Commun. Comput. Phys., 15 (2014), pp. 569-595.


Numerical Validation for High Order Hyperbolic Moment System of Wigner Equation

Ruo Li 1, Tiao Lu 1*, Yanli Wang 2, Wenqi Yao 3

1 School of Mathematical Sciences, HEDPS and LMAM, CAPT, Peking University, Beijing 100871, P.R. China.
2 School of Mathematical Sciences, BICMR, CAPT, Peking University, Beijing 100871, P.R. China.
3 School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China.

Received 9 October 2012; Accepted (in revised version) 12 August 2013
Available online 18 October 2013
doi:10.4208/cicp.091012.120813a

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.

AMS subject classifications: 82C10, 81-08, 47A57

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Key words: Wigner equation, NRxx method, moment method.

*Corresponding author.
Email: rli@math.pku.edu.cn (R. Li), tlu@math.pku.edu.cn (T. Lu), wangyanliwyl@gmail.com (Y. Wang), albee0926@sina.com (W. Yao)
 

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