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arXiv · 1803.04269

A Hybrid Discontinuous Galerkin Scheme for Multi-scale Kinetic Equations

Francis Filbet·Tao Xiong
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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.

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Francis Filbet, Tao Xiong. 2018-03-12. A Hybrid Discontinuous Galerkin Scheme for Multi-scale Kinetic Equations. https://doi.org/10.1016/j.jcp.2018.06.064

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