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An implicit Monte Carlo method for thermal radiation transport

Li Shu Li Gang Tian Dong-Feng Deng Li

An implicit Monte Carlo method for thermal radiation transport

Li Shu, Li Gang, Tian Dong-Feng, Deng Li
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  • The equations of thermal radiative transfer are mathematical models that describe the physical processes of photons scattering through and being absorbed in and emitted by a high-energy background material. These processes are important research objects of inertial confinement fusion (ICF). Numerical simulation is an indispensable method for this transportation equation. As an important method in the field of particle transportation, the Monte Carlo method has been widely employed in the fields of linear transportation of neutrons and high energy photons. However, traditional Monte Carlo method does not hold true when it is applied to the simulation of thermal radiation. In this research, an implicit Monte Carlo method based on calculable modeling and numerical simulation is studied. An integral transport equation that is suitable to Monte Carlo simulation is derived. A three-dimensional simulation code is developed, by which some thermal radiative transportation problems are simulated. The results of numerical experiments support that the implicit Monte Carlo method is applicable for thermal radiation transfer simulating. The work is expected to provide an important calculation method and tool for the thermal radiative transfer simulations of ICF.
    • Funds: Project supported by the National High Technology Research and Development Program of China (Grant No. 2012AA01A303) and the Science and Technology Development Foundation of China Academy of Engineering Physics (Grant No. 2012A0102005).
    [1]

    Zhang J, Chang T Q 2004 Fundaments of the Target Physics for Laser Fusion (Beijing: National Defense Industry Press) p1 (in Chinese) [张均, 常铁强 2004 激光核聚变靶物理基础(北京: 国防工业出版社)第1页]

    [2]

    Peng H M 2008 Radiation Transport and Radiation Hydrodynamics in Plasmas (Beijing: National Defense Industry Press) p38 (in Chinese) [彭惠民 2008 等离子体中辐射输运和辐射流体力学(北京: 国防工业出版社)第38页]

    [3]

    Bowers R L, Wilson J R 1991 Numerical Modeling in Applied Physics and Astrophysics (Boston: Jones and Bartlett Publishers) p347

    [4]

    James J D, William R M 1979 Transport Theory (London: A Wiley-Interscience Publication) p420

    [5]

    Du S H, Zhang S F, Feng T G, Wang Y Z 1989 Computer Simulation of Transport Problems (Changsha: Hunan Science and Technology Press) p304 [杜书华, 张树发, 冯庭桂, 王元璋 1989 输运问题的计算机模拟(湖南科技出版社)第304页]

    [6]

    Hammersly J M, Handscomb D C 1964 Monte Carlo Methods (New York: John Wiley & Sons Press)

    [7]

    Pei L C, Zhang X Z 1980 Monte Carlo Methods and Application in Particle Transportation (Beijing: Science Press) (in Chinese) [裴鹿成, 张孝泽 1980 蒙特卡罗方法及其在粒子输运问题中的应用(北京: 科学出版社)]

    [8]

    FLECK J A 1963 Computational Methods in the Physical Sciences (Vol. 1) (New York: McGraw-Hill) p43

    [9]

    Campbell P M, Nelson R G 1964 Livermore, Calif: Lawrence Radiation Laboratory Report UCRL-7838

    [10]

    Fleck J A, Cummings J D 1971 J. Computat. Phys. 8 313

    [11]

    Evans T M, Urbatsch T J 1998 Los Alamos National Laboratory report LA-UR-98-4722

    [12]

    Rathkopf J A, Miller D S, Owen J M, et al 2000 LLNL report UCRL-JC-137053

    [13]

    Evans T M, Urbatsch T J 2002 Los Alamos National Laboratory report NM 87545

  • [1]

    Zhang J, Chang T Q 2004 Fundaments of the Target Physics for Laser Fusion (Beijing: National Defense Industry Press) p1 (in Chinese) [张均, 常铁强 2004 激光核聚变靶物理基础(北京: 国防工业出版社)第1页]

    [2]

    Peng H M 2008 Radiation Transport and Radiation Hydrodynamics in Plasmas (Beijing: National Defense Industry Press) p38 (in Chinese) [彭惠民 2008 等离子体中辐射输运和辐射流体力学(北京: 国防工业出版社)第38页]

    [3]

    Bowers R L, Wilson J R 1991 Numerical Modeling in Applied Physics and Astrophysics (Boston: Jones and Bartlett Publishers) p347

    [4]

    James J D, William R M 1979 Transport Theory (London: A Wiley-Interscience Publication) p420

    [5]

    Du S H, Zhang S F, Feng T G, Wang Y Z 1989 Computer Simulation of Transport Problems (Changsha: Hunan Science and Technology Press) p304 [杜书华, 张树发, 冯庭桂, 王元璋 1989 输运问题的计算机模拟(湖南科技出版社)第304页]

    [6]

    Hammersly J M, Handscomb D C 1964 Monte Carlo Methods (New York: John Wiley & Sons Press)

    [7]

    Pei L C, Zhang X Z 1980 Monte Carlo Methods and Application in Particle Transportation (Beijing: Science Press) (in Chinese) [裴鹿成, 张孝泽 1980 蒙特卡罗方法及其在粒子输运问题中的应用(北京: 科学出版社)]

    [8]

    FLECK J A 1963 Computational Methods in the Physical Sciences (Vol. 1) (New York: McGraw-Hill) p43

    [9]

    Campbell P M, Nelson R G 1964 Livermore, Calif: Lawrence Radiation Laboratory Report UCRL-7838

    [10]

    Fleck J A, Cummings J D 1971 J. Computat. Phys. 8 313

    [11]

    Evans T M, Urbatsch T J 1998 Los Alamos National Laboratory report LA-UR-98-4722

    [12]

    Rathkopf J A, Miller D S, Owen J M, et al 2000 LLNL report UCRL-JC-137053

    [13]

    Evans T M, Urbatsch T J 2002 Los Alamos National Laboratory report NM 87545

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  • Received Date:  14 August 2013
  • Accepted Date:  26 September 2013
  • Published Online:  20 December 2013

An implicit Monte Carlo method for thermal radiation transport

  • 1. Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;
  • 2. China Academy of Engineering Physics, Mianyang 621900, China
Fund Project:  Project supported by the National High Technology Research and Development Program of China (Grant No. 2012AA01A303) and the Science and Technology Development Foundation of China Academy of Engineering Physics (Grant No. 2012A0102005).

Abstract: The equations of thermal radiative transfer are mathematical models that describe the physical processes of photons scattering through and being absorbed in and emitted by a high-energy background material. These processes are important research objects of inertial confinement fusion (ICF). Numerical simulation is an indispensable method for this transportation equation. As an important method in the field of particle transportation, the Monte Carlo method has been widely employed in the fields of linear transportation of neutrons and high energy photons. However, traditional Monte Carlo method does not hold true when it is applied to the simulation of thermal radiation. In this research, an implicit Monte Carlo method based on calculable modeling and numerical simulation is studied. An integral transport equation that is suitable to Monte Carlo simulation is derived. A three-dimensional simulation code is developed, by which some thermal radiative transportation problems are simulated. The results of numerical experiments support that the implicit Monte Carlo method is applicable for thermal radiation transfer simulating. The work is expected to provide an important calculation method and tool for the thermal radiative transfer simulations of ICF.

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