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A Hybrid Discontinuous Galerkin Scheme for Multi-scale Kinetic Equations

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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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      A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier–Stokes Equations

       S. Rebay,  F Bassi (1997)
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        Fluid dynamic limits of kinetic equations. I. Formal derivations

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          High-Order Accurate Discontinuous Finite Element Solution of the 2D Euler Equations

           F Bassi,  S. Rebay (1997)
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            Author and article information

            Journal
            12 March 2018
            1803.04269

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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            math.NA
            ccsd

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