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Conference Papers Year : 2023

A MUSCL-scheme on staggered grids for the Euler equations on unstructured meshes

Abstract

We set up a MUSCL approach for the 2D DDFV-like scheme introduced in [Goudon, Llobell, Minjeaud, 2022] for the full Euler equations, discretized with unstructured meshes. It is a finite volume staggered discretization framework where numerical densities, energies and velocities are stored on different locations. For the MUSCL scheme, a combination of several approaches is needed for the reconstruction of the densities and the velocities, in order to reach the second order accuracy. This work focuses on the reconstruction of the mass density and internal energy. The improved accuracy is already sensitive on problems containing contact discontinuities. We provide a set of numerical simulations to illustrate the enhanced accuracy.
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hal-04294739 , version 1 (20-11-2023)

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Charbel Ghosn, Thierry Goudon, Sebastian Minjeaud. A MUSCL-scheme on staggered grids for the Euler equations on unstructured meshes. FVCA 2023 - International Conference on Finite Volumes for Complex Applications, Oct 2023, Strasbourg, France. pp.141--149, ⟨10.1007/978-3-031-40860-1_15⟩. ⟨hal-04294739⟩
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