On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes

By Hervé Guillard, Angelo Murrone. 2004

196 citations recorded by the source corpus.

Abstract This paper presents an analysis of Godunov scheme in the low Mach number regime. We study the Riemann problem and show that the interface pressure contains acoustic waves of order O (M * ) where M * is the reference Mach number even if the initial data are well-prepared and contain only pressure fluctuations of order O (M * 2 ) . We then propose to modify the fluxes computed by Godunov type schemes by solving a preconditioned Riemann problem instead of the original one. We show that this strategy allows to recover a correct scaling of the pressure fluctuations. Numerical experiments confirm these theoretical results.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/e508fce3e33e024ca79990bf8baa0bbf775e355e

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In Applied Mathematics

1. Joelle Caro
2. Jean-Christophe Marongiu
3. Etienne Parkinson
4. Francis Leboeuf

In Computational Mechanics

1. Joelle Caro
2. Jean-Christophe Marongiu
3. Etienne Parkinson
4. Francis Leboeuf
5. Benedict D. Rogers
6. Damien Violeau

Citations in the corpus

• Free surface flows simulations in Pelton turbines using an hybrid SPH-ALE method (2010, methodology): “The use of Godunov type schemes in the limit of low Mach numbers as encountered in hydraulic flows is known to lead to this type of results (Guillard and Murrone 2004).”