Analysis of modified Godunov type schemes for the two-dimensional linear wave equation with Coriolis source term on cartesian meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:373

Article

Audusse, Emmanuel¹  Do Minh Hieu¹  Omnes, Pascal^1,2  Penel, Yohan^3,4,5 

[1] Univ Paris 13, LAGA, CNRS UMR 7539, Inst Galilee, 99 Ave JB Clement, F-93430 Villetaneuse, France

[2] CEA, Commissariat Energie Atom & Energies Alternat, DEN, STMF DM2S, F-91191 Gif Sur Yvette, France

[3] UPMC Univ Paris 06, Minist Ecol, CEREMA, Team ANGE, F-75005 Paris, France

[4] UPMC Univ Paris 06, Inria Paris, Sorbonne Univ, F-75005 Paris, France

[5] CNRS, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France

关键词: Shallow water equations;    Linear wave equation;    Coriolis source term;    Low Froude number;    Godunov scheme;    Cartesian mesh;   

DOI  :  10.1016/j.jcp.2018.05.015

来源: Elsevier

【 摘 要 】

The study deals with collocated Godunov type finite volume schemes applied to the two-dimensional linear wave equation with Coriolis source term. The purpose is to explain the wrong behaviour of the classic scheme and to modify it in order to avoid accuracy issues around the geostrophic equilibrium and in geostrophic adjustment processes. To do so, a Hodge-like decomposition is introduced. Then three different well-balanced strategies are introduced. Some properties of the associated modified equations are proven and then extended to the semi-discrete case. Stability of fully discrete schemes under a suitable CFL condition is established thanks to a Von Neumann analysis. Some numerical results reinforce the purpose and exhibit the concrete improvements achieved by the application of these new techniques in both linear and nonlinear cases. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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