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USER`S MANUAL for LSMONTE A Three

1. Dolaghan John S 1996 A Monte Carlo Simulation in Rarefied Gas Dynamics with Application to Physical Vapor Deposition Ph D Dissertation Department of Mechanical Engineering Col orado State University Fort Collins CO 80523 Golomb S W 1982 Shift Register Sequences Revised edition Aegean Park Press Maltby James D 1987 Three Dimensional Simulation of Radiative Heat Transfer by the Monte Carlo Method M S Thesis Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 Maltby James D 1990 Analysis of Electron Heat Transfer via Monte Carlo Simulation Ph D Dissertation Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 Maltby James D and Burns Patrick J 1991 Performance Accuracy and Convergence in a Three Dimensional Monte Carlo Radiative Heat Transfer Simulation Numerical Heat Transfer Part B Fundamentals 16 pp 191 209 Maltby James D Burns Patrick J and Winn C Byron 1986 Monte Carlo Simulation of Radi 42 ative Heat Transport in Passive Solar Buildings Proceedings of the 1986 American Solar Energy Society Conference Boulder Colorado June 9 11 1986 Maltby James D Zeeb Charles N Dolaghan John D and Burns Patrick J 1994 User s Man ual for MONT2D Version 2 6 and MONT3D Version 2 3 Department of Mechanical Engineer ing Colorado State University Fort Collins CO 80523 Marsaglia G 1
2. 2 If IPRINT 1 1 then exchange fractions are printed in the output file If I PRINT 1 0 they are written only to the binary exchange matrix files The user is cautioned that exchange factors may be extremely large requiring a long time to write and very large disk capacity 3 Lost photon information is written by default to the file st If this option IPRINT 2 1 then lost photon information is also written to the output file 4 Grid information contains a list of all surfaces found partially or wholly within grids Grid infor mation is written to the output file if this option IPRINT 3 1 The user is cautioned that this may produce a very large amount of output 5 Material property information is by default written to the plot file plt When setting this option IPRINT 4 1 this information is also written to the output file 6 It is often useful before beginning a run especially a large one to perform a data check and examine the output file for irregularities To accomplish this prepare the input file and initiate a run with IDATA 1 If upon examination of the output everything appears fine set IDATA 0 and proceed with the real run 7 The program dumps trajectory information to the trc file if this option is set This file is used to view the trajectories using the MPLOT program useful in establishing physical intuition If chosen a copious amount of information is printed to the file the use
3. Either of the relations expressed as equation 1 5 or 1 6 may be used to test the exchange factors or the exchange fractions for consistency convergence Indeed either of these relations may be used to manipulate the values in the matrix if either of equations 1 3 or 1 4 is used as a constraint 1 3 View Factors The codes may be used to compute view factors valid for diffuse reflectances independent of incident angle To do so all entries for curves of specular and diffuse reflectances and transmit tances must be set to 0 0 resulting in an emittance of 1 0 black for all surfaces In this limiting case exchange factors for blackbody surfaces are equivalent to view factors 1 4 Implementation The codes are typically used as preprocessors for thermal balance studies As such the matrix of exchange numbers output from the programs are used as input to a thermal balance code MONT3D is designed to be compatible with the thermal analysis codes LSDYNA available from the Livermore Software Technology Corporation and TOPAZ3D Shapiro 1985 developed at Lawrence Livermore National Laboratory SMOOTH Dolaghan et al 1992 is a postprocessor designed to take advantage of reciprocity to improve the accuracy of the estimates It operates on the output of MONT3D and produces output compatible with LSDYNA and TOPAZ3D Dola ghan s version of SMOOTH is not compatible with LSMONTE a new version that will be com patible is und
4. A9 ANBANDS 1 1 2 3 Notes 1 The first point A 0 is and the last point Anganps are omitted 2 Multiple records are used if needed 3 For a single band this record is omitted 29 5 SAMPLE INPUT FILES 5 1 General Description This section contains one sample input file to demonstrate the input format The problem is a 3 D cube rectangular prism with black inner surfaces Close examination of this file should assist the user in understanding how to generate an input file 5 2 3 D Box Figure 5 1 shows a 3 D geometry a cube not to scale for analysis Comparison of the picture with the input file box in shown below illustrates the right hand rule for 3 D surfaces One million photons per photon loop are emitted from each surface The reflectance of the inner surfaces is zero The nodes are at the vertices of a cube of edge length 10 Note that surfaces 1 through 6 are sequentially the bottom top left right back and front respectively The material is named Black Surface consists of one band is of type 0 standard emission has all surface prop erties zero and has Lambertian diffuse properties r 1 for emission 5 8 4 PO IES O 2 3 Figure 5 1 3 D Geometry of File box in GROUP 1 TEST 1 BLACK CUBE FILE BOX IN amp NUMNP NUMMAT NCURVE amp NSURE NBANDS 8 6 1 I 0 am
5. DELT is set to the default value of 0 01 Note that very small values of DELT result in unnecessary consumption of excessive computer time 4 In order to reduce the loss of photons the four nodes of a quadrilateral surface must be coplanar The code enforces coplanarity by dividing each quadrilateral element into two triangles By definition a triangle is coplanar This division is transparent to the user The dot product of the surface normals of both triangles is then calculated If the dot product differs from one by more than a specified tolerance SPLITOL indicating the two triangles are non coplanar to this degree a warning message is printed as this may be indicative of a potential problem with the geometry The range of acceptable values is 1 E 20 lt SPLITOL lt 0 1 If a value outside of this range is entered SPLITOL is set to the default value of 0 0001 5 All quadrilateral surfaces are split into two triangles from which emission is done separately Surfaces may be split along the line between nodes 1 and 3 or nodes 2 and 4 In LSMONTE surfaces are arbitrarily split along the line between nodes 1 and 3 However a check is made to ensure that splitting along the line between nodes 2 and 4 produces a similar total area If these areas are almost identical then the surface possesses good geometrical properties for splitting A poor match between the two total areas usually indicates that the surface is poorly defined geometrically
6. and the leaks file named alakazam lks Example 2 lsmonte f calendar The input file calender in must exist The following files will be created the restart file named cal ender rst the plot file named calander plt the lost photon trajectory file named calender 1st the absorption exchange factor file named calendar the trajectory file if required named calender trc the output file named calend out and the leaks file named calender Iks Example 3 lsmonte f tri e mi5run The input file tri in must exist The following files will be created the restart file named tri rst the plot file named tri plt the lost photon trajectory file named tri st the absorption exchange factor files named miS5run the trajectory file if required named fri trc the output file named tri out and the leaks file named tri lks 40 9 UNIX BATCH EXECUTION USING SCRIPTS This section describes the use of a UNIX shell script to submit multiple runs to be executed sequentially This has the advantage of running only one job at a time thereby avoiding the over head involved with swapping jobs in memory in and out of the CPU our tests have shown that the overhead under UNIX in so doing is prohibitively large The shell script in Figure 9 1 is an exam ple which runs LSMONTE three times for three separate problems input files In this example line one executes LSMONTE and redirects standard output to the file run The second line causes the script
7. The only difference in these material types is that for type 1 all zeros are written into the row of the exchange number matrix while for type 2 a single 1 is written into the diagonal position of the row of exchange number matrix and Table 2 1 Material Type Emission Specifications MTYPE Material Emission 2 No emission Fj 1 all other Fj 0 written 1 No emission all Fj 0 written 0 Emission in 8 according to e 0 IB 1 Beam emission in direction EX EY EZ 2 Emission according to function fen in sub routine getang all other elements in that row are zero To effect a plane of symmetry a material type of 1 or 2 should be selected and the surface interaction curves should all be constants at a value of zero but with a specular reflectance of 1 Material type 0 is the default material type where emission occurs randomly in and is distributed in O according to 8 for each band Ordinarily material types of O are used for all materials except planes of symmetry A material type of 1 specifies beam or collimated emission in a constant direction It is typically used to model beam solar radiation incident from the direction of the sun or other col limated radiation such as may emanate from a laser or other optically emitting device The emis sion occurs directly in global coordinates that are specified during input A material type of 2 causes emission to occur as specified i
8. The seventh subsection is next on debugging information gen erated by the program This is followed by the eighth subsection on the restart capability whereby a run may proceed from a previously calculated state The chapter concludes with a discussion of the pseudo random number generator 2 1 Nodes The description of the geometry of the radiation enclosure begins with the specification of the nodes also called nodal points of the enclosure A node is a point in three dimensional space defined by three coordinates in a Cartesian coordinate system X Y Z as depicted in Figure 2 1 Each node N in the enclosure is assigned a node number which must be positive and a member of the closed full set Ne 7 NUMNP where NUMNP is the total number of nodes for the problem Once the nodes of the enclosure have been specified radiating surfaces can be defined by specify ing assemblages of nodal points Section 3 3 defines nodal input AZ Node N X Y Z 5 F Figure 2 1 Global Coordinate System 2 2 Surfaces Radiating surfaces defined in three dimensions consist of planar quadrilaterals or triangles and are defined by specifying 4 nodal points If four distinct points are specified then the surface is a generalized quadrilateral as shown in Figure 2 2 a If it is desired to use triangular surfaces then the last two node numbers and only the last two node numbers must be identical as shown in Figure 2 2 b Two caveats apply h
9. after the second run with an additional 100 000 photons emitted per surface or 200 000 totat pho tons emitted per surface is 1 J2 times the error from the initial run with 100 000 photons emitted per surface 6 2 Output During First Execution of File box in pburns 1 Ismonte KKKKKK 1smonte KKKKKK Enter prefix for disk files 20 characters or less input file MUST have extension in box Processing the control cards subroutine ccards run til LSMONTE Revision tle GROUP 1 TI BLACK CUBE FILE BOX IN Processing the node input Reading the surface input Calculating surface quant Processing t Processing the ma Processing the ma Creating mat Calculating the inverse CDFs Setting up the nij and crh 1 0 the wavelengt terial terial Date 2000 12 04 23 09 40 t subroutine nodin t subroutine surfin tities subroutine surfcalc h input subroutine wavin property input subroutine matin curve input subroutine curvin terial property sets subroutine matcalc subroutine cumdis files subroutine nijcrhset Creating a grid for the geometry subroutine gridcalc Finding t Creating Creating the leaks 1ks the MPLOT plt he surfaces in the grid cells subroutine seging 3 file subroutine lksfile 3 file subroutine pltf
10. could be significantly non coplanar or defined with three nodes colinear and indicates that the surface should be redefined by the user usually by partitioning it into smaller quadrilaterals or triangles If the difference in areas exceeds a specified tolerance AREATOL a warning message is printed The range of acceptable values is 1 E 20 lt AREATOL lt 0 1 If a value outside of this range is entered AREATOL is set to the default value of 0 0001 3 2 4 Card 4 toggles Cols Format Entry Notes Output print control code IPRINT I as follows 1 1 Il IPRINT 1 exchange fractions written to output file 2 2 Il IPRINT 2 lost photons written to output file 3 3 Il IPRINT 3 grid information written to output file 4 4 Il IPRINT 4 complete material property information written 5 to output file 5 n IPRINT S unused at present 21 6 Il Data check code IDATA 6 IDATA 0 Normal execution exchange factors are calculated or IDATA 1 Data check only exchange factors are not calculated 7 Il Trajectory control code ITRACES 7 ITRACES 1 Trajectory information written to disk file trc extension or ITRACES 0 Trajectory information not written to disk file DEFAULT ITRACES 0 8 Il Trajectory control code IRESTART 8 IRESTART 1 Restart is done IRESTART 0 No restart is done DEFAULT IRESTART 0 Notes In general the information is printed if IPRINT I 1 and is not if IPRINTO 0
11. file of extension trc which may be subsequently read and plotted by the program MPLOT This feature is useful in obtaining a feel for the underlying physical processes and to ascertain that the simulation is pro ceeding as planned There is a copious amount of information written to the output file during the exercise of this option so it is suggested that the total number of photons emitted per surface be 1 000 or fewer For more information the reader is urged to consult the MPLOT documentation Burns 2000 2 8 Restart Capability The code has been designed to be restarted from a previously computed state For example the code may albeit rarely crash during execution for any of a host of reasons Alternatively the code may run to completion and subsequent examination of the answers indicates that they are not sufficiently accurate In either case it is desirable to begin a new simulation from the last avail able state so as to take advantage of previous work This prevents waste of computer resources in recomputing information already available A simulation may be restarted multiple times until the desired level of accuracy is attained To effect this the current state of the solution must periodically be written to disk so that it will be available for a restart run The information is written in block matrix form a block of rows at a time to the disk file of suffix nij A crash file of suffix crh allowi
12. loop NPHT is the photon emission number multiplier that is input for every surface Thus in each band for each surface NPHT NPHTON number of photons are emitted per photon conver gence loop In a restart run new photons are emitted thus if this is the second restart run and NPHTON base photons were emitted in each of the previous two runs an additional NPHTON base photons are emitted bringing the total to 3 NPHTON 2 The total number of reflections before a run is aborted will be 1 greater than NREFS NWARNS on any surface 3 Occasionally due to precision problems a photon is lost i e no receiving surface is found for a given photon path This input variable specifies the number of such occurrences on any surface before the run is aborted 4 NPLOOPS is the maximum number of full surface photon convergence loops In each full sur face emission for each band NPHT NPHOTON photons are emitted If convergence to the specified tolerance for the surface ERRMAX N see section 3 4 is not attained within NPLOOPS full surface emissions then a warning is printed to the screen and execution contin ues with the next surface If 0 is entered for NPLOOPS only one photon loop will be executed 5 ERRDEF is the default tolerance for convergence of the surface exchange fractions This may be overridden for a particular surface s during surface input as described in section 3 4 3 2 3 Card 3 run control Cols Format Entry No
13. to be read for that material property For example inputting 2 0 indicates that material property curve 2 will be read for this material property Curve numbers must be between 1 and NCURVE input on control card 1 3 Note the special handling of the default value 0 Values greater than zero are used asis Ifa value of 0 is read or the input is blank causing a value of 0 to be read then the default value of 1 is used Any negative value input causes a value of O to be used 4 Diffuse reflection or transmission occurs distributed in cone angle 8 according to the cosine power r in proportion to cos 8 sin 0 dO Values of r greater than one result in biasing the distribution toward the normal whereas values of r less than one result in biasing the distri bution toward the grazing angle 5 Values of r different from 1 have been observed to result in errors in reciprocity so the user is strongly encouraged to consider this when selecting values of r different from one 6 Lambertian behavior is achieved by using r 1 the recommended value 3 7 Material Property Curve Input Material property curves are input as specified by material Material property curves are input in sequential order for the number of material property curves specified in the material input 26 REPEAT CARDS 1 to NP 1 FOR EVERY CURVE INPUT CARD 1 curve information Cols Format Entry Note 1 5 I5 Curve number NC 1 6 10 I5 Num
14. 0 is modeled as proportional to cos 8 Usually r is picked as 1 to model dif fuse Lambertian behavior Electromagnetic theory indicates that r is usually lt 1 for metals and r is usually gt 1 for nonmetals An isotropic distribution in 6 in outgoing energy is obtained by setting r 0 The effect of r on the 0 distribution is shown in Figure 2 7 This figure displays cos as a function of 8 The curves have been normalized to their areas The normalization is such that for r 0 isotropic distribution the curve has the value of 1 at all angles It should be noted that a value of r other than 1 can cause the reciprocity relation of equations 1 5 and 1 6 to be violated there fore use of anything other than r 1 should be approached with extreme circumspection 11 o 8 a 0 A o 9 Incident Angle degrees bo cid Figure 2 6 Material Properties vs Incident Cone Angle Figure 2 7 Cosine Power Dependence of Emission as a Function of r and 8 The present material model provides for the specification of separate r s for diffuse reflec tance and transmittance for each material see section 3 6 2 5 Grid Tracing To reduce CPU time tracing photons a logical grid is placed over the geometry and each photon is traced through these logical grid cells until the first intersection point is encountered This 12 situation is depicted in 2 D in Figure 2 8 The algorithm was suggested in 1986 by Dave Margolies of
15. 3 3 Wavelength Band A agate E E sacs wits 24 36 Material IU ir a a E 24 3 7 Material Property Curve LPI AA eae i i 26 EXCHANGE MATRIX OUTPUT TEE ii 28 O O E E E 28 4 2 Output Format for Exchange Matrix Files ooooonnnconnnocccnoncccnnncccnnnccononcnononcncnnnnnnnnncnonnnos 28 SAMPER AN PUT e e Lo 30 Dik General Descrip A ceci 30 5 2 3D BOK oe 30 s PROGRAM EXECUTION cionado a os 32 6 1 Execution of Fle Boxin li dis 32 6 2 Output During Execution of File boxin coooocccnnncccnnnccconnnnnnnnnnonnnnononcnonnncnonnnccnonnncnnnnnnos 33 6 3 Output During Restart Execution of File boxin sessessssssssssessesssessseresseeesseesseesseessee 34 6 4 Execution of Other Input Files co ss ceivas ices Gosueae scansdaed oageia ta eceteatuemeeecianatac eee 36 IMPLEMENTACION idad 37 PL FC OMI VIDE ARS i ea E cn usc cles ace Beale ates Te ua odes E eas 37 7 2 Common Blocks Parameter Statements and the Size of Arrays o oooococcccconcccnoncnonannnnnnnos 37 Ted r TSC USO aai a Aine Mt N a a a a E abet te tat te 38 8 FILES AND FILE USAGE A i A EA 39 Sal Specifying File NAMES cia iii 39 9 UNIX BATCH EXECUTION USING SCRIPTS escisiones orinar dni 41 REFERENCES ii 42 Tables Table 1 1 Run times on a 233 MHz Pentium II Processor ccooconoconocononcnonnnonanononcnonccnnncnnnc ron cnn ncnnnos 5 Table 2 1 Material Type Emission Specifications sessssssssssesseesseesseessettsstessresseesseesssressresseessee 9 Table 2 2 Accuracy in E
16. 3 for more details on defining the initial seed Each initial seed creates a different sequence of random numbers so different answers are obtained However if enough photons are emitted to achieve statistical convergence then the answers whatever the initial seed will be identical to within a statistical tolerance It is not possible to traverse the same sequence of random numbers after a restart run involving emission from more than one surface Thus if a run is done with 20 000 photons emitted from each surface the answers will be different than if an initial run is done with 10 000 photons per surface followed by a restart from this final state where 10 000 additional photons are to be emitted However the comments above pertaining to convergence do apply If enough photons are emitted then the answers will converge to within a statistical tolerance to a final state independent of the order of emissions 18 3 INPUT DECK The following pages contain the instructions necessary to enable the user to construct the input file data deck required by the codes Default values are used if the input file contains blanks read as zero by FORTRAN Input lines are limited to 80 columns in width 3 1 Title Card Cols Format Entry Note 1 48 A48 Heading to appear on output 1 Note 1 Cards with the character amp in column 1 can be placed anywhere in the data deck for use as comment cards or as spaces All such cards
17. 985 A Current View of Random Number Generators Computing Science and Statistics Proceedings of the xvi Symposium on the Interface Billard ed Elsevier Science Publishers B V North Holland pp 3 10 Mascagni M Cuccaro S Pryor D and Robinson M 1995 A Fast High quality and Repro ducible Parallel Lagged Fibonacci Pseudorandom Number Generator J Computational Phys ics 119 pp 211 219 McHugh J 1995 Daylighting Design via Monte Carlo M S Thesis Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 McHugh J Hittle D and Burns P May 1998 The Energy Impact of Daylighting in an Ultra low Energy Building ASHRAE Journal pp 31 35 Pryor Daniel V and Burns Patrick J July 21 25 1986 A Parallel Monte Carlo Model for Radi ative Heat Transfer presented at the 1986 SIAM Meeting Boston MA Pryor D V Cuccaro S A Mascagni M and Robinson M L 1994 Implementation of a Por table and Reproducible Parallel Random Number Generator Proceedings Supercomputing 94 IEEE Computer Society Press Los Alamitos CA pp 311 319 Shapiro Arthur B 1985 TOPAZ3D A Three Dimensional Finite Element Heat Transfer Code Lawrence Livermore National Laboratory UCID 20484 Schweitzer Roland McHugh Jon Burns Patrick J and Zeeb Charles N 1993 Daylighting design via Monte Carlo with a corresponding scientific visualization P
18. USER S MANUAL for LSMONTE A Three dimensional Radiative Heat Transfer Analysis Computer Code Version 1 0 December 04 2000 by Charles N Zeeb and Patrick J Burns Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 Charles Zeeb ColoState EDU and Patrick Burns ColoState EDU 970 491 7479 and 970 491 5778 http www colostate edu pburns monte html Livermore Software Technology Corporation 7374 Las Positas Road Livermore CA 94550 http www 1stc com Table of Contents INTRODUCTION ici 1 tli Background ii A e E a E ERT aS 1 L2 Phe oretieal Fermi att Oi a a A O aaa 1 Neti View Factors aeea O 3 4 Implementation eaea cess wis ok ceca a hy aes eat a NN 3 1 5 Performance and Run Times viii aiii 4 COMPUTER CODE BACKGROUND inscriure 6 Ba A sasia Se Seal canes alter A hacen hart tiaa a banat sl tect tas 6 E a IO AETA acun edt casas cautious dosed E EE A E EEEE E E 6 Zed S rface CONC ALE ALIN eae e a E A ge we geen a S 7 24 Material Properties a a E a E I R E 8 25 Grid Traint sesu ks daca gustan o As 12 2 6 Number of Photons Convergence and Accuracy s ssessssssesssessersseseseresseeesseesseesseessee 13 2 7 Debugging Leak Checking Lost Photons and Trajectory Output Capabilities 15 2 8 Restart Capability uni i 17 2 9 Psetido Random NUDE AAA 17 INPUT DECK a a ee 19 Slt Title Card is 19 3 2 o COMO EAS O dos 19 Sed o E E E 23 3 4 Surface Data veian is 23
19. are ignored 3 2 Control Cards 3 2 1 Card 1 physical parameters Cols Format Entry Notes 1 10 110 Number of nodal points NUMNP 11 20 110 Number of surfaces NSURF 21 25 IS Number of materials NUMMAT 1 26 30 I5 Number of wavelength bands NBANDS 1 DEFAULT NBANDS 1 31 35 IS Number of material curves NCURVE 2 Notes 1 Radiative properties are defined as constant within individual wavelength bands 2 Material properties may be input as either constant within a wavelength band or varying by means of a curve See section 3 7 for additional information on the input of material property curves 3 2 2 Card 2 photon control Cols Format Entry Notes 1 10 110 Number of photons emitted per band per surface per emission loop NPHTON 1 11 15 I5 Maximum number of reflections allowed per photon before a warning is issued NREFS 2 DEFAULT NREFS 100 16 20 I5 Maximum number of warnings per surface before the run is aborted NWARNS 2 DEFAULT NWARNS 100 21 25 I5 Maximum number of lost photons per surface NLOST 3 DEFAULT NLOST 100 19 26 30 I5 Maximum number of photon convergence loops NPLOOPS 4 5 DEFAULT NPLOOPS 1 71 80 F10 0 Default convergence tolerance ERRDEF 4 5 DEFAULT ERRDEF 1 x 10 Note ERRDFF is entered at the end of the line not immediately after NPLOOPS Notes 1 NPHTON is the base number of photons per surface per wavelength band per photon
20. ber of points to be input for this curve NP 2 11 50 A40 Name of curve e g Window Specular Transmittance CNAME CARDS 2 to NP 1 angular input Cols Format Entry Note 1 10 E10 0 Cone angle 6 2 11 20 E10 0 Curve value Notes 1 Curves must be input for all negative specifications in material input NCURVE total curves must be input The names of the curves are not used anywhere else in the code 2 NP number of cards with angular data must be input for the curve Angles must be input in increasing order All curves must have values input at angles O and 90 degrees All material property values must be in the domain 0 1 27 4 EXCHANGE MATRIX OUTPUT FILE 4 1 General Description The exchange matrix files contain all of the information necessary to solve for the net radi ative exchange as described in Chapter 1 A single binary direct access file named by the user is generated for the exchange matri ces The file is direct access with record size 4 N SURF bytes Experience is that for large prob lems writing an ASCII file is prohibitively time consuming Therefore to reduce the time it takes to write the file and to conserve disk space binary files are much smaller than ASCH files a binary file is written This file is not in general transportable to other systems so that the thermal balance code must be run on the same system as the exchange matrix file is resident Finally the information in the file is not a
21. ble to be viewed by the user if one wishes to view the exchange fac tors one should set the print flag PRINT 1 in column 1 of control card 4 to 1 so that the exchange factors will be printed in the output file However the user is cautioned that the time it takes to write this information may be prohibitive for large problems over about 5 000 surfaces and one band The information written to the file follows The header contains control information and the surface areas This is followed by the surface emittances for all wavelength bands ordered from lowest band to highest Next are the exchange number matrices one for each band ordered from lowest band to highest The file is concluded with the wavelength bands 4 2 Output Format for Exchange Matrix Files The file of exchange numbers is a constant record length direct access binary file All quantities are 32 bit Integers are generally stored as binary in powers of 2 and reals are generally stored in IEEE standard 32 bit floating point format 4 2 1 Header Card One record of length NSURF Format Entry Note Integer 4 Geometry code NDIM 1 Integer 4 Number of surfaces NSURF Integer 4 Factor code FACT 2 Integer 4 Number of wavelength bands NBANDS Integer 4 Number of materials NUMMAT 3 Notes 1 NDIM is 3 denoting 3 dimensional results 2 IFACT is 2 indicating that the file contains exchange numbers as opposed to view factors 3 The number of materials is prov
22. e Here the user types the prefix of the input file which MUST have the extension in In this case the file is box in and the user enters box If the program cannot find the input file this error is trapped by the code and a diagnostic is printed Additional detail on the files used by the codes is given in Chapter 8 The program proceeds with reading of the input file The heading is printed along with the version number here 1 0 the date of last modification here 2000 12 04 or December 04 2000 Next the control portion of the input is read This establishes the numbers of nodes surfaces sometimes referred to as elements or surface elements wavelength bands materials and grids which are to be read by succeeding subroutines Then the input subroutines are executed one by one As each subroutine is entered information is printed concerning the processing being done followed by the name of the subroutine in parentheses This assists in debugging input files For example if the program crashes after the message Processing the node input subroutine nodin is printed there is almost certainly a problem with the nodal input or possibly the card images have been entered out of order The successful completion of the entire input phase is then indicated by the message input phase complete The solution phase occurs next After the specified number of full surface emission loops for each surface i
23. e increases linearly with number of photons For moderate problems about 1 000 surfaces it has been found that on the order of 100 000 photons per surface are required to achieve exchange factors accurate to within about one percent It is typical to observe convergence in a particular exchange factor as shown in Figure 2 9 The user is cautioned that false convergence may be indicated when compar ing two values on the curve as shown It is therefore wise to check the entire matrix of exchange factors for consistency reciprocity at several numbers of photons 13 alse Convergence Exchange Factor Convergence 1 10 10 10 10 10 10 Number of Photon Emissions Figure 2 9 Convergence vs Number of Photon Emissions To estimate the number of photons required to achieve a given level of accuracy Table 2 2 is provided The table gives for each exchange fraction F ip the number of photons Ny which Table 2 2 Accuracy in Exchange Fractions Exchange Level of Accuracy Fraction 1 2 3 10 50 for 38 377 584 9 594 396 1 535 103 383 776 15 351 10 3 803 184 950 796 152 127 38 032 1 521 Tik 345 744 86 436 13 830 3 457 138 must be emitted from surface i to achieve 95 confidence that the exchange fraction is within 1 2 5 10 and 50 of the exact answer The numbers of photon emissions per surface are cal culated from the formula for confidence intervals C for the exchange fraction from surface i to surface j
24. e subscripts i and j to denote the emitting and absorbing surfaces respectively and the superscript k to denote the wavelength band it can be shown that do EN Ak Qij P oT A 1 1 l where i j one way rate of radiative heat transfer emitted from surface i and absorbed by surface jin wavelength band k W emittance of surface i in wavelength band k number of photons emitted in wavelength band k from surface i and absorbed by sur face j total number of photons emitted in wavelength band k from surface i Stefan Boltzman constant 5 669x10 w Ae K absolute temperature of surface i K fraction of the blackbody energy of surface i in wavelength band k area of surface i m PS A 2 Ze k The ordinary definitions of the exchange factor Es and the exchange fraction F ij are as follows nt ae q ga 1 2 ij jik i The following rules apply to these quantities k k YE amp 1 3 J or k ZF 1 4 j Equations 1 3 and 1 4 express conservation of energy photons since all photons must be absorbed by a surface Given that there must be zero net heat flow between isothermal surfaces the second law of thermodynamics entropy principle follows from equation 1 1 as k k Ex A EA 15 or Arka Fa 1 6 iij yo ge The net radiative exchange in wavelength band k from surface i to surface j is then kok k kA Oj EA Ts vu 1 7 and 3 k kk k k_4
25. ed to simulated some special cases of other transport problems in enclosures If the Knudsen number is much less than 1 rarefied gas dynamics problems can be simulated a vacuum vessel Also some simple cases of molecular sputtering in an enclosure can be simulated 1 5 Performance and Run Times Monte Carlo has been termed the method of last resort as the perception used to be that run times are very long This viewpoint is no longer as relevant as it used to be Hardware is now much faster larger problems can be done in a reasonable amount of time LSMONTE has been highly optimized for performance in a variety of ways First a very efficient photon tracing algo rithm is employed Secondly all quantities for which it is appropriate are precomputed during the input phase to prevent repetitive computation during the solution phase Thirdly the grid tracing algorithm causes the total photon tracing time to scale in proportion to the number of surfaces to the power 1 5 rather than in proportion to the number of surfaces to the power 2 As the number of surfaces grows this represents a huge savings in solution time Significant time is also spent emitting and reflecting photons making the overall solution time scale approximately in propor tion to the number of surfaces The Monte Carlo method has the capability to model very sophisticated geometries and material properties not possible with other methods Also the Monte Carlo method i
26. eded a message detailing the parameters for which storage is insufficient is printed together with the allowable value and execution terminates If storage is exceeded various possibilities for remedi ation exist Storage exceeded for nodes surfaces wavelength bands or materials Unless the problem size can be reduced for example by removing surfaces and or nodes that do not participate in radi ation or reformulating the problem so as to reduce the numbers of nodes surfaces and or materials the storage parameters must be increased the code recompiled and the problem rerun Storage exceeded for grid parameters If iseg or igrd are not sufficiently large an easy fix is to reduce the size of the grid see section 3 2 6 to acceptable limits and rerun the problem recompilation is not required However another possible fix is to increase either iseg or igrd or both recompile the code and rerun the problem As iseg represents the total number of surfaces contained in the grid it is dependent upon the number of surfaces the grid size and the specific geometry of the problem The code is designed to indicate the total number of segments required even if this is above the allotted storage 7 3 Precision The code is compiled using 64 bit 8 byte floating point precision It is desirable to use 64 bit precision as the specification of co planar surfaces is particularly susceptible to precision errors and using 64 bit precision res
27. ee section 3 2 2 To be used with MPLOT Burns 2000 to plot particle trajectories 10 fn out Output file Contains echo of input and other information as determined by IPRINT See section 3 2 4 12 fn Iks Leaks file To be used with MPLOT Burns 2000 to identify potential leaks Files for unit numbers 1 3 to 7 9 10 and 12 are ASCII files and may be read and printed Files for unit numbers 2 and 8 are binary files and must be read by other programs For example unit 2 is used only by the LSMONTE code Unit 8 is written by LSMONTE and read by LSDYNA The UNIX utility od octal dump may be used to examine binary files do a man on od for instruc tions 8 1 Specifying File Names LSMONTE must have the names specified for all of the files shown in Table 8 1 This sec tion explains the naming conventions and methods of specifying these file names There are two methods of specifying the file names default and command line If no name s are specified on the command line the code will query the user via the console for a base 39 file name fn This base name is used as the prefix for all files in the run see above The com mand line method of specifying the file names allows the user more flexibility in defining file names Each file name can be specified independently according to the conventions in Table 8 2 Table 8 2 Command Line File Control File name to be specified Flag on co
28. er development However smoothing exchange factors is not required its only effects are to improve the accuracy of the exchange factors and to reduce the size of the exchange factor matrix Fundamentally the geometry and the material properties are the only quantities necessary to establish the exchange factors The exchange factors result from the interaction between the geometry and the material properties in a complex fashion and are unique to a particular geometry material property combination Therefore it is not possible to extend a set of exchange factors cal culated for a particular geometry material property combination to another geometry material property combination even if only the geometry or only the material properties vary After any changes the problem must be rerun However if view factors are calculated all properties black arbitrary diffuse reflectances may be included in the thermal analysis code since view factors are dependent on geometry alone Note that diffuse exchange with finite reflectances calculated from the present codes will yield slightly different answers than those obtained using the radiosity irra diation approach as the assumption in the radiosity approach is uniform radiosity irradiation over each surface which is not so for the present code Specularity or material property dependence on incident angle may not be modelled using view factors In addition to radiation exchange this code can also be us
29. ere none of the interior angles may exceed 180 i e no con cave corners are permitted and the four nodes should be coplanar to within a small tolerance This tolerance can be set and surfaces which exceed this tolerance are flagged with warnings The code will run even if quadrilaterals are non coplanar as every quadrilateral is split into two trian gles which by definition are planar However the user is cautioned that quadrilaterals are split arbi trarily along the line from N to N3 and the geometry simulated may vary from that intended unless the quadrilaterals are indeed coplanar to within a small tolerance See section 3 2 3 for more details N 3 N N Ny b 3 D Triangle 1 a 3 D Quadrilateral Figure 2 2 Radiating Surface Geometries It is very important to note that the outward normal n of the radiating surface is always defined as pointing into the enclosure The outward normal for both types of surfaces is defined consistent with the right hand rule i e if the fingers of the right hand are curled in the direction of increasing nodal point number N 1 gt N A gt then the thumb of the right hand indicates the direction of the outward normal This results in a counterclockwise convention for nodal point numbering when viewing the radiating side of the surface from above The back of the surface opposite the surface normal is transparent as far as the code is concerned and a leak will result from
30. es balanced against CPU usage A rough guess of the size of the exchange fractions is the reciprocal of the number of sur faces in the input file This yields the average exchange fraction size since the sum of any row of the exchange fraction matrix is 1 The number of photons required to be emitted to achieve an average level of accuracy may then be estimated from equation 2 2 or obtained from Table 2 2 through interpolation or extrapolation Errors in the temperatures calculated from radiative flux balances are smaller than errors in the exchange fractions due to the fourth root dependence of temperature upon radiative flux For small errors one may expect the errors in temperatures to be about one fourth of the errors in fluxes Emitting an equal number of photons from each surface may result in a waste of computer time since some surfaces contribute little to the radiative exchange A better approach would be to apportion the numbers of emissions to each surface based upon its estimated power output This is an approach which requires judgement gained through experience with specific geometries since the power outputs are generally not known a priori In any case the above approach provides a potentiometer which can be used judiciously to adjust solution accuracy Section 3 2 2 provides the details of the input for photon control and accuracy 2 7 Debugging Leak Checking Lost Photons and Trajectory Output Capa bilit
31. iative exchange in passive solar enclosures Maltby et al 1986 application to the Laser Isotope Separation LIS process Burns and Pryor 1989 Additional publications of interest are Burns et al 1990 Maltby and Burns 1991 Burns et al 1992 Schweitzer et al 1993 Burns and Pryor 1996 Burns and Pryor 1999 and Zeeb and Burns 1999 A number of related codes are available in the public domain These include the graphical post processor MPLOT Burns 2000 which plots geometries and material properties from LSMONTE MONT2D Maltby et al 1994 a Monte Carlo photon tracing code similar to LSMONTE but for two dimensional Cartesian and axisymmetric geometries MONT3V a code that simulates rarefied as dynamics with binary collisions Dolaghan 1991 MONT3E Crockett et al 1990 a code for simulating electron transport in three dimensions in the presence of a spa tially varying magnetic field and SPUT3D Dolaghan 1996 a code for simulating molecular redistribution during sputtering in three dimensional enclosures The same technique has also been used to simulate daylighting in building geometries McHugh et al 1998 McHugh 1995 Infor mation on these codes may be obtained from the authors of this manual 1 2 Theoretical Formulation The present computer codes are formulated in the Monte Carlo style where a large number of photons are emitted from each surface and traced until each is absorbed by another surface Using th
32. ided simply as a check it is not used in the calculation of the radiative exchange 28 4 2 2 Surface Areas One record of length NSURF the number of surfaces Format Entry Real 4 Surface areas from 1 to NSURF 4 2 3 Surface Emittances Data for Each Wavelength Band Repeated for each wavelength band from k 1 to NBANDS For every wavelength band One record of length NSURF Format Entry Note Real 4 Surface average emittances e from 1 to NSURF 1 Notes 1 The surface emittances are averaged over direction cone angle i e the values are hemispher ical emittances 4 2 4 Photon Exchange Number Matrix Data for Each Wavelength Band Repeated for each wavelength band from k 1 to NBANDS For every wavelength band NSURF records each of length NSURF Numbers of absorbed photons by surface i for all j Format Entry Note Integer 4 Numbers of absorbed photons 1 2 Notes 1 The data are presented by row i for all columns j That is the first row of numbers N 1 NSURF is written then row 2 is written etc 2 These files contain the full exchange matrices The program SMOOTH Dolaghan et al 1992 is being updated by Zeeb to process these files into an upper triangle including the diagonal of numbers of photons which have been smoothed to obey reciprocity 4 2 5 Wavelength Breakpoints For as many records as needed each of length NSURF Wavelength breakpoints in micrometers Format Entry Note Real 4 Wavelength breakpoints
33. ies The code is equipped to generate information useful in debugging input files A file con taining all the information in the input file geometry and material properties is written to disk dur ing the input phase of extension p t This plot file may be used with the stand alone graphics program MPLOT Burns 2000 to display the geometry and the material property curves An error in the specification of the geometry often results in a leak or hole in the enclo sure through which photons may be transmitted and lost Leaks may be caused due to disjoint surfaces missing surfaces incorrect node numbering on a surface misplaced nodal points or 15 insufficient precision in specifying coordinates During the input phase the geometry is checked for leaks and results are written to the output file An ASCII file of potential leaks of extension lks identified by type severity of leak is written for 3 D geometries This file may be used with MPLOT to highlight surfaces and sides of surfaces which have been identified as potential prob lems or leaks The three types of errors identified are Error 1 Reversed Edge This error occurs when two surfaces share the same edge If the surfaces are not defined so that both their surface normals are pointing inward or outward a reversed edge occurs An example is given in Figure 2 10 In Figure 2 10 a the edge between the two surfaces is correct and both surfaces have normal
34. ile Calculating the 2D bounding planes subroutine bplane2d input phase complete 33 band not converged not converged not converged not converged not converged not converged normal termination total time solution total time or input phase or solution phase total run time surf iter npht error 1 1 100000 2066E 02 2 100000 2066E 02 3 100000 2066E 02 4 100000 2066E 02 5 100000 2066E 02 6 100000 2066E 02 time log 10000D 01 secs 14000D 02 secs 15000D 02 secs all times measured in clock time total number of phot total number of phot tons lost tons emitted photons per cpu second whole run photons per cpu second solution pase Stop Program terminated pburns 2 seconds 0 60000D 06 40000 000 photons sec 42857 143 photons sec 6 3 Output During Restart Execution of File box in pburns 1 1smonte KkkKKKK JTomonte Enter prefix for disk files 20 characters or less input file MUST have extension in box Processing the control cards subroutine ccards run title GROUP 1 TI EST 1 BLACK CUBE FILE BOX IN LSMONTE Revision 1 0 Date 2000 12 04 23 09 40 Processing the node input subrou
35. in wavelength band k F 7 derived by Maltby Maltby 1990 2 2 where Z is taken from the standard normal tables and is 1 96 for 95 confidence Equation 2 2 14 yields the fractional accuracy in F k n b 100 time this value yields the percent accuracy LSMONTE is formulated to attain a specified accuracy for each row i of the exchange factor matrix The program is constructed to loop over successive emissions from each surface i if a preset accuracy tolerance is not met after a full surface emission To explain this we first note that equa tion 2 2 provides the confidence interval for only element ij of the exchange fraction matrix when emitting additional photons actually increases the accuracy of all elements in row 7 Equation 2 2 is modified to account for this with the rationale that exchange fractions affect the accuracy proportional to their size Thus we weight each confidence interval by its exchange fraction sum and then average by dividing this amount by the total number of sides N to yield the ad hoc row confidence factor for row i C ms 2 3 If the confidence as a fraction for emissions from surface i is not met after a full surface emission then the program continues to perform full surface emissions until either the specified confidence is met or a maximum number of full surface emissions have occurred This feature can be used with the restart option to effect a specified accuracy for the surfac
36. incor rect node numbering Each radiating surface is assigned a material number and all material properties are inde pendent of spatial position on a single surface Referring to Figure 2 3 one observes the local primed coordinate system with vertex at N and axes as shown Photons are emitted randomly from points on a surface a sufficient number of photons must be emitted from each surface to achieve random behavior for emission Section 3 4 defines surface input 2 3 Surface Concatenation Very early versions of the code named MONT3D permitted surface concatenation Cur rent versions do not due to the limitations associated with error checking and restart it is impossi ble to recover restart information from concatenated information as some information is lost during the concatenation process If it is desired concatenation can be done by a posteriori by operating on the exchange factor matrices but this requires manual manipulation by the user Z Y Figure 2 3 Global Local Coordinate Systems 2 4 Material Properties Material properties are defined and allocated to surfaces by specifying a material property for each surface Multiple surfaces may have the same material type When specifying material properties three items must be defined material type material emission and surface interaction curves Material types are presented in section 2 4 1 material emission is presented in section 2 4 2 and material
37. loop If NPHT is negative no photons will be emitted from the surface If NPHT 0 the base number of photons per surface NPHOTON will be emitted for each surface photon loop i e if NPHT is read as 0 NPHT is set to 1 4 Similar to INC above For each missing surface i 1 1 to NMISS generated 1 INCP extra photons are added to NPHT NPHTON 5 This is used as explained in section 2 6 to loop over full surface emissions until either the spec ified number of full surface emissions have occurred or convergence to this tolerance C defined in equation 2 3 is achieved whichever comes first 6 If no value is input or a value of 0 is read then this defaults to the global ERRDEF value input as described in section 3 2 2 3 5 Wavelength Band Data CARDS 1 to NBANDS 1 8 Condition NBANDS gt 1 omit otherwise Cols Format Entry Note 1 10 E10 0 Wave breakpoint number 2 micrometers 1 11 20 E10 0 Wave breakpoint number 3 micrometers 1 21 30 E10 0 Wave breakpoint number 4 micrometers 1 71 80 E10 0 Wave breakpoint number 8 micrometers 1 2 Notes 1 The first and last wave breakpoints are assumed to be 0 0 and 1 x 1019 in micrometers and should not be input Only breakpoints between 0 and should be input 2 No more than eight breakpoints should be input per card The total number of cards should be NBANDS 1 8 3 6 Material Input Material input cards are input by band for each material in order Fo
38. lost 0 total number of photons emitted 60000D 06 photons per cpu second whole run 40000 000 photons sec photons per cpu second solution pase 42857 143 photons sec Stop Program terminated 6 4 Execution of Other Input Files Execution of other input files produces similar output 36 7 IMPLEMENTATION The code runs on Macintosh systems Windows systems and various Unix systems selected with options in a Unix make file The system specific functions that exist in the code are the calls to the elapsed CPU time used only for performance metering calls to the time and date used to initialize the random number generator if bypassed the user may supply a seed for the ran dom number generator and calls to implement command line arguments A version may be com piled without any of these options that runs on any Unix system The code is almost ANSI standard Fortran 77 except for the bitwise intrinsic functions used in the random number generator We have yet to find a modern compiler without these functions Binary executable are available via ftp from the Livermore Software Technology Corpora tion www Istc com Versions exist for Windows Macintosh Sun HP IBM and generic Unix sys tems such as some compilers that run under linux The first section below includes details on compilation The second section contains infor mation on memory usage and storage The third and final section in this chapter con
39. mmand line Plot file name p P p or P Lost photon trajectory file name m M m or M Input file name 1 I i or I Absorption exchange factor file name e E e or E Trajectory file name t T t or T Output file name 0 O o or O Leaks file name 1 L l or L Family file name f F f of F Several conventions bear emphasizing If even one file name is specified on the command line the user will not be queried during execution for a filename Unless the family file name is entered at a minimum the names of the input file output file and exchange factor file must be specified independently on the command line with the other files deriving their base name from the input file name If the foption is used any file not explicitly specified will assume the naming convention indicated in Table 8 1 Those file names explicitly specified will override this default The maximum length of any base file name is 30 characters To clarify the command line conventions the following examples are offered Example 1 lsmonte i alakazam Okaboom e ardvark w M toasted The input file named alakazam must exist The following files will be created the restart file named alakazam rst the plot file named alakazam plt the lost photon trajectory file named toasted the absorption exchange factor file named ardvark the trajectory file if required named alakazam trc the output file named kaboom
40. n subroutine getang This is a very special material type that requires coding and compilation and should only be used by the sophisticated user when no other way of accomplishing the desired function exists 2 4 3 Surface Interactions and Material Property Curves The material properties curves that define a photon s interaction with a surface are defined in terms of a local spherical coordinate system Figure 2 4 defines the cone or polar angle 8 and the azimuthal or equatorial angle Q Photon surface material interactions of five types may occur Figure 2 5 a depicts a spec ular transmission whereby a photon passes straight through a specularly transmitting surface with no change in direction Figure 2 5 b depicts a diffuse transmission where the photon is transmitted but its outgoing direction is uniformly distributed in solid angle weighted by projected surface area This is akin to a diffuse reflection but from the back of the surface Figure 2 5 c depicts a specular mirrorlike reflection where the angle of incidence is the angle of reflection and Figure 2 5 d depicts a diffuse random reflection with an equal probability of reflection into any direction Here again we have exercised editorial license with this statement In truth a dif fuse reflection has an equal probability of reflection in any solid angle weighted by projected sur face area Finally the photon may be absorbed All ma
41. n vary considerably e Operating system The execution speed is dependent upon the operating system particularly the overhead introduced by the operating system For example LSMONTE will run under the linux operating system in about one half the time it runs under the Windows operating system e Compiler The execution speed depends upon the quality of the compiler However most modern compilers are mature and fairly efficient so that the differences in execution speed among compilers may not be that significant e Hardware Execution speed also depends upon hardware especially the Floating Point Unit FPU Different FPU s have different amounts of logic implemented in hardware making them relatively more or less efficient at processing e Amount of Input Output I O Execution speed also depends somewhat upon the amount of I O which is only significant for large files and or small numbers of photons emitted In par ticular writing exchange fractions in ASCII format to the output file can consume significant time for very large problems because the work of writing exchange fractions scales as Surfs while processing time scales as Surfs However the extra work is only significant for very large problems As an example writing the exchange fractions for the third example in Table 1 1 below mtgun in increases the total run time by only 548 secs or 3 5 The toggle for writ ing exchange fractions to the ASCII output file is de
42. ng X component for emission in global coordinates EXE MN IB Outgoing Y component for emission in global coordinates EYE MN IB Outgoing Z component for emission in global coordinates EZE MN IB 25 Notes Notes 1 2 hh A Notes 1 Band data must be input in order from 1 to NBANDS except as noted below 2 If for the first band input IB is set to zero the data input on cards 2 and 3 are taken as constant across all wavelength bands 3 Table 2 1 provides emission types for materials 4 The beam emission components are normalized such that a unit vector is obtained However for beam emission at least one non zero value must be input Thus EX EY EZ input as 1 1 0 is normalized to 0 7071 0 7071 0 CARD 3 band photon disposition one per band grouped with card 2 1 10 E10 0 Specular transmittance ps RHOS MN IB ITH 1 2 11 20 E10 0 Diffuse transmittance pg RHOD MN IB ITH 1 2 21 30 E10 0 Specular reflectance t TAUS MN IB ITH 1 2 31 40 E10 0 Diffuse reflectance tg TAUD MN IB ITH 1 2 41 50 E10 0 r dependence of diffuse reflectance RDIFFR MN IB 3 4 5 6 DEFAULT RDIFFR 1 51 60 E10 0 r dependence of diffuse transmittance RDIFFT MN IB 3 4 5 6 DEFAULT RDIFFT 1 Notes 1 Values must be between 0 and 1 In addition all values must sum up to 1 or less as the comple ment of the sum of these properties is the absorptance 2 Negative values input are taken as the negative of curves
43. ng the code to be restarted from a crash is also periodically written and is deleted if the run completes successfully as it is then unnecessary to effect a restart Section 3 2 3 in the following chapter provides addi tional detail of the control which can be exercised over writing states to the output file 2 9 Pseudo Random Numbers The pseudo random number generator used is a lagged Fibonacci generator The generator is a generalization of shift register sequences described by Golomb 1982 A number of investi gators have examined the properties of the lagged Fibonacci generator and established the condi tions for it to be robust and to generate pseudorandom sequences of high quality Anderson 1990 Brent 1992 Pryor et al 1994 Marsaglia 1985 Mascagni et al 1995 Zeeb and Burns 1997 Burns and Pryor 1999 To obtain good sequences of numbers in particular to pass the birthday spacings test a long generator must be used Brent 1992 To ensure this a 127 long lagged shift register sequence is used in the code yielding uncorrelated non repeating random sequences with a sub period of about 2 x 10 sufficient for virtually any application It is also directly amenable to par 17 allelization The generator uses an array of seeds which are generated using a bitwise binary shift register The initial seed can be specified by the user generated from the current time or set to a default debugging value See section 3 2
44. p NPHIN NWARNS NPLOOPS amp NREFS NLOST amp 2 4 6 8 1 2 4 6 8 2 2 4 6 8 3 2 4 6 8 4 2 4 6 8 5 2 4 6 8 6 2 4 6 8 7 2 4 6 8 8 amp ERRDEE 100000 1 1 e 6 amp NINCR NCPU DEL AREATOL amp INSEED SPLITOL 1 1 amp IPRNT 30 ITOGGLE 10000000 amp amp NGX NGY NGZ 1 1 ES INC amp NODE Ze 0 0 0 0 0 0 10 0 0 0 0 0 0 0 ERRMAX E 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 INM FIL fT CO NPHT INCP NMISS INC 0 00 0 00 0 00 0 00 0 00 0 00 N3 N4 N2 amp SURFACES MATERIAL NAME RDIFFT ri 1Black Surface MTYPE amp MATERTALS amp NMAT RHOS RDIFFR TRANS TRAND RHOD 0 0 0 0 0 0 0 0 31 6 PROGRAM EXECUTION 6 1 Execution of File box in The following details the execution of the code with the file box in The output to the screen has been captured and appears below in section 6 2 The command prompt is pburns n where n is the command number All input from the user is shown bold and italicized The executable file here is called smonte note that most systems are case sensitive and is invoked by typing its name shown at the first prompt All subsequent output is from the pro gram In this case the name of the input file is entered at the prompt from smont
45. property curves that define photon material interactions are presented in section 2 4 3 The cosine power dependence of the outgoing directional distribution function is presented in section 2 4 4 Section 3 6 provides the details of material property input and section 3 7 provides the details of material property curve input 2 4 1 Material Types Different material types are available to provide flexibility in the material model These material types allow different combinations of emission and photon material interactions to be defined A separate material must be defined for each set of material emission and photon material interactions Material property curves for photon material interactions may be input in tabular form allowing great flexibility in behavior A material is defined by a material type number that must be unique and a member of the full set such that the material type 1 NUMMAT where NUMMAT is the number of material types and a material name that is not used in the code but pro vided simply for convenience 2 4 2 Material Emission Material emission is defined by material type and determines how photons are emitted directionally from a surface Five possibilities exist for emission as defined in Table 2 1 Explana tion of material emission by type is provided below Material types 1 and 2 are intended for perfectly reflecting surfaces that do not participate in transport No emission occurs for these material types
46. r example if 3 materials with 2 bands are used then all material type data are read in for material 1 band 1 then material 1 band 2 then material 2 band 1 etc MN and IB are only used as checks to make sure the values are being entered in the right order If the information is not entered in the correct order the program will terminate with an error All material input cards must be input before any material property curves are input these cards control which material property curves are read 24 Cols 1 5 6 45 rials and 3 bands are modelled the sequence of materials cards and bands is 2 Material names are not used in the code except to name and thereby identify materials CARD 2 band photon emission one card per band grouped with card 3 Cols 1 5 6 10 11 30 31 50 51 70 Format I5 A40 Material name MNAME NMAT Format I5 I5 E20 0 E20 0 E20 0 CARD 1 material number and name Entry Material number NMAT Notes 1 Data are input in order of materials by band one card 1 input per material and NBANDS pairs of cards 2 and 3 input for all bands except as noted in note 2 for card 2 below Thus if 2 mate Table 3 1 Material Card Sequence Material Band Card 1 All 1 1 1 2 1 1 3 1 2 2 1 2 3 1 3 2 1 3 3 2 All 1 2 1 2 2 1 3 2 2 2 2 2 3 2 3 2 2 3 3 Entry Band number IB Emission type MTYPE MN IB domain 2 2 Outgoi
47. r is therefore advised to select this option only for very few photons per surface 8 If RESTART is 1 and no njj file from which to initiate a restart run exists a warning message is printed to the output file and the console and a new run proceeds If IRESTART is 0 no restart run is ever done if a nij file from which to initiate a restart run exists it is overwritten by the file from a new run the user is cautioned that this will result in the loss of information 3 2 5 Card 5 Grid Dimensions Cols Format Entry Notes 1 5 I5 Number of grid cells in the X direction NGX 1 6 10 I5 Number of grid cells in the Y direction NG Y 1 11 15 I5 Number of grid cells in the Z direction NGZ 1 22 Notes 1 For large geometries involving 1 000 to 5 000 surfaces grid dimensions of NGX NGY NGZ 25 are suggested as near optimal resulting in near minimum total CPU time 3 3 Nodal Point Data Cols 1 5 11 10 11 30 31 50 51 70 Format I5 I5 E20 0 E20 0 E20 0 Entry Note Node point number N Increment in number of points to be generated INC 1 DEFAULT INC 0 no nodes generated X coordinate X N Y coordinate Y N Z coordinate Z N Note 1 Nodal points are generated in increments of INC from the previous node input to the current node The coordinates are obtained by linearly interpolating all coordinates between the ones input on the previous card and ones input on the present card Ca
48. re must be taken such that there are exactly an integer number of generated nodes between the present node number and the one input on the previous card Note that as the program calculates and fills nodes these nodes should not also be input elsewhere 3 4 Surface Data Cols 1 5 6 10 11 15 16 20 21 25 26 30 31 35 36 40 41 45 46 50 51 60 61 65 66 70 71 80 Format I5 I5 I5 I5 I5 5X I5 I5 5X I5 10X I5 I5 E10 0 Entry Notes Surface number N 1 Node N NODES 1 N Node N NODES 2 N Node N3 NODES 3 N Node Ny NODES 4 N Skip Number of surfaces to be generated after current surface NMISS Increment of generation INC Skip Surface material number MATNUM N Skip Surface photon multiplier NPHT 3 DEFAULT NPHT 1 Photon increment INCP Convergence tolerance for surface ERRMAX N 5 DEFAULT for surface ERRMAX N ERRDEP 5 6 23 Notes 1 Surfaces can be input in any order The outward normal must be such that the right hand rule as explained in section 2 3 applies Unpredictable and erroneous results may occur if this conven tion is not adhered to for all surfaces 2 NMISS surfaces are generated by successively incrementing surface numbers by 1 and by incre menting all 4 node numbers by INC 3 NPHT is multiplied by NPHTON on control card 2 the base number of photons per surface to yield the total number of photon emissions per surface per photon
49. rlo Radiative Heat Transfer Numerical Heat Transfer Part B Fundamentals 16 pp 20 42 Burns Patrick J and Pryor Daniel V 1999 Large scale Radiative Heat Transfer via Monte Carlo Advances in Heat Transfer IX Begell House Press pp 79 158 Burns Patrick J Maltby James D and Christon Mark A 1990 Large Scale Surface to Surface Transport for Photons and Electrons via Monte Carlo Computing Systems in Engineering I 1 pp 75 99 Burns Patrick J Loehrke Richard I Dolaghan John S and Maltby James D 1992 Photon Tracing in Axisymmetric Enclosures Developments in Radiative Heat Transfer HTD Vol 203 pp 93 100 ASME New York Burns Patrick J 2000 MPLOT Computer Code contact the author at pburns colostate edu Crockett David V Maltby James D and Burns Patrick J 1990 User s Manual for MONT3E A Three Dimensional Electron Tracing Code with Non Uniform Magnetic Field Release 5 0 Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 Dolaghan John S Loehrke Richard I and Burns Patrick J 1992 User s Manual for SMOOTH Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 Dolaghan John S 1991 A Monte Carlo Simulation of Molecular Redistribution in an Enclosure due to Sputtering M S Thesis Department of Mechanical Engineering Colorado State Univer sity Fort Collins CO 80523
50. roceedings Supercom puting 1993 IEEE Computer Society Press Los Alamitos CA pp 250 259 Statton E Scott 1983 MONTE A Two Dimensional Monte Carlo Radiative Heat Transfer Code M S Thesis Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 Zeeb Charles N and Burns Patrick J 1997 Random Number Generator Recommendation Report prepared for V J Romero of Sandia National Laboratory available via the web at http www colostate edu pburns monte html Zeeb Charles N and Burns Patrick J August 1999 Performance enhancements in Monte Carlo Radiative Heat Transfer Proceedings ASME National Heat Transfer Conference Albuquer que NM 43
51. rptance within a given wavelength band are equal by virtue of Kirchoff s law these properties are determined as the complement of the others Thus specification of the specular and diffuse reflectances and transmittances uniquely defines the surface interaction prop erties within one wavelength band for a material Figure 2 6 depicts the material properties as functions of the incident cone angle 8 within a wavelength band k At any particular value of 6 e g 8 0 the incident photon has the following probabilities T 9 T 0 P 8 pa 0 and 1 t 8 tg 6 p 8 P4 8 for specular and diffuse transmission specular and diffuse reflection and absorption equal to emission respectively Each of these curves may be input as constant independent of incident cone angle or as a function of incident cone angle for every wavelength band for each material For curves the computer code parabolically interpolates between each 3 successive points entered When entering curves care must be taken to 1 include bounding points of 9 0 and 8 90 since no extrapolation is done and 2 to include enough points varying smoothly to result in good interpolation 1 e discontin uous jumps must be input as steep parabolas with 3 non coincident points used to define the jump 2 4 4 Diffuse Cosine Power Dependence In the present material model the probability for emission or re emission i e reflection of a photon at angle
52. s completed a message is printed indicating whether the exchange fractions have achieved the specified convergence tolerance In addition the wavelength band surface number total number of emitted photons summed over all full surface emissions and the calculated error are printed At the end of the run the overall program statistics are printed including the total CPU time for the run in seconds the total number of photons emitted and traced to absorption and the execution rate in number of photons per CPU second Finally upon completion of the run the message Stop program terminated is issued PC version only Then the command prompt is again issued by the operating system Then the output file box out is available the plot file box plt can be used with the MPLOT program to view the geometry and material properties etc Section 6 3 is the screen output generated by a restart run of box in For a restart run the only difference in the input file is that IRESTART is set to 1 The new input file must also be named the same as in the input file for the initial run here box in Specifically the only change in the input file is in the eighth character of Control Card 4 which is IRESTART amp ITOGGLE 10000001 In each run one photon loop each with 100 000 photons emitted per surface is executed Each doubling of photons causes the error to decrease by a factor of about 1 J2 thus the error 32
53. s guaranteed to converge not so with other methods Finally run times must be evaluated in context against the effort required to construct and debug input files which can take several person months for large complex geometries A theoretical development Burns and Pryor 1999 indicates the following approximate relation for scaling CPU time from one run subscript 1 to another run subscript 2 At Photons xBands xSurfs xClock Og gt At F Photons xBands xSurfs xClock Qg Ga where At total solution time secs Photons constant number of photons emitted per surface Bands number of wavelength bands Surfs number of surfaces Clock the clock rating of the CPU Mhz QE enclosure absorptance i e average area weighted absorptance of all surfaces The photon tracing basis for the approximate relation of eqn 1 9 has been validated for various geometries by Zeeb and Burns 1999 The relation of eqn 1 9 is approximate and is only valid at the optimal grid Grid tracing changes the scaling of CPU time from Surfs to Surfs gt pro viding significant savings in execution time for large geometries Additional details on grid tracing including guidance on selecting the optimal grid are given in Section 2 5 Factors that introduce variability into the run time include e Geometry Photon tracing times are dependent upon geometry Observations indicate that variability in run time from the average ca
54. s pointing into the page In Figure 2 10 b the edge is reversed and the normals of the two surfaces are pointed in opposite directions To see the type of problem this creates remember that the surfaces are transparent to pho tons that hit the back side of the surface These surfaces are oriented for photons coming in opposite directions This type of error almost certainly means the enclosure will loose excessive photons resulting in an error termination a correct edge b reversed edge Arrows represent direction of increasing node number Figure 2 10 Example of a Reversed Edge Error 2 No Match Found This error occurs when no match was found connecting at least one side of that sur face to the side of another surface This may or may not be okay 16 Error 3 Slip Surface This error occurs when an edge goes through a node point instead of terminating at it Although this is sometimes a fatal error it often is not If the slip surface creates no holes in the geometry then it should not cause the enclosure to loose photons When photons are lost the endpoints of each photon ray are written to a separate file of extension st which may then be read by the MPLOT program Then trajectories of the lost pho tons may be displayed on the geometry Because there is no terminus of the ray a fictitious end point is used An option is also available to write trajectory information to an output
55. scribed in Section 3 2 4 Table 1 1 below provides some measured run times on an IBM portable computer with a 233 MHz Pentium II chip running the Windows 2000 operating system Note that relatively large problems can be done in reasonable run times on relatively slow hardware In our experience in general run times are vastly less than the times spent preparing input files Table 1 1 Run times on a 233 Mhz Pentium II processor single wavelength band 100 000 photons per surface emitted Input File Photons per Number of Grid Run time Name Surface Surfaces NCA BS secs etf in 100 000 145 6x2x6 664 geo in 100 000 1 182 22x22x22 6 263 mtgun in 100 000 4 297 20x30x50 15 852 2 COMPUTER CODE BACKGROUND This chapter presents the background information necessary to run the Monte Carlo com puter code The first two subsections define the geometry of a radiating enclosure in terms of nodes and radiating surfaces The third subsection discusses surface concatenation which is no longer available in the code but may be done by the user in a post processing phase The fourth subsection describes material types the radiative properties to be specified versus incident cone angle and the cosine power dependence of diffuse reflection and transmittance The fifth subsection discusses grid tracing that dramatically reduces execution time The sixth subsection discusses accuracy ver sus the number of photons emitted
56. tains informa tion on precision 7 1 Compiling The code has been implemented with stubs that are subroutines containing system spe cific functions allowing various make files Invoking different make files causes various stub files to be selected with various options The following modules are common to all versions Ismmain f contains the main root program and subroutines common to input and solution phases Ismfile f contains file processing routines Isminput f contains basic input routines Ismmat f contains material input and initialization routines Ismpreproc f contains input preprocessing the input routines are split across sev eral modules due to their large size Ismsolve f contains solution phase routines Ismonte com contains common blocks used in the code for variable storage Ismonte par contains parameters for the code particularly some parameters set storage size for the executable see section 7 2 for more information 7 2 Common Blocks Parameter Statements and the Size of Arrays The code uses common blocks for variable storage making the code more robust and easier to modify A version of the code has been implemented and tested with dynamic memory alloca tion however the performance was poor and this approach was abandoned Therefore this imple mentation fixes the sizes of arrays by using specific parameters contained in the module Ismonte par These parameters limit the number of vario
57. terial property curves are independent of azimuthal angle but may depend upon cone angle 0 or be constant over 8 All properties are defined as constant gray within a particular radiative band k so that Kirchoff s law applies within each band Explicitly Photon Emission Vector Figure 2 4 Local Material Coordinate System V amp a Specular Transmission b Diffuse Transmission XA typ c Specular Reflection d Diffuse Reflection Figure 2 5 Photon Material Interactions 10 k k O O ee 0 0 1 1 0 1 0 p 0 pg 0 2 1 where Ke emittance in wavelength band k at outgoing cone angle 6 a0 absorbance in wavelength band k at incident cone angle O 0 specular transmittance in wavelength band k at incident cone angle 1 10 diffuse transmittance in wavelength band k at incident cone angle O oO specular reflectance in wavelength band k at incident cone angle 0 p 9 diffuse reflectance in wavelength band k at incident cone angle 6 Hereinafter the explicit dependence upon wavelength band k is dropped and an implicit dependence is carried Note that all surface interaction properties may be considered in terms of probability i e p 0 is the probability that a photon of incident angle O will be specularly reflected py 0 is the probability that a photon of incident angle O will be diffusely reflected etc As the emittance and abso
58. tes 1 5 IS Restart write increment NINCR 1 DEFAULT NINCR 100 6 15 110 Initial seed for the random number generator INSEED INSEED lt 0 Use the default internal value for the initial seed INSEED 0 The initial seed is obtained from the time and date or INSEED gt 0 Use the value INSEED for the initial seed 16 20 I5 Number of CPU s NCPU 2 DEFAULT NCPU 1 21 30 10X Skip 31 40 E10 0 Cone angle interval for numerical integration of material properties DELT 3 DEFAULT DELT 0 01 degrees 41 50 E10 0 Tolerance for warnings of noncoplanar surfaces SPLITOL 4 20 DEFAULT SPLITOL 0 0001 51 60 E10 0 Tolerance for warnings of area tolerance of split surfaces AREATOL 5 DEFAULT AREATOL 0 0001 Notes 1 After emission and tracing from every NINCR surfaces has completed the block of NINCR rows of the exchange factor matrix and the restart crash file are written to disk Thus it is pos sible to restart only every NINCR states Selecting a small value of NINCR will ensure that restart information is written frequently to disk The value of 100 is appropriate for NINCR 2 NCPU is applicable only in the parallel version and is ignored in the serial version of the code 3 DELT AQ the increment used in numerically integrating the cumulative distribution function for emission versus cone angle The acceptable range is 1E 7 lt DELT lt 0 1 If a value outside this range is entered for DELT
59. the Lawrence Livermore National Laboratory This algorithm has resulted in significant reduc tions in execution time MT Enclosure Photon Trajectory Figure 2 8 2 D Illustration of the Grid Tracing Algorithm Previous versions of the code permitted non uniform grid spacing in each of the coordinate directions The current version of the code permits only uniform grid spacing in each of the coor dinate directions but the uniform spacing may vary in each of the coordinate directions The opti mum grid differs from problem to problem and must be empirically determined by the user Zeeb Zeeb and Burns 1999 recently has improved the tracing algorithm and thoroughly investigated optimal grids A good starting guess for an optimal grid for moderate problems several thousand surfaces is 25 X 25 X 25 Also the performance curve versus grid size is very flat indicating that a wide range of grid sizes yields nearly optimal performance The input for defining the tracing grid is described in section 3 2 5 2 6 Number of Photons Convergence and Accuracy As Monte Carlo techniques are statistical in nature enough photons must be emitted from each surface to yield a statistically accurate result This number depends upon the geometry and to some extent upon the material properties As a general rule greater numbers of surfaces require greater numbers of photons emitted to achieve similar accuracy Execution tim
60. tine nodin 34 Reading the surface input subroutine surfin Calculating surface quantities subroutine surfcalc Processing the wavelength input subroutine wavin Processing the material proper ty input subroutine matin Processing the material curve input subroutine curvin Creating material property sets subroutine matcalc Calculating the inverse CDFs subroutine cumdis Setting up the nij and crh files subroutine nijcrhset Creating a grid for the geometry subroutine gridcalc Finding the surfaces in the grid cells subroutine seging Creating the leaks lks fil Creating the MPLOT plt fil e subrou tine lksfil e subrou tine pltfil e e Calculating the 2D bounding planes subroutine bplane2d input phase band surf iter not converged if 1 not converged 2 not converged 3 not converged 4 not converged 5 not converged 6 normal termination complete npht 200000 200000 200000 200000 200000 200000 35 error 1461E 02 E 02 18 02 E 02 E 02 E 02 4 14 14 4 4 33333 solution time log total time for input phase 10000D 01 secs total time for solution phase 14000D 02 secs total run time 15000D 02 secs all times measured in clock time seconds total number of photons
61. tment of Mechanical Engineering at Colorado State University CSU beginning with the work of Scott Statton in 1983 Statton 1983 continuing with the work of James D Maltby Maltby 1987 Maltby 1990 and most recently with the work of Charles N Zeeb Zeeb and Burns 1999 The code is capable of simulating geometries modelled as assemblages of generalized quadrilaterals which are constrained to be flat Curved surfaces must be approximated by a sufficient number of flat surfaces to capture the curvature Surfaces may absorb photons or they may reflect or transmit them specularly and or diffusely All exterior surfaces must be non transmissive it is left to the user to ensure this so that photons are not lost during tracing All material radiative properties may be explicit functions of the incident photon angle and be dependent upon energy through the band wavelength formulation Mark Havstad Charlie Landram and Donald L Brown at the Lawrence Livermore National Laboratory LLNL and Katherine Bryan of Oak Ridge National Laboratory have exhaustively exercised the code checking it for validity The code has been used by many individuals for over a decade on many problems including radiative heat transfer and rarefied gas dynamics A number of related publications exist wherein the code has been applied to various prob lems including a detailed test of the Separator Development Facility SDF Maltby 1987 the calculation of rad
62. to pause until line 1 has finished When the first run has completed the process continues with line 3 etc Ismonte f tcl gt runl wait Ismonte f tc2 gt run2 wait Ismonte f tc3 gt run3 Figure 9 1 Script submit The script file can be created with any ASCII editor and given any valid UNIX name here the file is named submit The files referred to in the script here tc runl etc can also have any valid UNIX name The files tc tc2 and tc3 must be the input files without the in extension to be used for the run Once the script is created it must have execute permission before it can be run This is accomplished with the UNIX command chmod This is accomplished as follows chmod 744 submit where is the UNIX prompt The script can be run in background by typing the script name followed by amp Alter nately it can be submitted using the UNIX commands at or batch The syntax of any of the UNIX commands can be obtained by referring to the man ual pages on your UNIX system 41 REFERENCES Anderson Stuart L 1990 Random Number Generators on Vector Supercomputers and Other Advanced Architectures SIAM Review 32 pp 221 251 Brent R P 1992 Uniform random number generators for supercomputers Proceedings 5th Australian Supercomputing Conference SASC Organizing Committee pp 95 104 unpub lished Burns Patrick J and Pryor Daniel V 1989 Vector and Parallel Monte Ca
63. ults in fewer photons being lost The exchange fraction files are always written in 32 bit binary format note that the only real numbers written are the surface areas and emittances as this saves storage space 38 8 FILES AND FILE USAGE This chapter briefly describes file usage For specificity a prefix of fn is used Table 8 1 gives the files used either pre existing or generated during execution by LSMONTE Table 8 1 LSMONTE Files Unit Name Function 1 fn scr Input file with comment cards stripped away File is generated by code and deleted before completion of run This is the file actually read during the input phase 2 fn crh Crash file in binary format deleted upon successful termination Con tains a list of the photon blocks that have been completed 3 fn plt Plot file to be used with the program MPLOT Burns 2000 Contains geometry and material property information 4 fn lst Contains lost photon trajectories if any This files may be used by MPLOT to display trajectories of lost photons MPLOT Burns 2000 5 stdin Standard input keyboard 6 stdout Standard output screen 7 fn in Input file with comment cards in a format described in chapter 3 This file is used to generate the file of unit 1 8 fn niz Exchange number matrix These are stored in binary format as described in chapter 4 9 fn trc Trajectory file written if ITRACES 0 s
64. us objects that can be stored including the number of surfaces number of wavelength bands and number of materials To increase the storage size the parameters must be changed requires editing smonte par and the program must be 37 recompiled The larger the arrays the more memory the program uses If the arrays become too large the program may be too large to be stored in available physical memory and the program execution speed will severely degrade as the program is swapped to and from the disk Or the code may not execute if swapping is not supported by the operating system In either case it is recommended that the code be recompiled so as to fit in available phys ical memory The parameters used to size arrays are iblk maximum number of surfaces before writing output used for blocking the matrix of exchange factors inod maximum number of nodes isrf maximum number of surfaces ibnd maximum number of wavelength bands imat maximum number of materials incg maximum number of grid cells in any coordinate direction igrd maximum number of grid cells iseg maximum number of surfaces either wholly or partially within all grid cells During execution a check is performed to ensure that storage is not exceeded After the input is read the code checks that the numbers of nodes surfaces wavelength bands materials material property curves and grid cells are not exceeded If any of the storage limits are exce
65. xchange Fractions arts ilatina tres 14 Table Matenal Card SEQuenCe ciales iodo EE E AERE EEEo 25 Tables ESMONTE Pales ita A A A AI AAA 39 Table 8 2 Command Line File Control Ann ti 40 Figures Figure 2 1 Global Coordinate SS iii ra 6 Figure 2 2 Radiating Surface Geometries idee eterna saat etree ii 7 Figure 2 3 Global local Coordinate Systems sp ls 8 Figure 2 4 Local Material Coordinate System eesesseseeseeeseeeessresseserssresseseresressesererresseserereessesse 10 Figure 2 5 Photon Material Interactions it tds 10 Figure 2 6 Material Properties vs Incident Cone Angle oooonoconnccniocanocanonncooncnannconnnonnncnoncnnnncnnnoo 12 Figure 2 7 Cosine Power Dependence of Emission as a Function of r and 0 eseese 12 Figure 2 8 2 D Illustration of the Grid Tracing Algorithm 2 0 0 0 cece eeeseeceeneeceeeeeceeeeeeeeeeeeneeeees 13 Figure 2 9 Convergence vs Number of Photon Emissions coooooonoconocononononnononononcnanoconn nono ncnnncnnnno 14 Figure 2 10 Example of a Reversed Pde 5 24 23 A Re a 16 Fig re 5 1 3 D Geometry of File DORIA A Sateen eee 30 Figure 9 1 Script submit a ala 41 11 1 INTRODUCTION 1 1 Background This manual encompasses the 3 D Monte Carlo radiative exchange factor computer code known as LSMONTE This version of the code was developed for the Livermore Software Tech nology Corporation LSTC from the last public domain version of the code MONT3D Maltby et al 1994 MONT3D was developed in the Depar

USER`S MANUAL for LSMONTE A Three

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