| Issue |
ESAIM: ProcS
Volume 58, 2017
LMLFN 2015 – Low Velocity Flows – Application to Low Mach and Low Froude regimes
|
|
|---|---|---|
| Page(s) | 1 - 26 | |
| DOI | https://doi.org/10.1051/proc/201758001 | |
| Published online | 08 November 2017 | |
Godunov type scheme for the linear wave equation with Coriolis source term
1 Université Paris 13, LAGA, CNRS UMR 7539, Institut Galilée, 99 Avenue J.-B. Clément, 93430 Villetaneuse Cedex, France
2 Commissariat à l’Énergie Atomique et aux Énergies Alternatives, CEA, DEN, DM2S-STMF, 91191 Gif-Sur-Yvette, France
3 Hydro-Québec, TransÉnergie, 75 boulevard René-Lévesque Ouest, Montréal (Qc), H2Z 1A4, Canada (current address)
4 Team ANGE, CEREMA (Ministry of Ecology, Sustainable Development and Energy) and Inria–Paris
5 Sorbonne Universités, UPMC Univ. Paris 06 and CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France
We propose a method to explain the behaviour of the Godunov finite volume scheme applied to the linear wave equation with Coriolis source term at low Froude number. In particular, we use the Hodge decomposition and we study the properties of the modified equation associated to the Godunov scheme. Based on the structure of the discrete kernel of the linear operator discretized by using the Godunov scheme, we clearly explain the inaccuracy of the classical Godunov scheme at low Froude number and we introduce a way to modify it to recover a correct accuracy.
© EDP Sciences, SMAI 2017
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