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Interplay Between Diffusion Anisotropy and Mesh Skewness in Hybrid High-Order Schemes Read chapter Read first chapter

2020 | OriginalPaper | Chapter

A Second Order Consistent MAC Scheme for the Shallow Water Equations on Non Uniform Grids

Authors : T. Gallouët, R. Herbin, J.-C. Latché, Y. Nasseri

Published in: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples

Publisher: Springer International Publishing

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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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previous chapter Well-Balanced Discretisation for the Compressible Stokes Problem by Gradient-Robustness
next chapter Post-processing of Fluxes for Finite Volume Methods for Elliptic Problems
Literature
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Arakawa, A., Lamb, V.: A potential enstrophy and energy conserving scheme for the shallow water equations. Mon. Weather Rev. 109, 18–36 (1981)CrossRef
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Doyen, D., Gunawan, H.: An explicit staggered finite volume scheme for the shallow water equations. In: Finite volumes for complex applications, VII. Methods and theoretical aspects, Springer Proceedings in Mathematics and Statistics, vol. 77, pp. 227–235. Springer, Cham (2014)
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Gallouët, T., Herbin, R., Latché: On the weak consistency of finite volumes schemes for conservation laws on general meshes. SeMA J. (2019) (online)
6.
Herbin, R., Latché, J.C., Nasseri, Y., Therme, N.: A decoupled staggered scheme for the shallow water equations. In: Accepted for publication, Proceedings of the 15 International Conference Zaragoza-Pau on Mathematics and its Applications, Jaca, 10–12 Sept 2018. https://​arxiv.​org/​abs/​1906.​11001 (2019)
7.
Herbin, R., Latché, J.C., Nguyen, T.: Consistent segregated staggered schemes with explicit steps for the isentropic and full Euler equations. Math. Model. Numer. Anal. 52, 893–944 (2018)MathSciNetCrossRef
Metadata
Title
A Second Order Consistent MAC Scheme for the Shallow Water Equations on Non Uniform Grids
Authors
T. Gallouët
R. Herbin
J.-C. Latché
Y. Nasseri
Copyright Year
2020
Book
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples

Print ISBN: 978-3-030-43650-6

Electronic ISBN: 978-3-030-43651-3

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-43651-3_9

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