsunami below lt domain gt add_quantity numeric None quantity None function None geospatial_data None file name None attribute name None alpha None location vertices poly gon None indices None smooth False verbose False use_cache False Module abstract_2d_finite_volumes domain passes off to abstract_2d_finite_volumes domain set_quantity This function is used to add values to individual quantities for a domain It has the same syntax as lt domain gt set_quantity name x A typical use of this function is to add structures to an existing elevation model Create digital elevation model from points file domain set_quantity elevation filename elevation_file pts verbose True Add buildings from file building_polygons building_heights anuga load_csv_as_building_polygons building_file B for key in building_polygons poly building_polygons key elev building_heights key B append poly elev domain add_quantity
70. eometry of the problem interactively and to identify boundary segments and regions using symbolic tags These tags may then be used to set the actual boundary conditions and attributes for different regions e g the Manning friction coefficient for each simulation Most ANUGA components are written in the object oriented programming language Python Software written in Python can be produced quickly and can be readily adapted to changing requirements throughout its lifetime Com putationally intensive components are written for efficiency in C routines working directly with Python numeric struc tures The animation tool developed for ANUGA is based on OpenSceneGraph an Open Source Software OSS component allowing high level interaction with sophisticated graphics primitives See for more back ground on ANUGA 1 While ANUGA works with discontinuities in the conserved quantities stage xmomentum and ymomentum it does not allow discontinuities in the bed elevation CHAPTER THREE Restrictions and limitations on ANUGA Although a powerful and flexible tool for hydrodynamic modelling ANUGA has a number of limitations that any potential user needs to be aware of They are The mathematical model is the 2D shallow water wave equation As such it cannot resolve vertical convection and consequently not breaking waves or 3D turbulence e g vorticity All spatial coordinates are assumed to be UTM meters As such ANUGA is unsuitable for
71. erical flux function using the central upwind scheme of KurNP20011 The symbol rn denotes the radius of the 7 th neighbour of triangle k The radii are calculated as radii of the inscribed circles of each triangle 7 4 Flux limiting The shallow water equations are solved numerically using a finite volume method on an unstructured triangular grid The upwind central scheme due to Kurganov and Petrova is used as an approximate Riemann solver for the computa tion of inviscid flux functions This makes it possible to handle discontinuous solutions To alleviate the problems associated with numerical instabilities due to small water depths near a wet dry boundary we employ a new flux limiter that ensures that unphysical fluxes are never encountered Let u and v be the velocity components in the x and y direction w the absolute water level stage and z the bed elevation The latter are assumed to be relative to the same height datum The conserved quantities tracked by ANUGA are momentum in the x direction u uh momentum in the y direction v vh and depth h w 2 The flux calculation requires access to the velocity vector u v where each component is obtained as u h and v v h respectively In the presence of very small water depths these calculations become numerically unreliable and will typically cause unphysical speeds We have employed a flux limiter which replaces the calculations above with the limited approximations
72. et certain parameters governing the mode of operation of the model specifying for instance where to store the model output 3 Input various quantities describing physical measurements such as the elevation to be specified at each mesh point vertex 4 Set up the boundary conditions 5 Carry out the evolution of the model through a series of time steps and output the results providing a results file that can be visualised 4 6 2 The Code Here is the code for runcairns py 4 6 An Example with Real Data 21 Script for running a tsunami inundation scenario for Cairns Source data such as directories specifi The output sww file OLD Australia elevation and boundary data is assumed to be available in d by project py is stored in directory named after th scenario i e slide or fixed_wave The scenario is defined by a triangular mesh created from project polygon the elevation data and a tsunami wave generated by a submarine mass failure Geoscience Australia Www 2004 present Import necessary modules Standard modules import os time sys import import Related major packages import anuga Application specific imports impor t project Definition of file names and polygons Preparation of topographic data Convert ASC 2 DEM 2 PTS using source data and store result in source data Create DEM from asc anuga asc2dem project Cr
73. evation depth For this example we simply assign a constant value to stage using the statement domain set_quantity stage 0 4 which specifies that the surface level is set to a height of 0 4 i e 0 4 units metres below the zero level Although it is not necessary for this example it may be useful to digress here and mention a variant to this requirement which allows us to illustrate another way to use set_quantity namely incorporating an expression involving other quantities Suppose instead of setting a constant value for the stage we wished to specify a constant value for the depth For such a case we need to specify that st age is everywhere obtained by adding that value to the value already specified for elevation We would do this by means of the statements h 0 05 Constant depth domain set_quantity stage expression elevation f h That is the value of stage is set to h 0 05 plus the value of elevat ion already defined The reader will probably appreciate that this capability to incorporate expressions into statements using set_ quantity greatly expands its power See Section 5 5 for more details 4 1 7 Boundary Conditions The boundary conditions are specified as follows Br anuga Reflective_boundary domain Bt anuga Transmissive_boundary domain Bd anuga Dirichlet_boundary 0 2 0 0 0 0 Bw anuga Time_boundary domain domain f lambda t 0 1xsin tx2x pi 0 3
74. ever other quantities that aren t updated by the equation are also assigned values using the same interface The code in the present example demonstrates a number of forms in which we can invoke set_quantity 4 1 6 1 Elevation The elevation or height of the bed is set using a function defined through the statements below which is specific to this example and specifies a particularly simple initial configuration for demonstration purposes def topography x y return x 2 This simply associates an elevation with each point x y of the plane It specifies that the bed slopes linearly in the x direction with slope gt and is constant in the y direction Once the function topography is specified the quantity elevation is assigned through the simple statement domain set_quantity elevation topography NOTE If using function to set elevation it must be vector compatible For example using square root will not work 4 1 6 2 Friction The assignment of the friction quantity a forcing term demonstrates another way we can use set_quantity to set quantities namely assign them to a constant numerical value domain set_quantity friction 0 1 This specifies that the Manning friction coefficient is set to 0 1 at every mesh point 4 1 6 3 Stage The stage the height of the water surface is related to the elevation and the depth at any time by the equation 10 Chapter 4 Getting Started 1 stage el
75. fined Do not have polygon lines cross or be on top of each other Also do not have polygons close to each other poly_geo_reference is the geo_reference of the bounding polygon and the interior polygons If none assume absolute Please pass one though since absolute references have a zone mesh_geo_reference is the geo_reference of the mesh to be created If none is given one will be automat ically generated It will use the lower left hand corner of bounding polygon absolute as the x and y values for the geo ref minimum_triangle_angle is the minimum angle allowed for each generated triangle This controls the slimness allowed for a triangle fail_if_polygons_outside if True the default an Exception in thrown if interior polygons fall out side the bounding polygon If False these will be ignored and execution continues WARNING Note that the dictionary structure used for the parameter boundary_tags is different from that used for the variable boundary that occurs in the specification of a mesh In the case of boundary the tags are the values of the dictionary whereas in the case of boundary_tags the tags are the keys and the value corresponding to a particular tag is a list of numbers identifying boundary edges labelled with that tag Because 5 3 Mesh Generation 43 of this it is theoretically possible to assign the same edge to more than one tag However an attempt to do this will cause an error WARNING Do not h
76. flow rate m s at which the quantity should change This can be either a constant or a function of time Positive values indicate inflow negative values indicate outflow Note The specified flow will be divided by the area of the inflow region and then applied to update the stage quantity centerand radius optionally restrict forcing to a circle with given center and radius polygon optionally restricts forcing to an area enclosed by the given polygon Example hydrograph Inflow center 320 300 radius 10 rate file_function QPMF_Rot_Sub13 tms domain forcing_terms append hydrograph Here OPMF_Rot_Sub13 tms is assumed to be a NetCDF file in the TMS format defining a timeseries for a hydrograph class Rainfall domain rate 0 0 center None radius None polygon None default_rate None ver bose False Module shallow_water shallow_water_domain This is a general class for implementing rainfall over the domain possibly restricted to a given circle or polygon This class will always modify the st age quantity Rainfall is based on the General_forcing class so the functionality is similar domain is the domain being evolved rate is the total rain rate over the specified domain Note Raingauge Data needs to reflect the time step For example if rain gauge is mm read every dt seconds then the input here is as mm dt so 10 mm in 5 minutes becomes 10 5x60 0 0333mm s This parameter can be either a constant or a fun
77. ge publish distribute sublicense and or sell copies of the Software and to permit persons to whom the Software is furnished to do so subject to the following conditions The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software HE SOFTWARE IS PROVIDED AS IS WITHOUT WARRANTY OF ANY KIND EXPRESS OR IMPLIED INCLUDING BUT NO LIMITED TO THE WARRANTIES OF ERCHANTABILITY FITNESS FOR A PARTICULAR PURPOSE AND ONINFRINGEMENT IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM DAMAGES OR OTHER LIABILITY WHETHER IN AN ACTION OF CONTRACT TORT OR OTHERWISE ARISING FROM OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE DE Abstract ANUGA is a hydrodynamic modelling tool that allows users to model realistic flow problems in complex 2D ge ometries Examples include dam breaks or the effects of natural hazards such as riverine flooding storm surges and tsunami The user must specify a study area represented by a mesh of triangular cells the topography and bathymetry frictional resistance initial values for water level called stage within ANUGA boundary conditions and forces such as rainfall stream flows windstress or p
78. gon polygon segment_tags None max triangle_area None geo_refer ence None region_tag None Module pmesh mesh This method adds a region to a Mesh instance Regions are commonly used to describe an area with an increased density of triangles by setting max_triangle_area polygon describes the region boundary to add to the lt mesh gt segment_tags specifies a list of segment tags one for each edge of the bounding polygon If geo_reference is not supplied the points data is assumed to be absolute region_tag sets the region tag lt mesh gt add_vertices point_data Module pmesh mesh Add user vertices to a mesh point_data is the list of point data and can be a list of x y values a numeric array or a geospatial_data instance lt mesh gt auto_segment alpha None raw_boundary True remove_holes False smooth_indents False ex pand_pinch False Module pmesh mesh Add segments between some of the user vertices to give the vertices an outline The outline is an alpha shape This method is useful since a set of user vertices need to be outlined by segments before generate_mesh is called alpha determines the smoothness of the alpha shape raw_boundary if True instructs the function to return the raw boundary i e the regular edges of the alpha shape remove_holes if True enables a filter to remove small holes small is defined by boundary points fraction smooth_indents if True removes sharp triangular indents in t
79. h over the domain and is achieved with the function sww2dem described in Section 6 1 9 ExportResults py demonstrates how this function can be used import os import sys import project import anuga scenario slide name cairns_ scenario print output dir name 4 7 Exploring the Model Output 31 which_var 3 if which_var 0 outname name quantityname if which_var Stage _stage stage Absolute Momentum Absolute momentum xmomentums 2 ymomentum 2 0 5 stage elevationt tl e 30 outname name _momentum quantityname xmomentumx x2 ymomentumx x 2 xx 0 5 if which_var Depth outname name _depth quantityname stag levation Depth if which_var Speed outname name _speed quantityname if which_var Elevation outname name _elevation quantityname elevation Elevation print start sww2dem anuga sww2dem name sww outnamet asc quantity quantityname cellsize 100 easting_min project eastingmin easting_max project eastingmax northing_min project northingmin northing_max project northingmax reduction max verbose True The script generates a maximum water depth ASCII grid at a defined resolution here 100 m which can then be viewed in a GIS environment for example The parameters used in the function are defined in project py
80. hapter 6 ANUGA System Architecture 6 1 5 Formats for Storing Arbitrary Points and Attributes A CSV TXT file is used to store data representing arbitrary numerical attributes associated with a set of points The format for an CSV TXT file is first line column names other lines x value y value attributes for example x y elevation friction Oxo Ont 49 20 3 1 97 2 38 45 07 0 38 Lal Late OL US The delimiter is a comma The first two columns are assumed to be x and y coordinates A PTS file is a NetCDF representation of the data held in an points CSV file If the data is associated with a set of N points then the data is stored using an N x 2 numeric array of float variables for the points and an N x 1 numeric array for each attribute 6 1 6 ArcView Formats Files of the three formats ASC PRJ and ERS are all associated with data from ArcView An ASC file is an ASCII representation of DEM output from Arc View It contains a header with the following format ncols 753 nrows 766 xllcorner 314036 58727982 yllcorner 6224951 2960092 cellsize 100 NODATA_value 9999 The remainder of the file contains the elevation data for each grid point in the grid defined by the above information A PRJ file is an ArcView file used in conjunction with an ASC file to represent metadata for a DEM 6 1 7 DEM Format A DEM file in ANUGA is a NetCDF representation of regular DEM data 6 1 8 Other Formats
81. he boundary expand_pinch if True tests for pinch off and corrects i e a boundary vertex with more than two edges lt mesh gt export_mesh_file ofile Module pmesh mesh This method is used to save a mesh to a file ofile is the name of the mesh file to be written including the extension Use the extension msh for the file to be in NetCDF format and t sh for the file to be ASCII format lt mesh gt generate_mesh maximum_triangle_area Module pmesh mesh minimum _triangle_angle 28 0 verbose True This method is used to generate the triangular mesh maximum_triangle_area sets the maximum area of any triangle in the mesh minimum_triangle_angle sets the minimum area of any triangle in the mesh These two parameters can be used to control the triangle density lt mesh gt import_ungenerate_file ofile tag None region_tag None Module pmesh mesh This method is used to import a polygon file in the ungenerate format which is used by arcGIS The polygons from the file are converted to vertices and segments ofile is the name of the polygon file 5 3 Mesh Generation 45 tag is the tag given to all the polygon s segments If tag is not supplied then the segment will not effect the water flow it will only effect the mesh generation region_tag is the tag given to all the polygon s segments If it is a string the tag will be assigned to all regions If it is a list the first value in the list wi
82. he mesh outline use the methods described below create_domain_from_regions bounding_polygon boundary_tags maximum triangle_area None mesh_ filename None interior_regions None interior_holes None poly_geo_ reference None mesh_geo_reference None minimum_triangle_angle 28 0 fail_if_polygons_outside True use_cache False verbose True Module interface py This higher level function allows a user to create a domain and associated mesh inside a specified polygon bounding_polygon is a list of points in Eastings and Northings relative to the zone stated in poly_ geo_reference if specified Otherwise points are just x y coordinates with no particular association to any location boundary_tags is a dictionary of symbolic tags For every tag there is a list of indices referring to segments associated with that tag If a segment is omitted it will be assigned the default tag maximum_triangle_area is the maximal area per triangle for the bounding polygon excluding the interior regions interior_holes lets you specify polygons as empty holes in the mesh This can be used to represent buildings pylons and other immovable structures These polygons do not need to be closed but their points must be specified in a counter clockwise order new in 1 2 mesh_filename is the name of the file to contain the generated mesh data interior_regions is a list of tuples consisting of polygon resolution for each region to be separately re
83. ia nor any of their employees makes any warranty express or implied or assumes any liability or responsibility for the accuracy completeness or usefulness of any information apparatus product or process disclosed or represents that its use would not infringe privately owned rights Reference herein to any specific commercial products process or service by trade name trademark manufacturer or otherwise does not necessarily constitute or imply its endorsement rec ommendation or favoring by the Australian Government Geoscience Australia or the Australian National University The views and opinions of authors expressed herein do not necessarily state or reflect those of the Australian Gov ernment Geoscience Australia or the Australian National University and shall not be used for advertising or product endorsement purposes This document does not convey a warranty express or implied of merchantability or fitness for a particular purpose ANUGA Manual typeset with ATEX Credits e ANUGA was developed by Stephen Roberts Ole Nielsen Duncan Gray and Jane Sexton It is currently being developed and maintained by Nariman Habili and Stephen Roberts License e ANUGA is freely available and distributed under the terms of the GNU General Public Licence Acknowledgments e Ole Nielsen James Hudson John Jakeman Rudy van Drie Ted Rigby Petar Milevski Joaquim Luis Nils Goseberg William Power Trevor Dhu Linda Stals Matt Har
84. ibutes loat y number_of_points loat elevation number_of_points loat z number_of_points nt volumes number_of_ volumes number_of_vertices loat time number_of_timesteps loat stage number_of_timesteps number_of points loat xmomentum number_of_timesteps number_of_ points loat ymomentum number_of_timesteps number_of_ points institution Geoscience Australia description Output from pyvolution suitable for plotting smoothing Yes order 1 starttime 0 xllcorner yllcorner sll ee 64 Chapter 6 ANUGA System Architecture 56 false_eastin Zone 500000 g false_northin 10000000 g wgs84 datum r UTM projection m units data a dws o sos nO 8 Ro A A E so 10 0 00 LN SF LO 0 DD en 1p a IC a HA O oomo O O O OGOGO H o o nO nn sO RON ON on on So oS x NO lt 00 Es LN TON ORM WD 4 N 8 xs 8 8 Ne a rr DODHOOMNO 0 00 SOOO o o H Ss Ss o os Soso os on a oS sn lO OM Ke LN TO 0 MO a H 8rd O 070 0 1 0 00 Or 0 o o E O Sos Ss on on on ono a ON YC WM oO NN MIO mo Ai BOP re Ni a 8h E H O 0090 00 OS 0 SiO O ODO Orel o A RON ys A S a N CT RA ae Mm e A At O sA mM N 0 0H no ee oP oss H NODC O Oo 0000000 w md o o nh on on on os SOA RON ON ono ono sn NINO O 209 Ps ns NN MI WOM DO ws R
85. ied dictionary The tags are ocean east north exterior south The command set_boundary stipulates that in the current example the right boundary varies with time as defined by the lambda function while the other boundaries are all reflective The reader may wish to experiment by varying the choice of boundary types for one or more of the boundaries In the case of Bd and Bw the three arguments in each case represent the stage z momentum and y momentum respectively Bw anuga Time_boundary domain domain f lambda t 0 1l sin t 2 pi 0 3 0 0 0 0 12 Chapter 4 Getting Started 4 1 8 Evolution The final statement for t in domain evolve yieldstep 0 1 duration 10 0 print domain timestepping_statistics causes the configuration of the domain to evolve over a series of steps indicated by the values of yieldstep and duration which can be altered as required The value of yieldstep controls the time interval between successive model outputs Behind the scenes more time steps are generally taken 4 1 9 Output The output is a NetCDF file with the extension sww It contains stage and momentum information and can be used with the ANUGA viewer anuga_viewer to generate a visual display see Section A 2 See Section 6 1 page 63 for more on NetCDF and other file formats The following is a listing of the screen output seen by the user when this example is run S pyth
86. instead length is the length of the slide or slump depth is the water depth to the centre of the sediment mass slope is the bathymetric slope Other slump or slide parameters can be included if they are known 50 Chapter 5 ANUGA Public Interface lt callable object gt file function filename domain None quantities None interpolation_ points None time_thinning 1 time_limit None verbose False output_centroids False use_cache False boundary poly gon None Module abstract_2d_finite_volumes util Reads the time history of spatial data for specified interpolation points from a NetCDF file and returns a callable object Values returned from the lt callable_object gt are interpolated values based on the input file using the underlying interpolation_function filename is the name of the input file This would be either an SWW TMS or STS file quantities is either the name of a single quantity to be interpolated or a list of such quantity names In the second case the resulting function will return a tuple of values one for each quantity If the NetCDF file uses names other than stage xmomentum and ymomentum the name s appearing in the file must be explicitly stated using the quantities keyword This is for example be the case if a tms file is used to specify time dependent precipitation In this case the keyword might be called rainfall both in the call to file_ function and in the tms
87. int width dy lenl length len2 width which yields a mesh of length 10m width 5m with 1m spacings To increase the resolution as we will later in this example one merely decreases the values of dx and dy The rest of this script is similar to the previous example on page 8 4 5 Model Output The following figure is a screenshot from the ANUGA visualisation tool anuga_viewer of output from this exam ple 16 Chapter 4 Getting Started pyVolution SW Figure 4 3 Simple channel example viewed with the ANUGA viewer 4 5 1 Changing boundary conditions on the fly Here is the code for the second version of the channel flow channel2 py Simple water flow example using ANUGA Water flowing down a channel with changing boundary conditions Ww Import necessary modules import anuga Setup computational domain length 10 width 5 dx dy 1 Resolution Length of subdivisions on both axes points vertices boundary anuga rectangular_cross int length dx int width dy lenl length len2 width domain anuga Domain points vertices boundary domain set_name channel2 Output name Setup initial conditions def topography x y return x 10 linear bed slope domain set_quantity elevation topography Use function for elevation domain set_quantity friction 0 01 Constant friction 4 5 Model Output 17 domain set_quantity stage
88. is a key associated with a Python dictionary options This dictionary stores settings such as the name of the directory used the maximum number of cached files allowed and so on The cache function allows the user also to specify a list of dependent files If any of these have been changed the function is recomputed and the results stored again USAGE result cache func args kwargs dependencies cachedir verbose compression evaluate test return_filename 77 A 2 anuga viewer The output generated by ANUGA may be viewed by means of the visualisation tool anuga_viewer which takes an SWW file generated by ANUGA and creates a visual representation of the data Examples may be seen in Figures 4 1 and 4 2 To view an SWW file with anuga_viewer in the Windows environment you have to run it in a command line as in anuga_viewer lt swwfile gt or if a georeferenced tif file or jpg cut to the same shape as the domain is needed anuga_viewer lt swwfile gt lt tif file gt 78 Appendix A Supporting Tools A 3 utilities polygons class lt callable gt Polygon_function regions default 0 0 geo_reference None Module utilities polygon Creates a callable object that returns one of a specified list of values when evaluated at a point x y de pending on which polygon from a specified list of polygons the point belongs to regions is a list of pairs P v where each P is a polygon and each v is either a c
89. island0 anuga read_polygon islands csv poly_islandl anuga read_polygon islandsl csv poly_island2 anuga read_polygon islands2 csv r r y poly_island3 anuga read_polygon islands3 csv poly_shallow anuga read_polygon shallow csv Optionally plot points making up these polygons plot_polygons bounding_polygon poly_cairns poly_island0 poly_islandl 4 6 An Example with Real Data 25 poly_island2 poly_island3 poly_shallow style boundingpoly verbose False Define resolutions max area per triangle for each polygon Make these numbers larger to reduce the number of triangles in the model and hence speed up the simulation default_res 10000000 Background resolution islands_res 100000 cairns_res 100000 shallow_res 500000 Define list of interior regions with associated resolutions interior_regions poly_cairns cairns_res poly_islandO islands_res poly_islandl islands_res poly_island2 islands_res poly_island3 islands_res poly_shallow shallow_res Data for exporting ascii grid eastingmin 363000 eastingmax 418000 northingmin 8026600 northingmax 8145700 Data for landslide slide_origin 451871 8128376 Assume to be on continental shelf slide_depth 500 Figure 4 5 illustrates the landscape of the region for the Cairns example Understan
90. it y_names called quantities The optional arguments vertex_coordinates and triangles represent the spatial mesh associated with the quantity arrays If omitted the function must be created using an STS file or a TMS file Since in practice values need to be computed at specified points the syntax allows the user to specify once and for all a list interpolation_points of points at which values are required In this case the function may be called using the form lt callable_object gt t id where id is an index for the list interpolation_points class lt callable_object gt Interpolation_function time quantities quantity_names None ver tex_coordinates None triangles None inter polation_points None time_thinning 1 ver bose False gauge_neighbour_id None Module fit_interpolate interpolate Given a time series i e a series of values associated with different times whose values are either just num bers or a set of numbers defined at the vertices of a triangular mesh such as those stored in SWW files Interpolation_function is used to create a callable object that interpolates a value for an arbitrary time t within the model limits and possibly a point x y within a mesh region The actual time series at which data is available is specified by means of an array time of monotonically increasing times The quantities containing the values to be interpolated are specified in an array or dictionary 5 5 Initial
91. limited using depth In this case we won t need any contribution from h and can accept any a E g a 1 reduces Equation 7 4 to whereas a 0 yields all well and good 2 hi gt hi In this case the the deep water vertex is closer to the bed than the shallow water vertex or even below the bed In this case we need to find an a that will ensure a positive depth Rearranging Equation 7 4Jand solving for a one obtains the bound Ensuring Equation 7 4 holds true for all vertices one arrives at the definition a hy a min gt thy hy which will guarantee that no vertex cuts through the bed Finally should h lt e and therefore a lt 0 we suggest setting a 0 and similarly capping a at 1 just in case 7 5 Slope limiting 73 74 CHAPTER EIGHT Basic ANUGA Assumptions 8 1 Time Physical model time cannot be earlier than 1 Jan 1970 00 00 00 If one wished to recreate scenarios prior to that date 1t must be done using some relative time e g 0 The ANUGA domain has an attribute starttime which is used in cases where the simulation should be started later than the beginning of some input data such as those obtained from boundaries or forcing functions hydrographs file_boundary etc The domain startime may be adjusted in file _boundary in the case the input data does not itself start until a later time 8 2 Spatial data 8 2 1 Projection All spatial data relates to the WGS84 datum or GDA94
92. lities polygon Plot a list of polygons to a file polygons_points isa list of polygons to plot style is a list of style strings to be applied to the corresponding polygon in polygons_points A polygon can be closed for plotting purposes by assigning the style string line to it in the appropriate place in the style list The default style is line figname is the path to the file to save the plot in If not specified use test_image png The function returns a list containing the minimum and maximum of the points in all the input polygons i e limin Tmazxr Yminr Ymaz l A 3 utilities polygons 81 A 4 coordinate_transforms 82 Appendix A Supporting Tools A 5 geospatial data This describes a class that represents arbitrary point data in UTM coordinates along with named attribute values class Geospatial_data data_points None attributes None geo reference None default_attribute name None file_name None latitudes None longitudes None points_are_lats_ longs False max_read_lines None load file_now True verbose False Module geospatial_data geospatial_data This class is used to store a set of data points and associated attributes allowing these to be manipulated by methods defined for the class The data points are specified either by reading them from a NetCDF or CSV file identified through the parameter file_name or by providing their x and y coordinates in metres either as a sequence of 2 t
93. ll be applied to the first polygon etc This function can be used to import building footprints 5 4 Initialising the Domain class Domain source None triangles None boundary None conserved_quantities None other_quanti ties None tagged_elements None geo reference None use_inscribed_circle False mesh_ filename None use_cache False verbose False full_send_dict None ghost_recv_dict None processor 0 numproc 1 number_of full nodes None number_of full_triangles None Module abstract_2d_finite_volumes domain This class is used to create an instance of a structure used to store and manipulate data associated with a mesh The mesh is specified either by assigning the name of a mesh file to source or by specifying the points triangle and boundary of the mesh 5 4 1 Key Methods of Domain lt domain gt set_name name Module abst ract_2d_finite_volumes domain page name is used to name the domain The name is also used to identify the output SWW file If no name is assigned to a domain the assumed name is domain lt domain gt get_name Module abstract_2d_finite _volumes domain Returns the name assigned to the domain by set_name If no name has been assigned returns domain lt domain gt set_datadir path Module abstract_2d_finite_volumes domain path specifies the path to the directory used to store SWW files Before this method is used to set the SWW directory path the assumed directory pa
94. lle and G Petrova SIAM Journal of Scientific Computing 23 3 707 740 2001 101
95. lutions The resulting mesh is output to a mesh file This term is used to describe a file of a specific format used to store the data specifying a mesh There are in fact two possible formats for such a file it can either be a binary file with extension msh or an ASCII file with extension t sh In the present case the binary file format msh is used See Section 6 1 page 63 for more on file formats In practice the details of the polygons used are read from a separate file project py Here is a complete listing of project py Common filenames and locations for topographic data meshes and outputs This file defines the parameters of the scenario you wish to run import anuga Define scenario as either slide or fixed_wave Choose one scenario fixed_wave Huge wave applied at the boundary scenario slide Slide wave form applied inside the domain Filenames name_stem cairns meshname name_stem msh Filename for locations where timeseries are to be produced gauge_filename gauges csv Domain definitions bounding polygon for study area bounding_polygon anuga read_polygon extent csv A anuga polygon_area bounding_polygon 1000000 0 o print Area of bounding polygon 2f km 2 A Interior region definitions Read interior polygons poly_cairns anuga read_polygon cairns csv poly_
96. minutes Figure 4 11 Time series information of the quantity depth for the Cairns Airport location for the slide and fixed wave scenario 38 Chapter 4 Getting Started CHAPTER FIVE ANUGA Public Interface This chapter gives an overview of the features of ANUGA available to the user at the public interface These are grouped under the following headings which correspond to the outline of the examples described in Chapter 4 e Establishing the Mesh Section 5 3 e Initialising the Domain Section 5 4 e Initial Conditions Section 5 5 e Boundary Conditions Section 5 6 e Forcing Terms Section 5 7 e Evolution Section 5 8 5 1 Documentation The listings here are intended merely to give the reader an idea of what each feature is and how it can be used they do not give full specifications for these the reader may consult the programmer s guide The code for every function or class contains a documentation string or docstring that specifies the precise syntax for its use This appears immediately after the line introducing the code between two sets of triple quotes Python has a handy tool that lets you easily navigate this documentation called pydoc In Linux it runs as a server which serves the documentation up to your web browser 1 Open a terminal at your anuga_source anuga folder 2 Start the python documentation server with pydoc p 6767 3 Open a browser and type in http localhost 6767 Now you ha
97. missive_momentum_set_stage_ boundary class in 53 Transmissive_stage_zero_momentum_ boundary class in 53 urs2sts in module 68 utilities polygon module 79 utilities polygon standard module 79 vertex X find_optimal_smoothing_parameter Geospatial_data method xmomentum ymomentum Index 99 100 BIBLIOGRAPHY nielsen2005 Hydrodynamic modelling of coastal inundation Nielsen O S Roberts D Gray A McPherson and A Hitchman In Zerger A and Argent R M eds MODSIM 2005 International Congress on Modelling and Simulation Modelling and Simulation Society of Australia and New Zealand December 2005 pp 518 523 ISBN 0 9758400 2 9 http www mssanz org au modsim05 papers nielsen pdf grid250 Australian Bathymetry and Topography Grid June 2005 Webster M A and Petkovic P Geoscience Aus tralia Record 2005 12 ISBN 1 920871 46 2 http www ga gov au meta ANZCWO0703008022 html ZR1999 Catastrophic Collapse of Water Supply Reservoirs in Urban Areas C Zoppou and S Roberts ASCE J Hydraulic Engineering 125 7 686 695 1999 Toro1999 Riemann problems and the waf method for solving the two dimensional shallow water equations E F Toro Philosophical Transactions of the Royal Society Series A 338 43 68 1992 KurNP2001 Semidiscrete central upwind schemes for hyperbolic conservation laws and hamilton jacobi equations A Kurganov S Noe
98. nd y z x 10 N len x for i in range N Step if LOS XEL lt 12 z i 0 4 0 05x y 4 Constriction if 27 lt x i lt 29 and y i gt 3 z i 2 Pole if x i 34 2 y i 2 xx2 lt 0 4xx2 z i 2 return z In addition changing the resolution to dax dy 0 1 creates a finer mesh resolving the new features better A screenshot of this model at time 15s is 20 Chapter 4 Getting Started pyVolution SWW Viewer Figure 4 4 More complex flow in a channel 4 6 An Example with Real Data The following discussion builds on the concepts introduced through the runup py example and introduces a second example runcairns py This refers to a hypothetical scenario using real life data in which the domain of interest surrounds the Cairns region Two scenarios are given firstly a hypothetical tsunami wave is generated by a submarine mass failure situated on the edge of the continental shelf and secondly a fixed wave of given amplitude and period is introduced through the boundary Each scenario has been designed to generate a tsunami which will inundate the Cairns region To achieve this suitably large parameters were chosen and were not based on any known tsunami sources or realistic amplitudes 4 6 1 Overview As in the case of runup py the actions carried out by the program can be organised according to this outline 1 Set up a triangular mesh 2 S
99. ne point or is constant one bin will be created If number_of_bins is omitted 10 bins will be created A 9 Finding the Optimal Alpha Value The function more to come very soon A 8 Numerical Tools 89 90 APPENDIX B ANUGA Full scale Validations B 1 Overview There are some long running validations that are not included in the small scale validations that run when you exe cute the validate_all py script in the anuga_validation automated_validation_test directory These validations are not run automatically since they can take a large amount of time and require an internet connec tion and user input B 2 Patong Beach The Patong Beach validation is run from the automated_validation_tests patong_beach_ validation directory Just execute the validate_patong py script in that directory This will run a Patong Beach simulation and compare the generated SWW file with a known good copy of that file The script attempts to refresh the validation data files from master copies held on the Sourceforge project site If you don t have an internet connection you may still run the validation as long as you have the required files You may download the validation data files by hand and then run the validation Just go to the ANUGA Sourceforge project download page at http sourceforge net project showfiles php group_id 172848 and select the validation_data package patong 1 0 release You need the data tgz file and one o
100. nto simulation if project scenario slide Function for submarine slide tsunami_source anuga slide_tsunami length 35000 0 depth project slide_depth slope 6 0 thickness 500 0 x0 project slide_origin 0 y0 project slide_origin 1 alpha 0 0 domain domain verbose True Setup boundary conditions print Available boundary tags domain get_boundary_tags Bd anuga Dirichlet_boundary tide 0 0 Mean water level Bs anuga Transmissive_stage_zero_momentum_boundary domain Neutral boundary if project scenario fixed_wave Huge 50m wave starting after 60 seconds and lasting 1 hour Bw anuga Time_boundary domain domain function lambda t 60 lt t lt 3660 x50 0 0 domain set_boundary ocean_east Bw bottom Bs onshore Bd top Bs if project scenario slide Boundary conditions for slide scenario domain set_boundary ocean_east Bd bottom Ba onshore Bd top BAF Evolve system through time 4 6 An Example with Real Data 23 H import time tO time time from numpy import allclose if project scenario slide Initial run without any event for t in domain evolve yieldstep 10 finaltime 60 print domain timestepping_statistics print domain boundary_statistics tags ocean_east Add slide to water surface if allclose t 60 domain add
101. oint against x1 y1 v2 y2 rtol is the relative tolerance to use when testing for coincidence atol is the absolute tolerance to use when testing for coincidence Returns True if the point is on the line else False indices count separate_points_by polygon points polygon closed True checkin put True verbose False separate_points_by_polygon Module utilities polygon Separate a set of points into points that are inside and outside a polygon 80 Appendix A Supporting Tools points is a list of points to separate polygon is the polygon used to separate the points closed determines whether points on the polygon edge should be regarded as inside or outside the polygon True means they are inside check_input specifies whether the input parameters are checked True means check the input parameters The function returns a tuple indices count where indices is a list of point indices from the input points list with the indices of points inside the polygon at the left and indices of points outside the polygon listed at the right The count value is the count from the left of the indices of the points inside the polygon lt area gt polygon_area polygon Module utilities polygon Returns area of an arbitrary polygon reference http mathworld wolfram com PolygonArea html Eminr Umarr Yminr Ymar Plot_polygons polygons points style None figname None label None verbose False Module uti
102. on Mesh method 44 lt mesh gt add_points_and_segments Mesh method 44 lt mesh gt add_region Mesh method 44 lt mesh gt add_region_from _polygon Mesh method 45 lt mesh gt add_vertices Mesh method 45 lt mesh gt auto_segment Mesh method 45 lt mesh gt export_mesh_file Mesh method 45 lt mesh gt generate_mesh Mesh method 45 lt mesh gt import_ungenerate_file Mesh method 45 lt quantity gt get_integral method 60 lt quantity gt get_maximum_location method 60 lt quantity gt get_maximum_value method lt quantity gt get_values method 59 lt quantity gt set_values method 59 Alpha_Shape class in 88 alpha_shape_via_files in module 88 ANUGA credits ii licence ii anuga_viewer atributes lt Geospatial_data gt get_ attributes Geospatial data method bathymetry boundary lt Alpha_shape gt get_ boundary Alpha_Shape method 88 boundary conditions conserved quantity create_domain_from_regions in module create_mesh_from_regions in module 42 csv2building_polygons in module 68 Culvert_flow class in 55 dem2pts in module 68 Digital Elevation Model DEM 95 Dirichlet boundary Dirichlet_boundary class in 52 Dirichlet_discharge_boundary class in 53 Documentation Domain class in 46 edge elevation
103. on runup py Time 0 0000 steps 0 0 Time 0 1000 delta t in 0 01373568 0 01683588 steps 7 7 Time 0 2000 delta t in 0 01203520 0 01357912 steps 8 8 Time 0 3000 delta t in 0 01144234 0 01193508 steps 9 9 Time 0 4000 delta t in 0 01141301 0 01152065 steps 9 9 4 2 Howto Run the Code The code can be run in various ways e from a Windows or Unix command line as in python runup py e within the Python IDLE environment e within emacs e within Windows by double clicking the runup py file 4 3 Exploring the Model Output The following figures are screenshots from the ANUGA visualisation tool anuga_viewer Figure 4 1 shows the domain with water surface as specified by the initial condition t 0 Figure 4 2 shows later snapshots for t 2 3 and t 4 where the system has been evolved and the wave is encroaching on the previously dry bed anuga_viewer is described in more detail in Section A 2 4 2 How to Run the Code 13 Figure 4 1 Runup example viewed with the ANUGA viewer Figure 4 2 Runup example viewed with ANGUA viewer 14 Chapter 4 Getting Started 4 4 A slightly more complex example 4 4 1 Overview The next example is about water flow in a channel with varying boundary conditions and more complex topographies These examples build on the concepts introduced through the runup py in Section 4 1 The example will be built up through three progressively more complex s
104. onstant value or a function of coordinates x and y specifying the return value for a point inside P default may be used to specify a value or a function for a point not lying inside any of the specified polygons When a point lies in more than one polygon the return value is taken to be the value for whichever of these polygon appears later in the list geo_reference refers to the status of points that are passed into the function Typically they will be relative to some origin Typical usage may take the form set_quantity elevation Polygon_function P1 vl P2 v2 default v3 geo_reference domain geo_reference lt polygon gt read_polygon filename split Module utilities polygon Reads the specified file and returns a polygon Each line of the file must contain exactly two numbers separated by a delimiter which are interpreted as coordinates of one vertex of the polygon filename is the path to the file to read split sets the delimiter character between the numbers on one line of the file If not specified the delimiter is the character populate_polygon polygon number_of points seed None exclude None Module utilities polygon Populates the interior of the specified polygon with the specified number of points selected by means of a uniform distribution function polygon is the polygon to populate number_of_points is the optional number of points seedis the optional s
105. ontaining the interior polygon and its resolution Additionally the user specifies a list of boundary tags one for each edge of the bounding polygon 42 Chapter 5 ANUGA Public Interface breaklines lets you force a split along a boundary within the mesh For example a kerb or the edge of a dyke could be specified here new in 1 2 interior_holes lets you specify polygons as empty holes in the mesh This can be used to represent buildings pylons and other immovable structures These polygons do not need to be closed but their points must be specified in a counter clockwise order new in 1 2 WARNING Note that the dictionary structure used for the parameter boundary_tags is different from that used for the variable boundary that occurs in the specification of a mesh In the case of boundary the tags are the values of the dictionary whereas in the case of boundary_tags the tags are the keys and the value corresponding to a particular tag is a list of numbers identifying boundary edges labelled with that tag Because of this it is theoretically possible to assign the same edge to more than one tag However an attempt to do this will cause an error WARNING Do not have polygon lines cross or be on top of each other This can result in regions of unspecified resolutions and ANUGA will give you an error Do not have polygon close to each other This can result in the area between the polygons having small triangles For more control over t
106. ospatial_data object file_name is the path to the CSV or PTS points file to write absolute determines if the exported data is absolute or relative to the Geospatial_data object geo reference If True the exported data is absolute as_lat_long exports the points data as latitudes and longitudes if True isSouthHemisphere has effect only if as_lat_long is True and causes latitude longitude values to be for the southern True or northern hemispheres False points lt Geospatial data gt get_data_points absolute True geo_reference None as_lat_ long False isSouthHemisphere True Module geospatial_data geospatial_data Get the coordinates for all the data points as an N x 2 array absolute determines if the exported data is absolute or relative to the Geospatial_data object geo_ reference If True the exported data is absolute geo_reference is the geo_reference the points are relative to if supplied as_lat_long exports the points data as latitudes and longitudes if True isSouthHemisphere has effect only if as_lat_long is True and causes latitude longitude values to be for the southern True or northern hemispheres False A 5 geospatial_data 83 lt Geospatial_data gt set_attributes attributes Module geospatial_data geospatial_data Set the attributes fora Geospatial_data object attributes is the new value for the object s attributes May be a dictionary or None atributes lt Geospatial_data gt get_a
107. oundary Conditions 11 4 1 8 Evolution q e s sopp cda a e Pe EE RE RS 13 EA eo ee a eb Pa REA GA wae edo Pee Phas 13 42 How to Run the Code s s seora e eR eR ee EE e a 13 4 3 Exploring the Model Output 2 0 0 0 0 0 2 20 00 0 2 0 2 0000 0 13 E Be peb He Bye yest ee SS ts a Bh ee seas de ead de BS eg EP 15 IEW i te eo Be ee oO ee oda eae lea eee be beans 15 44 22 OVERVIEW s iss sos ae a ee eA Ke eee Se Se ea eS 15 443 The Code ce eh hve ak EG BR SR as GBs Gee SS Soe be es oe eS 15 4 44 Establishing the Mesh e eoe cacas SG BMS ee ee EA SR Bee Bae 16 4 5 Model Outputl secre s seerti oe eR RR Ee eee ae ee AR 16 4 5 1 Changing boundary conditions on the fly 2 2 2 ee 17 452 OMP o 2284 Sekine SARA SOS HE Ae SOR we E Re ee Ee eS 18 4 5 3 Flow through more complex topographles o o 19 4 6 An Example with Real Datal e 21 IEW io ed RE ARE EOE bbe ee ee A a de da a 21 46 2 The Code i s sa soe dao eg AS ie ge Seek Rock Gee le Rabo we age Sw 21 4 6 3 Establishing the Mesh 2 0 0 0 2000000000000 0000 24 4 6 4 Initialising the Doma 29 4 6 5 Initial Conditions 29 MA soi kb a ee ea ASH a ge GA dee wee we ee ee 29 4 632 Friction s ajo a Re ee Ae Ey we se ee Be ee eee 29 46 5 9 O AR ee ee eae OR ee Be 29 46 6 Boun
108. points vertices and boundary In the code we are discussing these three variables are returned by the 4 1 A Simple Example 11 function rectangular The example given in Section 4 6Jillustrates another way of assigning the values by means of the function create_mesh_from_regions These variables store the data determining the mesh as follows You may find that the example given in Section 5 3 helps to clarify the following discussion even though that example is a non rectangular mesh e The variable points stores a list of 2 tuples giving the coordinates of the mesh points e The variable vertices stores a list of 3 tuples of numbers representing vertices of triangles in the mesh In this list the triangle whose vertices are points i points j points k is represented by the 3 tuple i J k e The variable boundary is a Python dictionary that not only stores the edges that make up the boundary but also assigns symbolic tags to these edges to distinguish different parts of the boundary An edge with endpoints points i and points j is represented by the 2 tuple i j The keys for the dictionary are the 2 tuples i 3 corresponding to boundary edges in the mesh and the values are the tags are used to label them In the present example the value boundary i 4 assigned to i 4 is one of the four tags left right top or bottom depending on whether the boundary edge represented by i j occur
109. r more of the patong sww BASIC TRIAL FINAL tgz files The BASIC validation is the quickest and the FINAL validation is the slowest The validate py script will use whatever files you have BASIC first and FINAL last 91 92 APPENDIX C Frequently Asked Questions The Frequently Asked Questions have been move to the online FAQ at https datamining anu edu au anuga wiki FrequentlyAskedQuestions 93 94 APPENDIX D Glossary Term Definition Page ANUGA Name of software joint development between ANU and GA bathymetry offshore elevation conserved quantity Digital Elevation Model DEM Dirichlet boundary edge elevation evolution finite volume method forcing term flux grid latitude longitude Manning friction coefficient mesh mesh file NetCDF node northing points file conserved stage x and y momentum DEMs are digital files consisting of points of elevations sampled sys tematically at equally spaced intervals A boundary condition imposed on a differential equation that specifies the values the solution is to take on the boundary of the domain A triangular cell within the computational mesh can be depicted as a set of vertices joined by lines the edges refers to bathymetry and topography integration of the shallow water wave equations over time The method evaluates the terms in the shallow water wave equation as fluxes at the surfaces of each finite vol
110. reated Files ee 64 6 1 3 SWW STS and TMS Formats 0 20 00 0 000020004 64 6 1 4 Mesh File Formats s s oni ee ee 66 6 1 5 Formats for Storing Arbitrary Points and Attributes o 67 6 1 6 ArcView Formats 67 617 DEM FA ec oe a ee eS Rp eee a Ee ee 67 61 8 Other Formats i lt e i ad ge ote ae Ge BAe Geek oe A aR eee e Bee A 67 6 1 9_ Basic File Conversions p lt e 6 6 eG ee AR Ra a OR La Re Pe 67 7 ANUGA mathematical background 69 7 1 Introduction aos eee Res HA ae ER AEE Oe De Ye el OR ee eee 69 T2 IMG vice os o A GUA Het oe Wp Se a oe AA BAS Bese oo Gs 69 17 3 Fimite Volume Method 2 2 2 ee 69 iA Flux limitin ces seen See eee hae eth e PASS Saba ee ee ee Phew N 71 T gt Slope RNA 72 8 75 75 75 75 75 76 77 AR PA EAN wae S 77 AS ie Beh trac NR ade ae pea Jas DA eee 78 A S geospatial_data Miscellaneous Functions A 6 Graphical Mesh Generator GU A 7 class Alpha_Shape A 8 Numerical Tools A 9 Finding the Optimal Alpha Value ANUGA Full scale Validations B 2 Patong Beach C Frequently Asked Questions J 91 91 91 93 95 97 CHAPTER ONE Introduction 1 1 Purpose The purpose of this user manual is to introduce the new user to the inundation software system describe what it can do and give step by step instructions for setting up and running hydrodynamic simulations The stable release of ANUGA and this manual are
111. reduction is assumed to be mean Triangles stored in the SWW file can be discontinuous reflecting the internal representation of the finite volume scheme this is a feature allowing for arbitrary steepness of the water surface gradient as well as the momentum gradients However for visual purposes and also for use with Field_boundary and File_boundary it 1s often desirable to store triangles with values at each vertex point as the average of the potentially discontinuous numbers found at vertices of different triangles sharing the same vertex location Storing one way or the other is controlled in ANUGA through the method lt domain gt store_vertices_ uniquely Options are e lt domain gt store_vertices_uniquely True Allow discontinuities in the SWW file e lt domain gt store_vertices_uniquely False Default Average values to ensure continuity in SWW file The latter also makes for smaller SWW files Note that when model data in the SWW file are averaged i e not stored uniquely then there will most likely be a small discrepancy between values extracted from the SWW file and the same data stored in the model domain This must be borne in mind when comparing data from the SWW files with that of the model internally 5 4 Initialising the Domain 47 lt domain gt set_quantities_to be stored quantity_dictionary Module shallow_water shallow_water_domain Selects quantities that is to be stored in the sww files The
112. ressure gradients 1f applicable ANUGA tracks the evolution of water depth and horizontal momentum within each cell over time by solving the shallow water wave equation governing equation using a finite volume method ANUGA also incorporates a mesh generator that allows the user to set up the geometry of the problem interactively as well as tools for interpolation and surface fitting and a number of auxiliary tools for visualising and interrogating the model output Most ANUGA components are written in the object oriented programming language Python and most users will interact with ANUGA by writing small Python programs based on the ANUGA library functions Computationally intensive components are written for efficiency in C routines working directly with Python numpy structures CONTENTS 1 AP A AN S eS 1 U2 SCOPE E A ANA 1 13 AUdIENCO sao or ad ed Sew a ee E Boe eS 1 2 Background 3 5 4 Getting Started 7 NS RN 7 4i COVES 55 as 2s Be A do e is 7 i is tes oy ee O O 7 is to eh aa ee eee ee eRe eee eae ee eee A 8 4 1 4 Establishing the Mesh 00 0 2000000002000 000004 9 4 1 5 Initialising the Doma 9 4 1 6 __ Initial Conditions sos sje ra RAS ee SEES Bee RS RES SS 10 A sc 454 ee boa bb be eee Bae ewe Sa Phe ee be eee eb 10 CN Friction a ben GAS ES SB OE Se Ee ER EEG SE BAIS 10 A o 8 akon e oY ERE KE E a Ry ee se Sa ae a Re es 10 4 1 7 B
113. ries data in mux2 format and converts it to STS format The optional filename ordering_filename specifies the permutation of indices of points to select along with their longitudes and latitudes This permutation will also be stored in the STS file If absent all points are taken and the permutation will be trivial i e 0 1 N 1 where N is the total number of points stored csv2building_ polygons file name floor_height 3 Module shallow_water data_manager Convert CSV files of the form easting northing id floors 422664 22 870785 46 2 0 422672 48 870780 14 2 0 422668 17 870772 62 2 0 422660 35 870777 17 2 0 422664 22 870785 46 2 0 422661 30 871215 06 3 1 422667 50 871215 70 3 1 422668 30 871204 86 3 1 422662 21 871204 33 3 1 422661 30 871215 06 3 1 to a dictionary of polygons with id as key The associated number of floors are converted to m above MSL and returned as a separate dictionary also keyed by id Optional parameter f loor_height is the height of each building story These can e g be converted to a Polygon_function for use with add_quantity as shown on page 50 68 Chapter 6 ANUGA System Architecture CHAPTER SEVEN ANUGA mathematical background 7 1 Introduction This chapter outlines the mathematics underpinning ANUGA 7 2 Model The shallow water wave equations are a system of differential conservation equations which describe the flow of a thin layer of fluid over terrain The form of the equ
114. s at the left right top or bottom of the rectangle bounding the mesh The function rectangular automatically assigns these tags to the boundary edges when it generates the mesh The tags provide the means to assign different boundary conditions to an edge depending on which part of the boundary it belongs to In Section 4 6 we describe an example that uses different boundary tags in general the possible tags are entirely selectable by the user when generating the mesh and not limited to left right top and bottom as in this example All segments in bounding polygon must be tagged If a tag is not supplied the default tag name exterior will be assigned by ANUGA Using the boundary objects described above we assign a boundary condition to each part of the boundary by means of a statement like domain set_boundary left Br right Bw top Br bottom Br It is critical that all tags are associated with a boundary condition in this statement If not the program will halt with a statement like Traceback most recent call last File mesh_test py line 114 in domain set_boundary west Bi east Bo north Br south Br File X inundation sandpits onielsen anuga_core source anuga abstract_2d_finite_volumes doma raise msg ERROR domain py Tag exterior has not been bound to a boundary object All boundary tags defined in domain must appear in the suppl
115. s found within the polygon and time_interval if specified the return value is None This indicates No Runup or Everything is dry is None This indicates No Runup or Everything is dry sww2timeseries swwfiles gauge filename production_dirs report None reportname None plot_quan tity None generate fig False surface None time_min None time_max None output_ centroids False time thinning 1 time_unit None title on None use_cache False ver bose False Module abstract_2d_finite_volumes util Read a set of SWW files and plot the time series for the prescribed quantities at defined gauge locations and prescribed time range swwfiles is a dictionary of SWW files with keys of label_id gauge_filename is the path to a file containing gauge data THIS NEEDS MORE WORK WORK ON FUNCTION _DOC__ STRING IF NOTHING ELSE time Q get_flow_through_cross_section filename polyline verbose False Module shallow_water data_manager Obtain flow m s perpendicular to specified cross section filename is the path to the SWW file 5 9 Queries of SWW model output files 61 output_centroids set to true to sample at the centre of the triangle containing the point This may be useful for debugging new in 1 2 polyline is the representation of the desired cross section it may contain multiple sections allowing for complex shapes Assumes absolute UTM coordinates Returns a tuple time Q where t ime is
116. s pie e ES H e a ooo O O Oo 000000 al o o x os o So N on on on on om dw Mm ONW w YN MM FO MM xs dd a Foo 0 Noe 000000m o o o x os o x oa Rr ie eg OS E S o LN OTD WD SNM TO 000 00 CO 6 WO LD O 00 ooooooo el o Ne o o RON S A A Nn N sn MM 100 gt NOM tO mo DO so id O To MEE E E gt E OS a CO iO O OO Co O o od o e RON ON ON on on E S S aN SOO 1x0 ONM TWO 000 00 O oO re qo ep e a OO SO OOO 0 00 O CO ea ASB o o N E S on E ES sd n nO AN ns NM TWO M0 OO st NO OV 00 Oooo0Oo0oOooo0oO O O OM o o o sn oO sO xc qa Ot MO CO OD 0 st 00 E E E ee a A NR OR 0 00 00 OO 0H0O0OMNO o xs Sox so sO oO on r TM AO W OV lO DM Koj TA le E OS er ee ae ee a Oi SOO 0 00 1 010 00 O a O 5 o o os sof SoN O sn 10M TWO OO 0 0 st ON O LD OV oo alee GRR a ne ee ee ee ee E E E 0 OOO OOO 6 0 0 0 0 0 0 ll ll x gt elevation H N m lt 19 a SN SM ST AWW O sO SCO SO 8 OO CO MO O 10 LO LO LO LO SOT ONOMOTHT OO d N M lt LO AS a o o o o HAON OM O SOL e gt i 7 Oo N M lt LO o e 57 o o e o x oe ae
117. sed as vertices in triangles Consequently polygons with points very close together will cause triangles with very small areas to be generated irrespective of the requested resolution Make sure points on polygons are spaced to be no closer than the smallest resolution requested 28 Chapter 4 Getting Started 4 6 4 Initialising the Domain Since we used create_domain_from_regions to create the mesh file we do not need to create the domain explicitly as the above function does both mesh and domain creation The following statements specify a basename and data directory and sets a minimum storable height which helps with visualisation and post processing if one wants to remove water less than 1cm deep for instance domain set_name cairns_ project scenario Name of SWW file domain set_datadir Store SWW output here domain set_minimum_storable_height 0 01 Store only depth gt 1cm 4 6 5 Initial Conditions Quantities for runcairns py are set using similar methods to those in runup py However in this case many of the values are read from the auxiliary file project py or in the case of elevation from an auxiliary points file 4 6 5 1 Stage The stage is initially set to 0 0 1 e Mean Sea Level by the following statements tide 0 0 domain set_quantity stage tide It could also take the value of the highest astronomical tide 4 6 5 2 Friction We assign the friction exactly as
118. skipped or not This is useful for example to avoid duplicate steps when multiple evolve processes are dove tailed The code specified by the user in the block following the evolve statement is only executed once every yieldstep even though ANUGA typically will take many more internal steps behind the scenes You can include evolve in a statement of the type for t in domain evolve yieldstep finaltime lt Do something with domain and t gt 5 8 Evolution 57 5 8 1 Diagnostics lt domain gt statistics Module abstract_2d_finite_volumes domain Outputs statistics about the mesh within the Domain lt domain gt timestepping_statistics track_speeds False triangle_id None Module abstract_2d_finite_volumes domain Returns a string of the following type for each timestep Time 0 9000 delta t in 0 00598964 0 01177388 steps 12 12 Here the numbers in steps 12 12 indicate the number of steps taken and the number of first order steps respectively The optional keyword argument t rack_speeds will generate a histogram of speeds generated by each trian gle if set to True The speeds relate to the size of the timesteps used by ANUGA and this diagnostics may help pinpoint problem areas where excessive speeds are generated The optional keyword argument triangle_id can be used to specify a particular triangle rather than the one with the largest speed lt domain gt boundary_statistics quantities None tags None
119. t The user must specify the domain to get access to the model time Optional argument default_boundary can be used to specify another boundary object to be used in case model time exceeds the time available in the file used by File_boundary The default_boundary could 52 Chapter 5 ANUGA Public Interface be a simple Dirichlet condition or even another Time_boundary typically using data pertaining to another time interval class File _boundary filename domain time_thinning 1 time_limit None boundary_polygon None default_ boundary None use_cache False verbose False Module abstract_2d_finite_volumes generic_boundary_conditions This method may be used if the user wishes to apply a SWW file STS file or a time series file TMS to a boundary segment or segments The boundary values are obtained from a file and interpolated to the appropriate segments for each conserved quantity Optional argument default_boundary can be used to specify another boundary object to be used in case model time exceeds the time available in the file used by File_boundary The default_boundary could be a simple Dirichlet condition or even another File_boundary typically using data pertaining to another time interval class Field_boundary filename domain mean_stage 0 0 time_thinning 1 time_limit None boundary_poly gon None default_boundary None use_cache False verbose False Module shallow_water shallow_water_domain This method works in the same
120. t domain gt get_centroid_coordinates absolute False Module abst ract_2d_finite_volumes domain Return centroid coordinates for all triangles as an Mx2 array absolute is a boolean which determines whether coordinates are to be made absolute by taking georeference into account Default is False as many parts of ANUGA expect relative coordinates lt domain gt get_triangles indices None Module abstract_2d_finite_volumes domain Return an Mx3 integer array where M is the number of triangles Each row corresponds to one triangle and the three entries are indices into the mesh nodes which can be obtained using the method get_nodes indices if specified is the set of triangle ids of interest lt domain gt get_disconnected_triangles Module abstract_2d_finite_volumes domain Get the domain mesh based on nodes obtained from get_vertex_coordinates Returns an Mx3 array of integers where each row corresponds to a triangle A triangle is a triplet of indices into point coordinates obtained from get_vertex_coordinates and each index appears only once This provides a mesh where no triangles share nodes hence the name disconnected triangles and different nodes may have the same coordinates This version of the mesh is useful for storing meshes with discontinuities at each node and is e g used for storing data in SWW files The triangles created will have the format 48 Chapter 5 ANUGA Public Interface 3 M 3 3x
121. tags None geo_reference None Module pmesh mesh This method is used to add a hole within a region that is to define a interior region where the triangular mesh will not be generated to a Mesh instance The region boundary is described by the polygon passed in Additionally the user specifies a list of boundary tags one for each edge of the bounding polygon polygon is the polygon that defines the hole to be added to the lt mesh gt segment_tags If geo_reference is None then the default geo_reference is used lt mesh gt add_points_and_segments points segments None segment_tags None Module pmesh mesh This adds points and segments connecting the points to a mesh points is a list of points segments is a list of segments Each segment is defined by the start and end of the line by its point index e g use segments 0 1 1 2 to make a polyline between points 0 1 and 2 segment_tags may be used to optionally define a tag for each segment lt mesh gt add_region x y geo_reference None tag None Module pmesh mesh This method adds a region to a mesh outline x and y define a point on the already defined region that is to be added to the mesh 44 Chapter 5 ANUGA Public Interface If geo_reference is not supplied the points data is assumed to be absolute tag 2 A region instance is returned This can be used to set the resolution of the added region lt mesh gt add_region_ from _poly
122. th is default_datadir specified in config py Since different operating systems use different formats for specifying pathnames it is necessary to specify path separators using the Python code os sep rather than the operating specific ones such as or For this to work you will need to include the statement import os in your code before the first use of set_ datadir For example to set the data directory to a subdirectory data of the directory project you could use the statements import os domain set_datadir project os sep data lt domain gt get_datadir Module abstract_2d_finite_volumes domain Returns the path to the directory where SWW files will be stored Tf the path has not previously been set with set_datadir this method will return the value default_ datadir specified in config py 46 Chapter 5 ANUGA Public Interface lt domain gt set_minimum allowed height minimum_allowed_height Module shallow_water shallow_water_domain Set the minimum depth in metres that will be recognised in the numerical scheme including limiters and flux computations minimum_allowed_height is the new minimum allowed height value Default value is 107 metre but by setting this to a greater value e g for large scale simulations the computa tion time can be significantly reduced lt domain gt set_minimum storable height minimum_storable_height Module shallow_water shallow_water_domain
123. that may drive the system such as rainfall abstraction of water wind stress or atmospheric pressure gradients Fric tional resistance from the different terrains in the model is represented by predefined forcing terms In this example the boundary is reflective on three sides and a time dependent wave on one side The present example represents a simple scenario and does not include any forcing terms nor is the data taken from a file as 1t would typically be The conserved quantities involved in the problem are stage absolute height of water surface momentum and y momentum Other quantities involved in the computation are the friction and elevation Water depth can be obtained through the equation depth stag levation 4 1 2 Outline of the Program In outline runup py performs the following steps 1 Sets up a triangular mesh 2 Sets certain parameters governing the mode of operation of the model specifying for instance where to store the model output 3 Inputs various quantities describing physical measurements such as the elevation to be specified at each mesh point vertex 4 Sets up the boundary conditions 5 Carries out the evolution of the model through a series of time steps and outputs the results providing a results file that can be viewed 4 1 3 The Code For reference we include below the complete code listing for runup py Subsequent paragraphs provide a commen tary that des
124. the vertices of each of the triangles volumes Consequently information arrays stored within an STS file such as elevat ion can be accessed in exactly the same way as it would be extracted from an SWW file A TMS file is used to store time series data that is independent of position 6 1 4 Mesh File Formats A mesh file is a file that has a specific format suited to triangular meshes and their outlines A mesh file can have one of two formats it can be either a TSH file which is an ASCII file or an MSH file which is a NetCDF file A mesh file can be generated from the function create_mesh_from_regions see Section 5 3 and be used to initialise a domain A mesh file can define the outline of the mesh the vertices and line segments that enclose the region in which the mesh is created and the triangular mesh itself which is specified by listing the triangles and their vertices and the segments which are those sides of the triangles that are associated with boundary conditions In addition a mesh file may contain holes and or regions A hole represents an area where no mesh is to be created while a region is a labelled area used for defining properties of a mesh such as friction values A hole or region is specified by a point and bounded by a number of segments that enclose that point A mesh file can also contain a georeference which describes an offset to be applied to x and y values e g to the vertices 66 C
125. tion reads points from the specified point file point_file computes the associated alpha shape either using the specified value for alpha or if no value is specified automatically setting it to an optimal value and outputs the boundary to a file named boundary_file This output file lists the coordinates x y of each point in the boundary using one line per point lt Alpha_shape gt set_boundary_type raw_boundary True remove holes False smooth_indents False expand_pinch False boundary_points fraction 0 2 Module alpha_shape This function sets internal state that controls how the Alpha_shape boundary is presented or exported raw_boundary sets the type to raw if True i e the regular edges of the alpha shape remove_holes if True removes small holes small is defined by boundary_points_fraction smooth_indents if True removes sharp triangular indents in the boundary expand_pinch if True tests for pinch off and corrects preventing a boundary vertex from having more than two edges boundary lt Alpha shape gt get_boundary Module alpha_shape Returns a list of tuples representing the boundary of the alpha shape Each tuple represents a segment in the boundary by providing the indices of its two endpoints See set_boundary_type page 88 lt Alpha_shape gt write_boundary file name Module alpha_shape Writes the list of 2 tuples returned by get_boundary to the file ile_name using one line per tuple
126. to use The function returns a tuple min_covar alpha where min_covar is the minumum normalised co variance and alpha is the alpha value that created it A plot file is also written A 5 geospatial_data 85 This is an example of function usage convariance_value alpha find_optimal_smoothing_parameter data_file fileName alpha_list 0 0001 0 01 1 mesh_file None mesh_resolution 3 north_boundary 5 south_boundary 5 east_boundary 5 west_boundary 5 plot_name all_alphas seed_num 100000 verbose False NOTE The function will not work if the data_file extent is greater than the boundary_poly polygon or any of the boundaries e g north_boundary etc 86 Appendix A Supporting Tools A 6 Graphical Mesh Generator GUI The program graphical_mesh_generator py in the pmesh module allows the user to set up the mesh of the problem interactively It can be used to build the outline of a mesh or to visualise a mesh automatically generated Graphical Mesh Generator will let the user select various modes The current allowable modes are vertex segment hole or region The mode describes what sort of object is added or selected in response to mouse clicks When changing modes any prior selected objects become deselected In general the left mouse button will add an object and the right mouse button will select an object A selected object can de deleted by pressing the the middle mouse button scroll bar
127. ttributes attribute name None Module geospatial_data geospatial_data Get a named attribute from a Geospatial_data object attribute_name is the name of the desired attribute If None return the default attribute lt Geospatial data gt get_all_attributes Module geospatial_data geospatial_data Get all attributes of aGeospatial_data object Returns None or the attributes dictionary which may be empty lt Geospatial_data gt set_default_attribute_name default_attribute_name Module geospatial_data geospatial_data Set the default attribute name of a Geospatial_data object default_attribute_name is the new default attribute name lt Geospatial_data gt set_geo_reference geo_reference Module geospatial_data geospatial_data Set the internal geo_reference of a Geospatial_data object geo_reference is the new internal geo_reference for the object If None will use the default geo_reference If the Geospatial_data object already has an internal geo_reference then the points data will be changed to use the new geo_reference lt Geospatial data gt _ add other Module geospatial_data geospatial_data The __add__ method is defined so it is possible to add two Geospatial_data objects geospatial lt Geospatial_data gt clip polygon closed True verbose False Module geospatial_data geospatial_data Clip a Geospatial_data object with a polygon polygon is the polygon to clip the Geospatial_data object with This m
128. ulvert No 2 description This culvert is a circular test with d 1 2m end_point0 9 0 1 5 end_point1 30 0 3 5 diameter 1 20 invert_level0 7 culvert_routine boyd_generalised_culvert_model number_of_barrels 1 verbose True domain forcing_terms append culvert1 domain forcing_terms append culvert2 5 8 Evolution lt domain gt evolve yieldstep None finaltime None duration None skip_initial_step False Module abstract_2d_finite_volumes domain This method is invoked once all the preliminaries have been completed and causes the model to progress through successive steps in its evolution storing results and outputting statistics whenever a user specified period yieldstep is completed Generally during this period the model will evolve through several steps internally as the method forces the water speed to be calculated on successive new cells yieldstep is the interval in seconds between yields where results are stored statistics written and the domain is inspected or possibly modified If omitted an internal predefined yieldstep is used Internally smaller timesteps may be taken duration is the duration of the simulation in seconds finaltime is the time in seconds where simulation should end This is currently relative time so it s the same as duration If both duration and finaltime are given an exception is thrown skip_initial_step is a boolean flag that decides whether the first yield step is
129. ume Because the flux en tering a given volume is identical to that leaving the adjacent volume these methods are conservative Another advantage of the finite volume method is that it is easily formulated to allow for unstructured meshes The method is used in many computational fluid dynamics packages the amount of flow through the volume per unit time Evenly spaced mesh The angular distance on a mericlear north and south of the equator ex pressed in degrees and minutes The angular distance east or west between the meridian of a particular place on Earth and that of the Prime Meridian located in Greenwich England expressed in degrees or time Triangulation of domain A TSH or MSH file A point at which edges meet A rectangular x y coordinate measurement of distance north from a north south reference line usually a meridian used as the axis of ori gin within a map zone or projection Northing is a UTM Universal Transverse Mercator coordinate A PTS or CSV file 95 polygon resolution reflective boundary stage anuga_viewer time boundary topography transmissive boundary vertex A sequence of points in the plane ANUGA represents a polygon either as a list consisting of Python tuples or lists of length 2 or as an N x 2 numeric array where NV is the number of points The unit square for example would be represented either as 0 0 1 0 1 1 0 1 orasarray 0 0 1 0 1 1 0
130. unities Geoscience Australia and the Australian National University are developing a hydrodynamic inundation modelling tool called ANUGA to help simulate the impact of these hazards The core of ANUGA is the fluid dynamics module called shallow_water which is based on a finite volume method for solving the Shallow Water Wave Equation The study area is represented by a mesh of triangular cells By solving the governing equation within each cell water depth and horizontal momentum are tracked over time A major capability of ANUGA is that it can model the process of wetting and drying as water enters and leaves an area This means that it is suitable for simulating water flow onto a beach or dry land and around structures such as buildings ANUGA is also capable of modelling hydraulic jumps due to the ability of the finite volume method to accommodate discontinuities in the solutior To set up a particular scenario the user specifies the geometry bathymetry and topography the initial water level stage boundary conditions such as tide and any forcing terms that may drive the system such as rainfall abstraction of water wind stress or atmospheric pressure gradients Gravity and frictional resistance from the different terrains in the model are represented by predefined forcing terms See section 5 7 for details on forcing terms available in ANUGA The built in mesh generator called graphical_mesh_generator allows the user to set up the g
131. uples of floats or as an M x 2 numeric array of floats where M is the number of points Coordinates are interpreted relative to the origin specified by the object geo_reference which contains data indicating the UTM zone easting and northing If geo_reference is not specified a default is used Attributes are specified through the parameter attributes set either to a list or array of length M or to a dictionary whose keys are the attribute names and whose values are lists or arrays of length M One of the attributes may be specified as the default attribute by assigning its name to default_attribute_name If no value is specified the default attribute is taken to be the first one Note that the Geospat ial_data object currently reads entire datasets into memory i e no memomry block ing takes place For this we refer to the set_quantity method which will read PTS and CSV files into ANUGA using memory blocking allowing large files to be used lt Geospatial_data gt import_points_file file_name delimiter None verbose False Module geospatial_data geospatial_data Import a TXT CSV or PTS points data file into a codeGeospatial_data object file_name is the path to a TXT CSV or PTS points data file delimiter is currently unused lt Geospatial_data gt export_points_file filename absolute True as lat_long False isSouthHemi sphere True Module geospatial_data geospatial_data Export a CSV or PTS points data file from a Ge
132. utili ties polygon 80 lt callable gt Polygon_function class in util ities polygon lt point gt point_in_polygon utilities polygon lt polygon gt read_polygon in module utili ties polygon 79 Ymar plot_ in module utilities polygon in mod in module Umin r polygons ANUGA i ANUGA 95 lt Alpha_shape gt set_boundary_type pha_Shape method 88 lt Alpha_shape gt write_boundary Shape method 88 lt Geospatial_data gt __add__ data method 84 lt Geospatial_data gt export_points_file Geospatial_data method lt Geospatial_data gt get_all_attributes Geospatial_data method Emin 1 maz Al Alpha Geospatial_ INDEX lt Geospatial_data gt import_points_file Geospatial_data method lt Geospatial_data gt set_attributes Geospatial_data method lt Geospatial_data gt set_default_ attribute_name Geospatial_data method 84 lt Geospatial_data gt set_geo_referencel Geospatial_data method lt callable_object gt Interpolation_ function class in 51 lt callable_object gt file _function in module 51 lt domain gt add_quant ity method 50 lt domain gt boundary_statistics method lt domain gt evolve method 57 lt domain gt get_boundary_tags method 52 lt domain gt get_centroid_coordinates Domain method 48 lt domain gt get_datadir Domain method 4
133. utside Returns a numeric array comprising the indices of the points in the list that lie outside the polygon If none of the points are outside returns zeros 0 1 ie an empty numeric array Compare with inside_polygon page 79 lt boolean gt is_inside polygon point polygon closed True verbose False Module utilities polygon Determines if a single point is inside a polygon point is the point to test polygon is the polygon to test point against closed is a flag that forces the function to consider a point on the polygon edge to be inside or outside if True a point on the edge is considered inside the polygon Returns True if point is inside polygon Compare with inside _polygon page 79 lt boolean gt is_outside polygon point polygon closed True verbose False Module utilities polygon Determines if a single point is outside a polygon point is the point to test polygon is the polygon to test point against closed is a flag that forces the function to consider a point on the polygon edge to be outside or inside if True a point on the edge is considered inside the polygon Compare with out side_polygon page 80 lt boolean gt point_on_line point line rtol 1 0e 5 atol 1 0e 8 Module utilities polygon Determine if a point is on a line to some tolerance The line is considered to extend past its end points point is the point to test z y line is the line to test p
134. ve a real time programmers guide for ANUGA and an easy way to find the functions you are interested in Pydoctor and other Python doc generators look nicer and have graphs etc but pydoc works straight out of the box 5 2 Public vs Private Interface To simplify the process of writing scripts ANUGA has a public API which packages up all the commonly used functionality of ANUGA in the one place To use it simply import the anuga module like so import anuga You can now use the public API like so Note the anuga prefix 39 anuga sww2dem in sww out asc If you wish to delve under the hood and modify the way ANUGA runs at a more advanced level you need to specify the full location of the module like so from anuga fit_interpolate interpolate import Interpolation_interface All modules are in the folder inundation or one of its subfolders and the location of each module is described relative to inundation Rather than using pathnames whose syntax depends on the operating system we use the format adopted for importing the function or class for use in Python code For example suppose we wish to specify that the function create_mesh_from_regions is in a module called mesh_interface in a subfolder of inundation called pmesh In Linux or Unix syntax the pathname of the file containing the function relative to inundation would be pmesh mesh_interface py while in Windows syntax it would be
135. way as File_boundary except that it allows for the value of stage to be offset by a constant specified in the keyword argument mean_stage This functionality allows for models to be run for a range of tides using the same boundary information from STS SWW or TMS files The tidal value for each run would then be specified in the keyword argument mean_stage If mean_stage 0 0 Field_boundary and File_boundary behave identically Note that if the optional argument default_boundary is specified its stage value will be adjusted by mean_stage just like the values obtained from the file See File_boundary for further details class Transmissive_momentum_set_stage_boundary domain None function None Module shallow_water shallow_water_domain This boundary returns the same momentum conserved quantities as those present in its neighbour volume but sets stage as ina Time_boundary The underlying domain must be specified when boundary is instantiated This type of boundary is useful when stage is known at the boundary as a function of time but momenta or speeds aren t This class is specific to the shallow water equation as it works with the momentum quantities assumed to be the second and third conserved quantities In some circumstances this boundary condition may cause numerical instabilities for similar reasons as what has been observed with the simple fully transmissive boundary condition see Page 52 This could for example be the case
136. x topography defined by a function of vectors x and y z x 10 N len x for i in range N Step 1 10 x XTi lt 12 z i 0 4 0 05x y 1 Constriction if 27 lt x i lt 29 and y i gt 3 z 1 2 Pole 4 5 Model Output if x i 34 xx2 y i 2 2 lt 0 4xx2 z i 2 return z domain set_quantity elevation topography elevation is a function domain set_quantity friction 0 01 Constant friction domain set_quantity stage xpression elevation Dry initial condition Setup boundary conditions pz Bi anuga Dirichlet_boundary 0 4 0 0 Inflow Br anuga Reflective_boundary domain Solid reflective wall Bo anuga Dirichlet_boundary 5 0 0 Outflow domain set_boundary left Bi right Bo top Br bottom Br Evolve system through time for t in domain evolve yieldstep 0 1 finaltime 16 0 print domain timestepping_statistics if domain get_quantity stage get_values interpolation_points 10 2 5 gt 0 print Stage gt 0 Changing to outflow boundary domain set_boundary right Bo This example differs from the first two versions in that the topography contains obstacles This is accomplished here by defining the function topography as follows def topography x y Complex topography defined by a function of vectors x a
137. ygons for the Cairns example The statement remainder_res 10000000 domain anuga create_domain_from_regions project bounding_polygon boundary_tags top 0 ocean_east 1 bottom 2 onshore 3 maximum_triangle_area project default_res mesh_filename project meshname interior_regions project interior_regions use_cache True verbose True is then used to create the mesh taking the bounding polygon to be the polygon bounding_polygon specified in project py The argument boundary_tags assigns a dictionary whose keys are the names of the boundary tags used for the bounding polygon top ocean_east bottom and onshore and whose values identify the indices of the segments associated with each of these tags The polygon may be arranged either clock wise or counter clock wise and the indices refer to edges in the order they appear Edge O connects vertex O and vertex 1 edge 1 connects vertex and 2 and so forth Here the values associated with each boundary tag are one element lists but they can have as many indices as there are edges If polygons intersect or edges coincide or are even very close the resolution may be undefined in some regions Use the underlying mesh interface for such cases see Chapter 5 2 If a segment is omitted in the tags definition an Exception is raised Note that every point on each polygon defining the mesh will be u

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