A Hybrid Discontinuous Galerkin Scheme for Multi-scale Kinetic Equations

TL;DR

This paper introduces a hybrid discontinuous Galerkin method for multi-scale kinetic equations, enabling model selection and efficient numerical flux computation, demonstrated through various numerical simulations.

Contribution

It presents a novel multi-dimensional hybrid DG scheme utilizing moment realizability matrices for model selection and flux approximation in multi-scale kinetic problems.

Findings

Effective model selection indicator developed

Numerical flux constructed for asymptotic fluid limit

Numerical simulations validate method performance

Abstract

We develop a multi-dimensional hybrid discontinuous Galerkin method for multi-scale kinetic equations. This method is based on moment realizability matrices, a concept introduced by D. Levermore, W. Morokoff and B. Nadiga for one dimensional problem. The main issue addressed in this paper is to provide a simple indicator to select the most appropriate model and to apply a compact numerical scheme to reduce the interface region between different models. We also construct a numerical flux for the fluid model obtained as the asymptotic limit of the flux of the kinetic equation. Finally we perform several numerical simulations for time evolution and stationary problems.