数值计算与计算机应用
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数值计算与计算机应用  2018, Vol. 39 Issue (2): 111-134    DOI:
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求解Vlasov-Poisson方程组的一种时间分裂傅里叶谱方法
张志红1, 梁艳2, 王汉权1
1. 云南财经大学统计与数学学院, 昆明 650221;
2. 云南大学数学与统计学院, 昆明 650091
A TIME-SPLITTING-FOURIER SPECTRAL METHOD FOR VLASOV-POISSON SYSTEM
Zhang Zhihong1, Liang Yan2, Wang Hanquan1
1. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China;
2. School of Mathematics and Statistics, Yunnan University, Kunming 650091, China
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摘要 Vlasov-Poisson方程组是天体物理学和等离子体物理学的一类重要的动力学模型.本文为Vlasov-Poisson方程组设计了一种高效的数值计算方法——时间分裂傅里叶谱方法.在离散该方程组时,我们在时间方向采用时间分裂法,在空间变量方向和速度变量方向均采用傅里叶谱方法.本文首先对一维、二维Vlasov-Poisson方程组的四个守恒量做了分析和证明,然后分别用时间分裂傅里叶谱方法求解一维、二维的Vlasov-Poisson方程组,并给出了详细的算法求解过程.最后通过数值模拟结果证实该方法的准确性和可靠性,并验证了四个守恒量.
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关键词Vlasov-Poisson方程组   时间分裂傅里叶谱方法   守恒律   数值计算     
Abstract: Vlasov-Poisson system is a kind of important mechanical model of astrophysics and plasma physics. This paper will propose a highly efficient numerical calculation method for Vlasov-Poisson system, which is the time-splitting-Fourier spectral method. We use timesplitting scheme in time direction and Fourier spectral method in the space variable direction and speed variable direction to discretize the equations. We firstly analyze and prove the four conservation laws of the one and two dimension of Vlasov-Poisson equations. Secondly, we give the detailed algorithm on how to solve one and two dimensional of Vlasov-Poisson system respectively. Finally, we show the numerical accuracy and reliability of the proposed method from the numerical results.
Key wordsVlasov-Poisson system   splitting-Fourier spectral method   conservation laws   numerical computation   
收稿日期: 2017-06-07;
基金资助:

本文受国家自然科学基金(11261065、91430103)和教育部新世纪优秀人才基金(NCET-13-0995)资助.

引用本文:   
. 求解Vlasov-Poisson方程组的一种时间分裂傅里叶谱方法[J]. 数值计算与计算机应用, 2018, 39(2): 111-134.
. A TIME-SPLITTING-FOURIER SPECTRAL METHOD FOR VLASOV-POISSON SYSTEM[J]. Journal of Numerical Methods and Computer Applicat, 2018, 39(2): 111-134.
 
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