Abstract
We propose in this paper a formally second order scheme for the numerical simulation of the shallow water equations in two space dimensions, based on the so-called Marker-And-Cell (MAC) staggered discretization on non uniform grids. For the space discretization, we use a MUSCL-like scheme for the convection operators while the pressure gadient is centered; time discretization is performed with the Heun scheme. The scheme preserves the positivity of the water height and “lake at rest” steady states. Its consistency in the Lax-Wendroff sense is proven.
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Gallouët, T., Herbin, R., Latché, JC., Nasseri, Y. (2020). A Second Order Consistent MAC Scheme for the Shallow Water Equations on Non Uniform Grids. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_9
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DOI: https://doi.org/10.1007/978-3-030-43651-3_9
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