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Numerical Validation for High Order Hyperbolic Moment System of Wigner Equation

Published online by Cambridge University Press:  03 June 2015

Ruo Li,
Tiao Lu,
Yanli Wang and
Wenqi Yao
Ruo Li*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P.R. ChinaHEDPS and LMAM, Peking University, Beijing 100871, P.R. ChinaCAPT, Peking University, Beijing 100871, P.R. China
Tiao Lu*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P.R. ChinaHEDPS and LMAM, Peking University, Beijing 100871, P.R. ChinaCAPT, Peking University, Beijing 100871, P.R. China
Yanli Wang*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P.R. ChinaBICMR, Peking University, Beijing 100871, P.R. ChinaCAPT, Peking University, Beijing 100871, P.R. China
Wenqi Yao*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China
*
Email:rli@math.pku.edu.cn
Corresponding author.Email:tlu@math.pku.edu.cn
Email:wangyanliwyl@gmail.com
Email:albee0926@sina.com
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Abstract

A globally hyperbolic moment system upto arbitrary order for the Wigner equation was derived in [6]. For numerically solving the high order hyperbolic moment system therein, we in this paper develop a preliminary numerical method for this system following the NRxx method recently proposed in [8], to validate the moment system of the Wigner equation. The method developed can keep both mass and momentum conserved, and the variation of the total energy under control though it is not strictly conservative. We systematically study the numerical convergence of the solution to the moment system both in the size of spatial mesh and in the order of the moment expansion, and the convergence of the numerical solution of the moment system to the numerical solution of the Wigner equation using the discrete velocity method. The numerical results indicate that the high order moment system in [6] is a valid model for the Wigner equation, and the proposed numerical method for the moment system is quite promising to carry out the simulation of the Wigner equation.

Keywords

82C1081-0847A57Wigner equationNRxx methodmoment method

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Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 3 , March 2014, pp. 569 - 595
Copyright
Copyright © Global Science Press Limited 2014

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