Construction of modified Godunov type schemes accurate at any Mach number for the compressible Euler system

Stéphane Dellacherie (1) , Pascal Omnes (2, 3) , Pierre-Arnaud Raviart (4)

1 CEA-DES (ex-DEN) - CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire)
2 LAGA - Laboratoire Analyse, Géométrie et Applications
3 DM2S - Département de Modélisation des Systèmes et Structures
4 LJLL - Laboratoire Jacques-Louis Lions

Through a linear analysis, we show how to modify Godunov type schemes applied to the compressible Euler system to make them accurate at any Mach number. This allows to propose all Mach Godunov type schemes. A linear stability result is proposed and a formal asymptotic analysis justifies the construction in the barotropic case when the Godunov type scheme is a Roe scheme. We also underline that we have to introduce a cut-off in the all Mach correction to avoid the creation of non-entropic shock waves.

Mots clés: Roe scheme; Compressible Euler system; linear wave equation; low Mach number flow; Godunov scheme; Roe scheme.

Domaines: Analyse numérique [math.NA]

Stéphane Dellacherie, Pascal Omnes, Pierre-Arnaud Raviart. Construction of modified Godunov type schemes accurate at any Mach number for the compressible Euler system. 2013. ⟨hal-00776629v1⟩