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

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

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (6): 2219-2232.doi: 10.1016/S0252-9602(11)60395-0

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

Shi Jin^1,2, Li Wang²

1. Department of Mathematics, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 20040, China;
2. Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706, USA

收稿日期:2011-08-13 出版日期:2011-11-20 发布日期:2011-11-20
基金资助:
This research was partially supported by NSF grant No. DMS-0608720, and NSF FRG grant DMS-0757285. SJ was also supported by a Van Vleck Distinguished Research Prize and a Vilas Associate Award from University of Wisconsin-Madison.

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

Shi Jin^1,2, Li Wang²

1. Department of Mathematics, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 20040, China;
2. Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706, USA

Received:2011-08-13 Online:2011-11-20 Published:2011-11-20
Supported by:
This research was partially supported by NSF grant No. DMS-0608720, and NSF FRG grant DMS-0757285. SJ was also supported by a Van Vleck Distinguished Research Prize and a Vilas Associate Award from University of Wisconsin-Madison.

摘要/Abstract

摘要：

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.

关键词: Vlasov-Poisson-Fokker-Planck equation, high field limit, asymptotic-preserving schemes

Abstract:

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

中图分类号:

82D10

Shi Jin, Li Wang. AN ASYMPTOTIC PRESERVING SCHEME FOR THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM IN THE HIGH FIELD REGIME[J]. 数学物理学报(英文版), 2011, 31(6): 2219-2232.

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

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

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