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热辐射输运问题的高效蒙特卡罗模拟方法

许育培 李树

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热辐射输运问题的高效蒙特卡罗模拟方法

许育培, 李树

An efficient Monte Carlo simulation method for thermal radiation transport

Xu Yu-Pei, Li Shu
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  • 惯性约束聚变研究中, 热辐射光子在介质中的输运以及热辐射光子与介质的相互作用是重要研究课题,蒙特卡罗方法是该类问题的重要研究手段之一. 隐式蒙特卡罗方法虽然能正确地模拟热辐射在介质中的输运过程, 但当模拟重介质(材料的吸收系数大)问题时, 该方法花费的计算时间将变得很长, 导致模拟效率很低. 本文以离散扩散蒙特卡罗方法为基础, 开发了“离散扩散蒙特卡罗方法辐射输运模拟程序”, 可以较好地解决重介质区的计算效率问题, 但是离散扩散蒙卡罗方法在模拟轻介质区时精度不够高. 辐射输运问题中通常既有轻介质也有重介质, 为了能同时解决蒙特卡罗方法模拟的效率和精度问题, 本文研究了离散扩散蒙特卡罗方法与隐式蒙特卡罗方法相结合的模拟方法, 并提出了新的扩散区与输运区界面处理方法, 研制了混合蒙特卡罗方法的辐射输运模拟程序. 典型辐射输运问题模拟显示: 在模拟重介质问题时, 该程序能大幅缩短模拟时间, 且能取得与隐式蒙特卡罗方法一致的结果; 在模拟轻重介质均存在的问题时, 与隐式蒙特卡罗方法相比, 混合蒙特卡罗方法的模拟精度与其相当且计算效率同样能够得到显著提升.
    Thermal radiation transfer in material and the interaction between radiative photon and material are important research projects of the inertial confinement fusion, and Monte Carlo method is one of the important researching methods. Based on the implicit integral-differential transport equation, traditional implicit Monte Carlo method can accurately simulate the thermal radiation transport in material. However, the implicit Monte Carlo method would take quite a long computational time when the opacity is increased because scattering events are dominant in particles’ histories, thus reducing the simulation efficiency. In this paper, based on discrete diffusion Monte Carlo method, i.e. a radiation transport code, the discrete diffusion Monte Carlo radiation transport simulation, is developed. The code increases the efficiency of thermal radiation simulations in a high opacity range, but it can yield insufficiently accurate results in a low opacity range. There exist low opacity material and high opacity material in the inertial confinement fusion. In this work, investigated are several numerical techniques that can improve the utility and accuracy of discrete diffusion Monte Carlo for grey thermal radiation simulation. First, the discrete diffusion Monte Carlo method and implicit Monte Carlo method are combined. Second, a new method of treating the interface between the diffusive region and the transport region is proposed. Finally, a hybrid radiative transfer program is developed. In order to verify the hybrid radiative transfer program and the new interface method, a series of numerical experiments for typical thermal radiation transport problem is conducted. In these problems, materials with different opacities are tested. Then the simulation efficiencies and curves of temperature, obtained by the two Monte Carlo methods, are analyzed. According to the simulation results, the program can not only accurately simulate the radiation transport in material with high opacity, but also remarkably increase the simulation efficiency. This is because many implicit Monte Carlo steps are substituted by one diffusive step and the details in the diffusive step are ignored. Also, the propagation of thermal radiation depicted with figures and tables are consistent with the radiation transport theory. In addition, the results from the hybrid Monte Carlo method reach the same accuracy as that from the implicit Monte Carlo method, and the simulation efficiency is remarkably increased.
      通信作者: 李树, li_shu@iapcm.ac.cn
    • 基金项目: 中国工程物理研究院于敏基金(批准号: FZ025)和国家自然科学基金(批准号: 11775033, 11775030)资助的课题
      Corresponding author: Li Shu, li_shu@iapcm.ac.cn
    • Funds: Project supported by the Yu Min Foundation of China Academy of Engineering Physics (Grant No. FZ025) and the National Natural Science Foundation of China (Grant Nos. 11775033, 11775030)
    [1]

    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

    Peng H M 2008 Radiation Transport and Radiation Hydrodynamics in Plasmas (Beijing: National Defense Industry Press) p38 (in Chinese)

    [2]

    Hammersly J M, Handscomb D C 1964 Monte Carlo Method (New York: John Wiley & Sons Press) p76

    [3]

    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) 第18页

    Pei L C, Zhang X Z 1980 Monte Carlo Method and Application in Particle Transportation (Beijing: Science Press) p18 (in Chinese)

    [4]

    Fleck J A 1963 Computational Method in the Physical Sciences (New York: McGraw-Hill) p43

    [5]

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

    [6]

    Fleck J A, Cummings J D 1971 J. Comput. Phys. 8 313Google Scholar

    [7]

    Fleck J A, Canfield E H 1984 J. Comput. Phys. 54 508Google Scholar

    [8]

    Giorla J, Sentis R 1987 J. Comput. Phys. 70 145Google Scholar

    [9]

    Urbatsch T J, Morel J E, Gulick J C 1999 Proceedings of the ANS conference on Mathematics and Computation, Reactor Physics, and Environmental Analysis in Nuclear Applications Madrid, Spain, September 27–30, 1999 p262

    [10]

    Evans T M, Urbatsch T J, Lichtenstein H 2000 Proceedings of the Monte Carlo 2000 International Conference Lisbon, Portugal, October 23–26, 2000

    [11]

    Gentile N A 2001 J. Comput. Phys. 172 543Google Scholar

    [12]

    Densmore J D, Urbatsch T J, Evans T M, Buksas M W 2005 American Nuclear Society Topical Meeting in Mathematics and Computations Avignon, France, September 12–15, 2005

    [13]

    Densmore J D, Urbatsch T J, Evans T M, Buksas M W 2007 J. Comput. Phys. 222 485Google Scholar

    [14]

    Cleveland M A, Gentile N, Palmer T S 2010 J. Comput. Phys. 229 5707Google Scholar

    [15]

    Densmore J D, Thompson K G, Urbatsch T J 2012 J. Comput. Phys. 231 6924Google Scholar

    [16]

    李树, 李刚, 田东风, 邓力 2013 物理学报 62 249501Google Scholar

    Li S, Li G, Tian D F, Deng L 2013 Acta Phys. Sin. 62 249501Google Scholar

    [17]

    李树, 陈耀华, 姬志成, 章明宇, 任国利, 霍文义, 闫威华, 韩小英, 李志超, 刘杰, 蓝可 2018 物理学报 67 025202Google Scholar

    Li S, Chen Y H, Ji Z C, Zhang M Y, Ren G L, Huo W Y, Yan W H, Han X Y, Li Z C, Liu J, Lan K 2018 Acta Phys. Sin. 67 025202Google Scholar

    [18]

    Mihalas D, Mihalas B W, Fu A, Arnett W D 1986 Phys. Today 39 90Google Scholar

    [19]

    谢仲生 2004 核反应堆物理分析 (西安: 西安交通大学出版社) 第62页

    Xie Z S 2004 Analysis of Nuclear Reactor Physics (Xi’an: Xi’an Jiaotong University Press) p62 (in Chinese)

    [20]

    Szilard R H, Pomraning G C 1992 Nucl. Sci. Eng. 112 256Google Scholar

    [21]

    Habetle G J, Matkowsky B J 1975 J. Math. Phys. 16 846Google Scholar

    [22]

    Densmore J D, Davidson G, Carrington D B 2006 Ann. Nucl. Energy 33 583Google Scholar

    [23]

    Cashwell E D, Everett C J 1959 A Practical Manual on the Monte Carlo Method for Random Walk Problem (London: Pergamon Press) p19

  • 图 1  不同时刻的物质温度空间分布比较(σ0 = 500)

    Fig. 1.  Material temperature in different moments (σ0 = 500).

    图 2  不同时刻的辐射温度空间分布比较(σ0 = 500)

    Fig. 2.  Radiative temperature in different moments (σ0 = 500).

    图 3  不同时刻的物质温度空间分布比较(σ0 = 500)

    Fig. 3.  Material temperature in different moments (σ0 = 500).

    图 4  不同时刻的辐射温度空间分布比较(σ0 = 500)

    Fig. 4.  Radiative temperature in different moments (σ0 = 500).

    图 5  不同时刻的物质温度空间分布比较(σ0 = 500, Np = 500000)

    Fig. 5.  Material temperature in different moments (σ0 = 500, Np = 500000).

    图 6  不同时刻的辐射温度空间分布比较(σ0 = 500, Np = 500000)

    Fig. 6.  Radiative temperature in different moments (σ0 = 500, Np = 500000).

    图 7  不同时刻介质中物质温度的空间分布比较

    Fig. 7.  Material temperature in different moments.

    表 1  不同σ0取值下IMC与DDMC方法的模拟时间对比

    Table 1.  Simulation time of IMC method and DDMC method in different initial cross sections.

    σ0/keV3·cm–1IMC time/sDDMC time/sSpeed up
    200330.4143.32.3
    500505.8139.93.6
    1000894.2142.16.3
    20001158.6142.28.1
    下载: 导出CSV

    表 2  不同σ0取值下, IMC与DDMC方法的模拟时间比较

    Table 2.  Simulation time of IMC method and DDMC method in different initial cross sections.

    σ0/keV3·cm–1IMC time/sDDMC time/sSpeed up
    2001184.4298.24.0
    5002357.6291.88.1
    10004348.7288.615.1
    20008406.4287.729.2
    下载: 导出CSV
  • [1]

    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

    Peng H M 2008 Radiation Transport and Radiation Hydrodynamics in Plasmas (Beijing: National Defense Industry Press) p38 (in Chinese)

    [2]

    Hammersly J M, Handscomb D C 1964 Monte Carlo Method (New York: John Wiley & Sons Press) p76

    [3]

    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) 第18页

    Pei L C, Zhang X Z 1980 Monte Carlo Method and Application in Particle Transportation (Beijing: Science Press) p18 (in Chinese)

    [4]

    Fleck J A 1963 Computational Method in the Physical Sciences (New York: McGraw-Hill) p43

    [5]

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

    [6]

    Fleck J A, Cummings J D 1971 J. Comput. Phys. 8 313Google Scholar

    [7]

    Fleck J A, Canfield E H 1984 J. Comput. Phys. 54 508Google Scholar

    [8]

    Giorla J, Sentis R 1987 J. Comput. Phys. 70 145Google Scholar

    [9]

    Urbatsch T J, Morel J E, Gulick J C 1999 Proceedings of the ANS conference on Mathematics and Computation, Reactor Physics, and Environmental Analysis in Nuclear Applications Madrid, Spain, September 27–30, 1999 p262

    [10]

    Evans T M, Urbatsch T J, Lichtenstein H 2000 Proceedings of the Monte Carlo 2000 International Conference Lisbon, Portugal, October 23–26, 2000

    [11]

    Gentile N A 2001 J. Comput. Phys. 172 543Google Scholar

    [12]

    Densmore J D, Urbatsch T J, Evans T M, Buksas M W 2005 American Nuclear Society Topical Meeting in Mathematics and Computations Avignon, France, September 12–15, 2005

    [13]

    Densmore J D, Urbatsch T J, Evans T M, Buksas M W 2007 J. Comput. Phys. 222 485Google Scholar

    [14]

    Cleveland M A, Gentile N, Palmer T S 2010 J. Comput. Phys. 229 5707Google Scholar

    [15]

    Densmore J D, Thompson K G, Urbatsch T J 2012 J. Comput. Phys. 231 6924Google Scholar

    [16]

    李树, 李刚, 田东风, 邓力 2013 物理学报 62 249501Google Scholar

    Li S, Li G, Tian D F, Deng L 2013 Acta Phys. Sin. 62 249501Google Scholar

    [17]

    李树, 陈耀华, 姬志成, 章明宇, 任国利, 霍文义, 闫威华, 韩小英, 李志超, 刘杰, 蓝可 2018 物理学报 67 025202Google Scholar

    Li S, Chen Y H, Ji Z C, Zhang M Y, Ren G L, Huo W Y, Yan W H, Han X Y, Li Z C, Liu J, Lan K 2018 Acta Phys. Sin. 67 025202Google Scholar

    [18]

    Mihalas D, Mihalas B W, Fu A, Arnett W D 1986 Phys. Today 39 90Google Scholar

    [19]

    谢仲生 2004 核反应堆物理分析 (西安: 西安交通大学出版社) 第62页

    Xie Z S 2004 Analysis of Nuclear Reactor Physics (Xi’an: Xi’an Jiaotong University Press) p62 (in Chinese)

    [20]

    Szilard R H, Pomraning G C 1992 Nucl. Sci. Eng. 112 256Google Scholar

    [21]

    Habetle G J, Matkowsky B J 1975 J. Math. Phys. 16 846Google Scholar

    [22]

    Densmore J D, Davidson G, Carrington D B 2006 Ann. Nucl. Energy 33 583Google Scholar

    [23]

    Cashwell E D, Everett C J 1959 A Practical Manual on the Monte Carlo Method for Random Walk Problem (London: Pergamon Press) p19

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出版历程
  • 收稿日期:  2019-08-31
  • 修回日期:  2019-10-30
  • 刊出日期:  2020-01-20

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