Numerical Validation for High Order Hyperbolic Moment System of Wigner Equation

Numerical Validation for High Order Hyperbolic Moment System of Wigner Equation

Year:    2014

Communications in Computational Physics, Vol. 15 (2014), Iss. 3 : pp. 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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.091012.120813a

Communications in Computational Physics, Vol. 15 (2014), Iss. 3 : pp. 569–595

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:   

  1. The Wigner function of ground state and one-dimensional numerics

    Zhan, Hongfei | Cai, Zhenning | Hu, Guanghui

    Journal of Computational Physics, Vol. 449 (2022), Iss. P.110780

    https://doi.org/10.1016/j.jcp.2021.110780 [Citations: 3]
  2. Solving Vlasov-Poisson-Fokker-Planck Equations using NRxx method

    Wang, Yanli | Zhang, Shudao

    Communications in Computational Physics, Vol. 21 (2017), Iss. 3 P.782

    https://doi.org/10.4208/cicp.220415.080816a [Citations: 4]
  3. An Advective-Spectral-Mixed Method for Time-Dependent Many-Body Wigner Simulations

    Xiong, Yunfeng | Chen, Zhenzhu | Shao, Sihong

    SIAM Journal on Scientific Computing, Vol. 38 (2016), Iss. 4 P.B491

    https://doi.org/10.1137/15M1051373 [Citations: 20]
  4. A Hybrid SBP-SAT/Fourier Pseudo-spectral Method for the Transient Wigner Equation Involving Inflow Boundary Conditions

    Sun, Zhangpeng | Yao, Wenqi | Yu, Qiuping

    Journal of Scientific Computing, Vol. 100 (2024), Iss. 2

    https://doi.org/10.1007/s10915-024-02582-6 [Citations: 0]
  5. Comparison of deterministic and stochastic methods for time-dependent Wigner simulations

    Shao, Sihong | Sellier, Jean Michel

    Journal of Computational Physics, Vol. 300 (2015), Iss. P.167

    https://doi.org/10.1016/j.jcp.2015.08.002 [Citations: 12]