Multiscale Computations for Kinetic and Related Problems

Asymptotic analyses for the study of asymptotic-preserving schemes for two-species collisional plasma with disparate masses

Liu Liu

University of Texas at Austin

In this talk, we will introduce an efficient, asymptotic-preserving (AP) numerical method to study the dynamics of a disparate mass binary gas or of a plasma in both the homogeneous and inhomogeneous case, at relaxation time scale, in the framework of the Boltzmann or Fokker-Planck-Landau equation. We rigorously prove that our numerical scheme is AP, meaning that the limit of our discretized numerical scheme is consistent with the implicit scheme of the continuous limit system shown by Degond and Desreux and other physicists. There are several original and new ideas used in designing the scheme, and it provides a rigorous foundation for the (ongoing) numerical implementation of AP schemes to the so-called "epochal relaxation phenomenon" first pointed by Grad. This is a joint work with Shi Jin and Irene Gamba.