球坐标动量空间下相对论Vlasov方程的数值算法

计算物理 ›› 2017, Vol. 34 ›› Issue (5): 543-554.

所属专题：超强激光等离子体相互作用的数值模拟

• 专题:超强激光等离子体相互作用的数值模拟 • 上一篇下一篇

球坐标动量空间下相对论Vlasov方程的数值算法

张华^1,2, 吴思忠¹, 周沧涛^1,2, 何民卿¹, 蔡洪波^1,2, 曹莉华^1,2, 朱少平¹, 贺贤土^1,2

1. 北京应用物理与计算数学研究所, 北京 100094;
2. 北京大学应用物理与技术中心, 北京 100871

收稿日期:2017-03-30 出版日期:2017-09-25 发布日期:2017-09-25
作者简介:张华(1977-),男,博士,副研究员,从事激光等离子体数值模拟研究,E-mail:zhang_hua@iapcm.ac.cn
基金资助:
大科学装置国家重点研发计划（2016YFA0401100）及国家自然科学基金（91230205，11575031）资助项目

Numerical Method for Relativistic Vlasov Equation in Cartesian-Spherical Coordinate System

ZHANG Hua^1,2, WU Sizhong¹, ZHOU Cangtao^1,2, HE Minqing¹, CAI Hongbo^1,2, CAO Lihua^1,2, ZHU Shaoping¹, HE Xiantu^1,2

1. Institute of Applied Physics and Computational Mathematics, Beijing, 100094, China;
2. Center of Applied Physical Technology, Peking University, Beijing 100871, China

Received:2017-03-30 Online:2017-09-25 Published:2017-09-25

摘要/Abstract

摘要： 针对相对论Vlasov方程动量区间跨度大、难以计算的困难，将相对论Vlasov方程在球坐标动量空间中进行数值求解.对相对论Vlasov方程球坐标动量空间构造4阶非分裂守恒型数值格式.数值模拟相对论Landau阻尼问题并与解析理论进行比较，验证数值模型和算法的有效性.对激光等离子体相互作用进行初步模拟分析，表明通过采用球坐标下的动量空间，可在相对较少动量网格情形下，获得与粒子模拟可相互验证的结果.

关键词: 相对论Vlasov方程, 相对论Landau阻尼, 等离子体

Abstract: We study numerical method for relativistic Vlasov equation and present a scheme for computing Vlasov equation based on Cartesian-spherical coordinate system, which can be used to reduce number of numerical grid for momentum space. Furthermore, a 4th order non-splitting finite volume scheme is proposed in order to solve momentum parts of relativistic Vlasov equation. In test problems, especially relativistic Landau problem, laser-plasma interaction are solved by using the scheme. We confirm the scheme with theoretically analysis as well as numerical comparison with results of PIC method.

Key words: relativistic Vlasov equation, relativistic Landau damping, plasma

中图分类号:

张华, 吴思忠, 周沧涛, 何民卿, 蔡洪波, 曹莉华, 朱少平, 贺贤土. 球坐标动量空间下相对论Vlasov方程的数值算法[J]. 计算物理, 2017, 34(5): 543-554.

ZHANG Hua, WU Sizhong, ZHOU Cangtao, HE Minqing, CAI Hongbo, CAO Lihua, ZHU Shaoping, HE Xiantu. Numerical Method for Relativistic Vlasov Equation in Cartesian-Spherical Coordinate System[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(5): 543-554.

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球坐标动量空间下相对论Vlasov方程的数值算法

Numerical Method for Relativistic Vlasov Equation in Cartesian-Spherical Coordinate System

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