搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

高温热辐射输运模拟的蒙特卡罗全局降方差方法

李树 王旸 姬志成 蓝可

引用本文:
Citation:

高温热辐射输运模拟的蒙特卡罗全局降方差方法

李树, 王旸, 姬志成, 蓝可

Global variance reduction method for Monte Carlo simulation of thermal radiation transport

Li Shu, Wang Yang, Ji Zhi-Cheng, Lan Ke
PDF
HTML
导出引用
  • 针对隐式蒙特卡罗方法模拟高温热辐射输运问题时存在的“辐射强度计算误差时间空间分布严重不均匀”现象, 通过理论分析和数值模拟手段, 找到决定误差大小的主要因素为“网格内的辐射径迹长度记录数”. 据此提出“隐式蒙特卡罗全局降方差方法”并推导相应的计算公式. 该方法主要包含如下3个关键技术: 1)针对辐射输运蒙特卡罗模拟的自适应动态分配源粒子方法; 2)与自适应动态分配源粒子相匹配的动态权窗设计技术及粒子权无偏估计算法; 3)辐射强度的解析估计降方差方法. 针对这3个关键技术, 设计蒙特卡罗数值模拟方案, 编写相应的数值模拟程序模块. 典型辐射输运问题模拟结果显示: 隐式蒙特卡罗全局降方差方法能够使网格辐射强度计算误差在整个时空范围内分布相对比较均匀, 最大误差可控, 计算效率提升10倍左右. 新方法在激光惯性约束聚变的黑腔辐射输运模拟应用中取得了显著效果.
    The implicit Monte Carlo (IMC) method is an important numerical approximation method of simulating the thermal radiative transfer problems under high temperature condition. However, one problem plaguing the IMC method is that the calculation error distributions of the radiation specific intensities are highly asymmetric in space and time. By theoretical analysis and numerical simulations, we find that the error is affected by the records of track in the tallying mesh. Accordingly, a global variance reduction method for implicit Monte Carlo simulation is developed and the corresponding formulas are derived. This method includes three key techniques: 1) the automated dynamic distribution method for the Monte Carlo simulation source particles; 2) the dynamic weight-window technique and the none-bias weight revise algorithm that is suited to the particle distribution method; 3) the analytical estimation variance reduction method of the radiation specific intensity. In view of the above, a three-dimensional simulation code, named IMC3D, is developed to simulate the thermal radiative transfer phenomena. The typical thermal radiative transport problem, known as Marshak wave, is simulated. The simulation results indicate that the global variance reduction method for implicit Monte Carlo makes the statistical errors much more symmetric in space and time and the maximum of error is controllable, thereby increasing the calculation speed approximately 10 times. The new IMC method and code are used for simulating the radiative transportation in hohlraum of ICF successfully.
      通信作者: 李树, li_shu@iapcm.ac.cn
    • 基金项目: 国家自然科学基金(批准号: 12035002)和中国工程物理研究院于敏基金(批准号: FZ025)资助的课题.
      Corresponding author: Li Shu, li_shu@iapcm.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12035002) and the Yu Min Foundation of China Academy of Engineering Physics, China (Grant No. FZ025).
    [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39, 232页

    Peng H M 2008 Radiation Transport and Radiation Hydrodynamics in Plasmas (Beijing: National Defense Industry Press) pp39, 232

    [2]

    Lindl J D 1995 Phys. Plasmas 2 3933Google Scholar

    [3]

    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—9页

    Zhang J, Chang T Q 2004 Fundaments of the Target Physics for Laser Fusion (Beijing: National Defense Industry Press) pp1–9 (in Chinese)

    [4]

    阿采尼, 迈尔·特尔·费恩 著 (沈百飞译) 2008 惯性聚变物理 (北京: 科学出版社) 第23, 254页

    Stefano Atzeni, Jurgen Meyer-ter-Vehn (translated by Shen B F) 2008 The Physics of Inertial Fusion (Beijing: Science Press) pp23, 254 (in Chinese)

    [5]

    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1—20页

    Pei L C, Zhang X Z 1980 Monte Carlo Method and Application in Particle Transportation (Beijing: Science Press) pp1–20 (in Chinese)

    [6]

    Kalos M H, Whitlock P A 2022 Monte Carlo Methods (Weinheim: WILEY-VCH Verlag GmbH & Co KGaA) pp1–34

    [7]

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

    [8]

    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 LA-UR-05-3781

    [9]

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

    [10]

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

    [11]

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

    [12]

    Cleveland M A, Wollaber A B 2018 J. Comput. Phys. 359 20Google Scholar

    [13]

    Marinak M M, Remington B A, Weber S V, Tipton R E, Haan S W, Budil K S, Landen O L, Kilkenny J D, Wallace R 1995 Phys. Rev. Lett. 75 3677Google Scholar

    [14]

    Rathkopf J A, Miller D S, Owen J M, et al. 2000 KULL: LLNL's ASCI Inertial Confinement Fusion Simulation Code (Livermore: Lawrence Livermore National Laboratory) UCRL-JC-137053

    [15]

    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

    [16]

    李树, 邓力, 田东风, 李刚 2014 物理学报 63 239501Google Scholar

    Li S, Deng L, Tian D F, Li G 2014 Acta Phys. Sin. 63 239501Google Scholar

    [17]

    李树, 蓝可, 赖东显, 刘杰 2015 物理学报 64 145203Google Scholar

    Li S, Lan K, Lai D X Liu J 2015 Acta Phys. Sin. 64 145203Google Scholar

    [18]

    Li S, Lan K, Liu J 2015 Laser Part. Beams 33 731Google Scholar

    [19]

    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

    [20]

    Marshak R E 1958 Phys. Fluids 1 24Google Scholar

    [21]

    Pomraning G C 1979 J. Quant. Spectrosc. Radiat. Transfer 21 249Google Scholar

    [22]

    Hurricane O A, Hammer J H 2006 Phys. Plasmas 13 113303Google Scholar

    [23]

    Cooper M A 1999 Ph. D. Dissertation (Ann Arbor: University of Michigan)

    [24]

    Lan K, Liu J, Lai D X, Zheng W D, He X T 2014 Phys. Plasmas 21 010704Google Scholar

    [25]

    Huo W Y, Liu J, Zhao Y Q, Zheng W D, Lan K 2014 Phys. Plasmas 21 114503Google Scholar

    [26]

    Lan K, Liu J,  Li Z, et al. 2016 Matter and Radiation at Extremes 1 8Google Scholar

    [27]

    Haan S W, Lindl J D,  Callahan D A, et al. 2011 Phys. Plasmas 18 051001Google Scholar

    [28]

    Cao H, Chen Y H, Zhai C L, Zheng C Y, Lan K 2017 Phys. Plasmas 24 082701Google Scholar

  • 图 1  Marshak波辐射温度分布(104粒子/步)

    Fig. 1.  Radiation temperature for the Marshak wave (104 particles/step).

    图 2  Marshak波辐射温度误差分布(105粒子/步)

    Fig. 2.  Statistical error of radiation temperature for the Marshak wave (105 particles/step).

    图 3  Marshak波辐射温度分布(105粒子/步)

    Fig. 3.  Radiation temperature for the Marshak wave (105 particles/step).

    图 4  Marshak波辐射温度误差分布(105粒子/步)

    Fig. 4.  Statistical error of radiation temperature for the Marshak wave (105 particles/step).

    图 5  3个时刻的MC模拟源粒子分布

    Fig. 5.  MC simulated source particles for three time step.

    图 6  3个时刻的辐射强度误差分布

    Fig. 6.  Statistical error of radiation intensity for different time step.

    图 7  基于权窗的轮盘赌和分裂技术示意图

    Fig. 7.  Weight window with splitting and Russian Roulette.

    图 8  解析估计示意图

    Fig. 8.  Analytical estimation for specific intensity tally.

    图 9  源粒子分配数比较(old vs. new 1)

    Fig. 9.  Comparison of the source particles (old vs. new 1).

    图 10  误差分布比较(old vs. new 1)

    Fig. 10.  Comparison of statistical error (old vs. new 1).

    图 11  源粒子分配数比较(old vs. new 2)

    Fig. 11.  Comparison of the source particles (old vs. new 2).

    图 12  误差分布比较(old vs. new 2)

    Fig. 12.  Comparison of statistical error (old vs. new 2).

    图 13  误差分布比较(new 2 vs. new 3)

    Fig. 13.  Comparison of statistical error (new 2 vs. new 3)

    图 14  误差分布比较(old vs. new 3)

    Fig. 14.  Comparison of statistical error (old vs. new 3).

    图 15  六孔球腔网格剖分图

    Fig. 15.  Profile of the octahedral spherical hohlraum.

    图 16  黑腔壁光斑分布

    Fig. 16.  Spots on the wall of the hohlraum.

    图 17  激光能源注入强度曲线

    Fig. 17.  Curve of laser power inject to the intensity.

    图 18  黑腔辐射温度曲线比较(IMC3D vs. Haan[27])

    Fig. 18.  Comparison of the radiation temperature (IMC3D vs. Haan[27]).

    表 1  计算时间及计算效率比较

    Table 1.  Comparison of calculated CPU time and efficiency.

    原方法情况I情况II情况III
    实际计算时间/min606852863971
    时间比值(情况x/原方法)1.01.41.41.6
    7.4 ns时刻波头误差0.060110.027990.021790.01445
    等效计算时间/min60618511356
    效率提升(情况x/原方法)1.03.275.3610.82
    : 等效时间折算方法. 根据“误差与源粒子数的1/2次方呈反比”、“源粒子数与计算时间呈正比”原则, 在误差相等条件下, 等效 时间 = 情况 x 实际计算时间×(情况 x 误差的2次方/原方法误差的2次方).
    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39, 232页

    Peng H M 2008 Radiation Transport and Radiation Hydrodynamics in Plasmas (Beijing: National Defense Industry Press) pp39, 232

    [2]

    Lindl J D 1995 Phys. Plasmas 2 3933Google Scholar

    [3]

    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—9页

    Zhang J, Chang T Q 2004 Fundaments of the Target Physics for Laser Fusion (Beijing: National Defense Industry Press) pp1–9 (in Chinese)

    [4]

    阿采尼, 迈尔·特尔·费恩 著 (沈百飞译) 2008 惯性聚变物理 (北京: 科学出版社) 第23, 254页

    Stefano Atzeni, Jurgen Meyer-ter-Vehn (translated by Shen B F) 2008 The Physics of Inertial Fusion (Beijing: Science Press) pp23, 254 (in Chinese)

    [5]

    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1—20页

    Pei L C, Zhang X Z 1980 Monte Carlo Method and Application in Particle Transportation (Beijing: Science Press) pp1–20 (in Chinese)

    [6]

    Kalos M H, Whitlock P A 2022 Monte Carlo Methods (Weinheim: WILEY-VCH Verlag GmbH & Co KGaA) pp1–34

    [7]

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

    [8]

    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 LA-UR-05-3781

    [9]

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

    [10]

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

    [11]

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

    [12]

    Cleveland M A, Wollaber A B 2018 J. Comput. Phys. 359 20Google Scholar

    [13]

    Marinak M M, Remington B A, Weber S V, Tipton R E, Haan S W, Budil K S, Landen O L, Kilkenny J D, Wallace R 1995 Phys. Rev. Lett. 75 3677Google Scholar

    [14]

    Rathkopf J A, Miller D S, Owen J M, et al. 2000 KULL: LLNL's ASCI Inertial Confinement Fusion Simulation Code (Livermore: Lawrence Livermore National Laboratory) UCRL-JC-137053

    [15]

    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

    [16]

    李树, 邓力, 田东风, 李刚 2014 物理学报 63 239501Google Scholar

    Li S, Deng L, Tian D F, Li G 2014 Acta Phys. Sin. 63 239501Google Scholar

    [17]

    李树, 蓝可, 赖东显, 刘杰 2015 物理学报 64 145203Google Scholar

    Li S, Lan K, Lai D X Liu J 2015 Acta Phys. Sin. 64 145203Google Scholar

    [18]

    Li S, Lan K, Liu J 2015 Laser Part. Beams 33 731Google Scholar

    [19]

    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

    [20]

    Marshak R E 1958 Phys. Fluids 1 24Google Scholar

    [21]

    Pomraning G C 1979 J. Quant. Spectrosc. Radiat. Transfer 21 249Google Scholar

    [22]

    Hurricane O A, Hammer J H 2006 Phys. Plasmas 13 113303Google Scholar

    [23]

    Cooper M A 1999 Ph. D. Dissertation (Ann Arbor: University of Michigan)

    [24]

    Lan K, Liu J, Lai D X, Zheng W D, He X T 2014 Phys. Plasmas 21 010704Google Scholar

    [25]

    Huo W Y, Liu J, Zhao Y Q, Zheng W D, Lan K 2014 Phys. Plasmas 21 114503Google Scholar

    [26]

    Lan K, Liu J,  Li Z, et al. 2016 Matter and Radiation at Extremes 1 8Google Scholar

    [27]

    Haan S W, Lindl J D,  Callahan D A, et al. 2011 Phys. Plasmas 18 051001Google Scholar

    [28]

    Cao H, Chen Y H, Zhai C L, Zheng C Y, Lan K 2017 Phys. Plasmas 24 082701Google Scholar

  • [1] 刘庆康, 张旭, 蔡洪波, 张恩浩, 高妍琦, 朱少平. 强度调制宽带激光对受激拉曼散射动理学爆发的抑制. 物理学报, 2024, 73(5): 055202. doi: 10.7498/aps.73.20231679
    [2] 熊皓, 钟哲强, 张彬, 隋展, 张小民. 基于束间动态干涉的快速匀滑新方法. 物理学报, 2020, 69(6): 064206. doi: 10.7498/aps.69.20190962
    [3] 许育培, 李树. 球几何中辐射源粒子抽样方法的改进. 物理学报, 2020, 69(11): 119501. doi: 10.7498/aps.69.20200024
    [4] 许育培, 李树. 热辐射输运问题的高效蒙特卡罗模拟方法. 物理学报, 2020, 69(2): 029501. doi: 10.7498/aps.69.20191315
    [5] 杨钧兰, 钟哲强, 翁小凤, 张彬. 惯性约束聚变装置中靶面光场特性的统计表征方法. 物理学报, 2019, 68(8): 084207. doi: 10.7498/aps.68.20182091
    [6] 赵英奎, 欧阳碧耀, 文武, 王敏. 惯性约束聚变中氘氚燃料整体点火与燃烧条件研究. 物理学报, 2015, 64(4): 045205. doi: 10.7498/aps.64.045205
    [7] 李树, 李刚, 田东风, 邓力. 热辐射输运问题的隐式蒙特卡罗方法求解. 物理学报, 2013, 62(24): 249501. doi: 10.7498/aps.62.249501
    [8] 晏骥, 郑建华, 陈黎, 林稚伟, 江少恩. X射线相衬成像技术应用于高能量密度物理条件下内爆靶丸诊断. 物理学报, 2012, 61(14): 148701. doi: 10.7498/aps.61.148701
    [9] 景龙飞, 黄天晅, 江少恩, 陈伯伦, 蒲昱东, 胡峰, 程书博. 神光-Ⅱ和神光-Ⅲ原型内爆对称性实验的模型分析. 物理学报, 2012, 61(10): 105205. doi: 10.7498/aps.61.105205
    [10] 宋天明, 易荣清, 崔延莉, 于瑞珍, 杨家敏, 朱托, 侯立飞, 杜华冰. ICF实验软X射线能谱仪对辐射能流时间关联测量的时标系统. 物理学报, 2012, 61(7): 075208. doi: 10.7498/aps.61.075208
    [11] 张占文, 漆小波, 李波. 惯性约束聚变点火靶候选靶丸特点及制备研究进展. 物理学报, 2012, 61(14): 145204. doi: 10.7498/aps.61.145204
    [12] 晏骥, 江少恩, 苏明, 巫顺超, 林稚伟. X射线相衬成像应用于惯性约束核聚变多层球壳靶丸检测. 物理学报, 2012, 61(6): 068703. doi: 10.7498/aps.61.068703
    [13] 占江徽, 姚欣, 高福华, 阳泽健, 张怡霄, 郭永康. 惯性约束聚变驱动器连续相位板前置时频率转换晶体内部光场研究. 物理学报, 2011, 60(1): 014205. doi: 10.7498/aps.60.014205
    [14] 张锐, 王建军, 粟敬钦, 刘兰琴, 丁磊, 唐军, 刘华, 景峰, 张小民. 基于波导相位调制器的光谱色散平滑技术实验研究. 物理学报, 2010, 59(9): 6290-6298. doi: 10.7498/aps.59.6290
    [15] 张锐, 王建军, 粟敬钦, 刘兰琴, 邓青华. 基于线性调频脉冲的光谱色散平滑技术实验研究. 物理学报, 2010, 59(2): 1088-1094. doi: 10.7498/aps.59.1088
    [16] 程文雍, 张小民, 粟敬钦, 赵圣之, 董军, 李平, 周丽丹. 利用运动光束抑制高功率激光小尺度自聚焦. 物理学报, 2009, 58(10): 7012-7016. doi: 10.7498/aps.58.7012
    [17] 姚欣, 高福华, 高博, 张怡霄, 黄利新, 郭永康, 林祥棣. 惯性约束聚变驱动器终端束匀滑器件前置时频率转换系统优化研究. 物理学报, 2009, 58(7): 4598-4604. doi: 10.7498/aps.58.4598
    [18] 姚欣, 高福华, 张怡霄, 温圣林, 郭永康, 林祥棣. 激光惯性约束聚变驱动器终端光学系统中束匀滑器件前置的条件研究. 物理学报, 2009, 58(5): 3130-3134. doi: 10.7498/aps.58.3130
    [19] 姚 欣, 高福华, 李剑峰, 张怡霄, 温圣林, 郭永康. 光束取样光栅强激光近场调制及诱导损伤研究. 物理学报, 2008, 57(8): 4891-4897. doi: 10.7498/aps.57.4891
    [20] 姚 欣, 高福华, 温圣林, 张怡霄, 李剑峰, 郭永康. 谐波分离和光束取样集成光学元件强激光近场调制及损伤特性研究. 物理学报, 2007, 56(12): 6945-6953. doi: 10.7498/aps.56.6945
计量
  • 文章访问数:  2040
  • PDF下载量:  74
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-02-16
  • 修回日期:  2023-05-04
  • 上网日期:  2023-05-05
  • 刊出日期:  2023-07-05

/

返回文章
返回