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Solving Vlasov-Poisson-Fokker-Planck Equations using NRxx method

Part of: Numerical analysis: Ordinary differential equations Equations of mathematical physics and other areas of application Optics, electromagnetic theory - Basic methods

Published online by Cambridge University Press:  07 February 2017

Yanli Wang  and
Shudao Zhang
Yanli Wang*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, P.R. China
Shudao Zhang*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, P.R. China
*
*Corresponding author. Email addresses:wang_yanli@iapcm.ac.cn (Y. Wang), zhang_shudao@iapcm.ac.cn (S. Zhang)
*Corresponding author. Email addresses:wang_yanli@iapcm.ac.cn (Y. Wang), zhang_shudao@iapcm.ac.cn (S. Zhang)
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Abstract

We present a numerical method to solve the Vlasov-Poisson-Fokker-Planck (VPFP) system using the NRxx method proposed in [4, 7, 9]. A globally hyperbolic moment system similar to that in [23] is derived. In this system, the Fokker-Planck (FP) operator term is reduced into the linear combination of the moment coefficients, which can be solved analytically under proper truncation. The non-splitting method, which can keep mass conservation and the balance law of the total momentum, is used to solve the whole system. A numerical problem for the VPFP system with an analytic solution is presented to indicate the spectral convergence with the moment number and the linear convergence with the grid size. Two more numerical experiments are tested to demonstrate the stability and accuracy of the NRxx method when applied to the VPFP system.

Keywords

Moment closureFokker-Planck operatorVPFP systemspectral convergence

MSC classification

Secondary: 35Q83: Vlasov-like equations 65L20: Stability and convergence of numerical methods 78M05: Method of moments
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 3 , March 2017 , pp. 782 - 807
Copyright
Copyright © Global-Science Press 2017 

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