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

2020 | OriginalPaper | Chapter

Semi-implicit Two-Speed Well-Balanced Relaxation Scheme for Ripa Model

Authors : Emmanuel Franck, Laurent Navoret

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

Publisher: Springer International Publishing

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Abstract

In this paper, we propose a semi-implicit well-balanced scheme for the Ripa model based on a two-speed relaxation. The method both preserves equilibria and has an implicit step that reduces to the inversion of a constant Laplacian. Numerical simulations show that the scheme well capture low-Froude flows.

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previous chapter Application of an Unstructured Finite Volume Method to the Shallow Water Equations with Porosity for Urban Flood Modelling
next chapter Kinetic Over-Relaxation Method for the Convection Equation with Fourier Solver
Literature
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Coulette, D., Franck, E., Helluy, P., Ratnani, A., Sonnendrueker, E.: Implicit time schemes for compressible fluid models based on relaxation methods. Comput. Fluids 188(30), 70–85 (2019)MathSciNetCrossRef
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Bouchut, F., Franck, E., Navoret, L.: A low cost semi-implicit low-Mach relaxation scheme for the full Euler equations, preprint 2019
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Berthon, C., Desveaux, V., Klingenberg, C.: Well-balanced scheme to capture non explicit steady-states: Ripa model. Math. Comput. 85(300) (2016)
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Iampietro, D., Daube, F., Galon, P., Herard, J.M.: A Mach-sensitive implicit-explicit scheme adapted to compressible multi-scale flows. J. Comput. Appl. Math. 340(1), 122–150 (2018)MathSciNetCrossRef
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Toro, E.F., Vaquez-Cendon, M.E.: Flux splitting schemes for the Euler equations. Comput. Fluids 70 (2012)
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Jin, S., Levermore, D.: Numerical schemes for hyperbolic conservation laws with stiff relaxation terms. J. Comput. Phys. 126, 449–467 (1996)MathSciNetCrossRef
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Franck, E., Mendoza, L.: Finite volume scheme with local high order discretization of the hydrostatic equilibrium for the Euler equations with external forces. J. Sci. Comput. 69(1) (2016)
Metadata
Title
Semi-implicit Two-Speed Well-Balanced Relaxation Scheme for Ripa Model
Authors
Emmanuel Franck
Laurent Navoret
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_70

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