A Hybrid Discontinuous Galerkin Scheme for Multi-scale Kinetic Equations

Francis Filbet (1) , Tao Xiong (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Xiamen University

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.

Domaines: Analyse numérique [math.NA]

Francis Filbet, Tao Xiong. A Hybrid Discontinuous Galerkin Scheme for Multi-scale Kinetic Equations. Journal of Computational Physics, 2018, 372, pp.841-863. ⟨10.1016/j.jcp.2018.06.064⟩. ⟨hal-01718000⟩