AN ASYMPTOTIC PRESERVING SCHEME FOR THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM IN THE HIGH FIELD REGIME

doi:10.1016/S0252-9602(11)60395-0

Abstract

Abstract:

The Vlasov-Poisson-Fokker-Planck system under the high field scaling de-scribes the Brownian motion of a large system of particles in a surrounding bath where both collision and field effects (electrical or gravitational) are dominant. Numerically solving this system becomes challenging due to the stiff collision term and stiff nonlinear transport term with respect to the high field. We present a class of Asymptotic-Preserving scheme which is efficient in the high field regime, namely, large time steps and coarse meshes can be used, yet the high field limit is still captured. The idea is to combine the two stiff terms and treat them implicitly. Thanks to the linearity of the collision term, using the discretization described in [Jin S, Yan B. J. Comp. Phys., 2011, 230: 6420-6437] we only need to invert a symmetric matrix. This method can be easily extended to higher dimensions. The method is shown to be positive, stable, mass and asymptotic preserv-ing. Numerical experiments validate its efficiency in both kinetic and high field regimes including mixing regimes.

Key words: Vlasov-Poisson-Fokker-Planck equation, high field limit, asymptotic-preserving schemes

CLC Number:

82D10

Shi Jin, Li Wang. AN ASYMPTOTIC PRESERVING SCHEME FOR THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM IN THE HIGH FIELD REGIME[J].Acta mathematica scientia,Series B, 2011, 31(6): 2219-2232.

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