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arXiv · 1810.11445

Asymptotic-preserving schemes for two-species binary collisional kinetic system with disparate masses I: time discretization and asymptotic analysis

Irene M. Gamba·Shi Jin·Liu Liu
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Abstract

We develop efficient asymptotic-preserving time discretization schemes to solve the disparate mass kinetic system of a binary gas or plasma in the "relaxation time scale" relevant to the epochal relaxation phenomenon. Since the resulting model is associated to a parameter given by the square of the mass ratio between the light and heavy particles, we develop an asymptotic-preserving scheme in a novel decomposition strategy using the penalization method for multiscale collisional kinetic equations. Both the Boltzmann and Fokker-Planck-Landau (FPL) binary collision operators will be considered. Other than utilizing several AP strategies for single-species binary kinetic equations, we also introduce a novel splitting and a carefully designed explicit-implicit approximation, which are guided by the asymptotic analysis of the system. We also conduct asymptotic-preserving analysis for the time discretization, for both space homogenous and inhomogeneous systems.

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Irene M. Gamba, Shi Jin, Liu Liu. 2018-10-26. Asymptotic-preserving schemes for two-species binary collisional kinetic system with disparate masses I: time discretization and asymptotic analysis. https://arxiv.org/abs/1810.11445

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