An explicit MUSCL scheme on staggered grids with kinetic-like fluxes for the barotropic and full Euler system

Thierry Goudon 1 Julie Llobell 2 Sebastian Minjeaud 3, 2
1 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
3 CASTOR - Control, Analysis and Simulations for TOkamak Research
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We present a second order scheme for the barotropic and full Euler equations. The scheme works on staggered grids, with numerical unknowns stored at dual locations, while the numerical fluxes are derived in the spirit of kinetic schemes. We identify stability conditions ensuring the positivity of the discrete density and energy. We illustrate the ability of the scheme to capture the structure of complex flows with 1d and 2d simulations on mac grids.
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Submitted on : Wednesday, November 6, 2019 - 10:24:05 AM
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Thierry Goudon, Julie Llobell, Sebastian Minjeaud. An explicit MUSCL scheme on staggered grids with kinetic-like fluxes for the barotropic and full Euler system. Communications in Computational Physics, Global Science Press, In press. ⟨hal-02350773⟩

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