Issue |
ESAIM: M2AN
Volume 58, Number 4, July-August 2024
|
|
---|---|---|
Page(s) | 1263 - 1299 | |
DOI | https://doi.org/10.1051/m2an/2024035 | |
Published online | 19 July 2024 |
An explicit well-balanced scheme on staggered grids for barotropic Euler equations
Université Côte d’Azur, CNRS, Inria, LJAD, Parc Valrose, 06108 Nice, France
* Corresponding author: Sebastian.MINJEAUD@unice.fr
Received:
4
May
2023
Accepted:
7
May
2024
In this paper, we introduce a specific modification of the numerical fluxes in order to insure the well-balanced property of schemes on staggered grids for the Euler equations. This property is crucial for the numerical representation of equilibrium solutions of balance laws with source terms, like when describing flows subjected to gravity and a complex topography. We propose first and second order versions of the well-balanced scheme. The performances of the method are evaluated through a series of 1D and 2D benchmarks.
Mathematics Subject Classification: 65M08 / 76M12 / 76NXX / 35Q31
Key words: Finite volume schemes / staggered grids / well-balanced schemes / balance laws / shallow-Water
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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