Volume 15, Issue 3
Numerical Validation for High Order Hyperbolic Moment System of Wigner Equation

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

Published online: 2014-03

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• Abstract

A globally hyperbolic moment system up to 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 NR$xx$ method recently proposed in [8], to validate the moment system of the Wigner equation. The developed method 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.

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@Article{CiCP-15-569, author = {}, title = {Numerical Validation for High Order Hyperbolic Moment System of Wigner Equation}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {3}, pages = {569--595}, abstract = {

A globally hyperbolic moment system up to 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 NR$xx$ method recently proposed in [8], to validate the moment system of the Wigner equation. The developed method 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.091012.120813a}, url = {http://global-sci.org/intro/article_detail/cicp/7106.html} }
TY - JOUR T1 - Numerical Validation for High Order Hyperbolic Moment System of Wigner Equation JO - Communications in Computational Physics VL - 3 SP - 569 EP - 595 PY - 2014 DA - 2014/03 SN - 15 DO - http://doi.org/10.4208/cicp.091012.120813a UR - https://global-sci.org/intro/article_detail/cicp/7106.html KW - AB -

A globally hyperbolic moment system up to 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 NR$xx$ method recently proposed in [8], to validate the moment system of the Wigner equation. The developed method 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.

Ruo Li, Tiao Lu, Yanli Wang & Wenqi Yao. (2020). Numerical Validation for High Order Hyperbolic Moment System of Wigner Equation. Communications in Computational Physics. 15 (3). 569-595. doi:10.4208/cicp.091012.120813a
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