A Hybrid Discontinuous Galerkin Scheme for Multi-scale Kinetic Equations
This work addresses the challenge of efficiently simulating multi-scale kinetic equations, which is important for computational physics, but the results appear incremental as they extend existing one-dimensional concepts to multiple dimensions.
The authors develop a hybrid discontinuous Galerkin method for multi-scale kinetic equations using moment realizability matrices, introducing a simple model-selection indicator and a compact numerical scheme to reduce interface regions. Numerical simulations demonstrate effectiveness for time evolution and stationary problems.
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.