Comparison of Monte Carlo Strategies for Radiative Transfer in Participating Media

Abstract A review of various strategies for implementing Monte Carlo analysis of radiative media is presented. Comparisons of the performance (defined as the variance of the results multiplied by the CPU time required for solution) are presented for three common methods used in Monte Carlo solution. Methods of treating complex geometries are also explored and compared, and a ray-tracing technique based on finite-element models of the geometry is presented. The finite-element models allow use of commercial codes for describing complex geometries, and also allow efficient coupling of the Monte Carlo radiative model with other finite-element-based thermal models. The utility and performance of the direct simulation Monte Carlo ray-tracing methods in engineering problems involving realistic properties are examined. Strategies are compared for treating anisotropic scattering distributions, nonuniform temperatures and radiative properties, and spectral property variations. The effects of scattering on ray tracing and the necessary modifications to the algorithms are evaluated, and the performance and accuracy of these algorithms are evaluated and recommendations are suggested. The difficulties in handling inhomogeneous properties and spectrally dependent properties are presented, and some possible approaches are proposed and compared. Monte Carlo strategies for solving radiative transfer in participating media are described for use on parallel processors using different common architectures. An example benchmark problem is carried out to demonstrate the degree of speedup that can be obtained.

[1]  Improved Algorithms for Monte Carlo Analysis of Radiative Heat Transfer in Complex Participating Media , 1995 .

[2]  K. Ramachandran,et al.  Mathematical Statistics with Applications. , 1992 .

[3]  Pei-feng Hsu,et al.  Benchmark Solutions of Radiative Heat Transfer Within Nonhomogeneous Participating Media Using the Monte Carlo and YIX Method , 1997 .

[4]  Ephraim M Sparrow,et al.  Monte carlo radiation solutions—effect of energy partitioning and number of rays , 1973 .

[5]  Horst D. Simon.  Scientific Applications of the Connection Machine , 1992 .

[6]  The Radiative Heat Transfer of Gas in a Three Dimensional System Calculated by Monte Carlo Method , 1969 .

[7]  M. N. Özişik,et al.  Radiative transfer in an isotropically scattering two-region slab with reflecting boundaries , 1981 .

[8]  A backward Monte Carlo estimator for the multiple scattering of a narrow light beam , 1996 .

[9]  D. K. Edwards,et al.  Radiation Heat Transfer in Nonisothermal Nongray Gases , 1967 .

[10]  C. R. Howarth,et al.  Optical constants of carbons and coals in the infrared , 1968 .

[11]  Michael A. Arbib,et al.  Natural and Artificial Parallel Computation , 1990 .

[12]  Gary Demos,et al.  3D Image Synthesis on the Connection Machine , 1989, Int. J. High Speed Comput..

[13]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[14]  Kazuhiko Kudo,et al.  Monte Carlo simulation of indoor radiant environment , 1990 .

[15]  M. Pinar Mengüç,et al.  On ‘‘Radiative transfer in three-dimensional rectangular enclosures containing inhomogeneous,anisotropically scattering media’’ , 1985 .

[16]  E. Lewis,et al.  Computational Methods of Neutron Transport , 1993 .

[17]  Ted Belytschko,et al.  Finite Elements, An Introduction , 1982 .

[18]  A. E. Fincham,et al.  Parallel Computation , 1999, Algorithms and Theory of Computation Handbook.

[19]  W. R. Martin,et al.  Experiences with different parallel programming paradigms for Monte Carlo particle transport leads to a portable toolkit for parallel Monte Carlo , 1993 .

[20]  Accuracy control in Monte Carlo radiative calculations , 1993 .

[21]  John R. Howell,et al.  Application of Monte Carlo to Heat Transfer Problems , 1969 .

[22]  W. F. McColl.  The challenge of general purpose parallel computing , 1994 .

[23]  R. O. Buckius,et al.  MONTE CARLO METHODS FOR RADIATIVE HEAT TRANSFER IN SCATTERING MEDIA , 1994 .

[24]  William H. Beyer,et al.  CRC standard mathematical tables , 1976 .

[25]  Richard G. Wilmoth.  Application of a parallel DSMC method to hypersonic rarefied flows , 1991 .

[26]  M. Pinar Mengüç,et al.  Thermal Radiation Heat Transfer , 2020 .

[27]  K. Rhee,et al.  Blackbody radiation functions , 1984 .

[28]  Ulrich Grigull,et al.  Progress in heat and mass transfer , 1969 .

[29]  Terry Wall,et al.  Radiative scatter by fly ash in pulverized-coal-fired furnaces: application of the Monte Carlo method to anisotropic scatter , 1983 .

[30]  M. Modest.  Radiative heat transfer , 1993 .

[31]  J. R. Howell,et al.  Monte carlo solution of thermal transfer through radiant media between gray walls. , 1964 .

[32]  Christon,et al.  Spatial domain-based parallelism in large scale, participating-media, radiative transport applications , 1996 .

[33]  Wataru Nakayama.  Computers and Computing in Heat Transfer Science and Engineering , 1992 .

[34]  Development of a monte carlo method for numerical analysis on radiative energy transfer through non‐grey‐gas layer , 1992 .

[35]  Per Brinch Hansen.  The Nature of Parallel Programming , 1989 .

[36]  R. D. Skocypec,et al.  Summary on comparison of radiative heat transfer solutions for a specified problem , 1992 .

[37]  Ihab H. Farag.  Non luminous gas radiation - Approximate emissivity models , 1982 .

[38]  A. B. Carlson,et al.  DSMC analysis in a heterogeneous parallel computing environment , 1992 .

[39]  Investigation of radiative interaction in laminar flows using Monte Carlo simulation , 1993 .

[40]  Improvement of analytical method on radiative heat transfer in nongray media by Monte Carlo method , 1994 .

[41]  A. Balakrishnan,et al.  Thermal radiation by combustion gases , 1973 .

[42]  M. Brewster.  Thermal Radiative Transfer and Properties , 1992 .

[43]  R. O. Buckius,et al.  Rigorous development for radiation heat transfer in nonhomogeneous absorbing, emitting and scattering media , 1992 .

[44]  Linda J. Hayes,et al.  PARALLEL COMPUTATIONS IN HEAT TRANSFER , 1986 .

[45]  Probability distributions and error estimates for Monte Carlo solutions of radiation problems , 1969 .

[46]  R. Siegel.  Transient radiative cooling of a droplet-filled layer , 1987 .

[47]  C. Tien.  Annual Review of Heat Transfer , 1993 .

[48]  Kazuhiko Kudo,et al.  Radiative heat transfer by the Monte Carlo method , 1995 .

[49]  M. Kobiyama.  Reduction of Computing Time and Improvement of Convergence Stability of the Monte Carlo Method Applied to Radiative Heat Transfer With Variable Properties , 1989 .