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Pré-Publication, Document De Travail Année : 2015

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

Résumé

Through a linear analysis of a perturbed wave equation, 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 a family of all Mach Godunov type schemes and to justify existing all Mach schemes. In the non-linear barotropic case and when the Godunov type scheme is a Roe scheme, a linear stability result is proposed and a formal asymptotic analysis justifies the construction by showing how it is related with the linear analysis of a perturbed wave equation. All the studied numerical results show that the all Mach Godunov scheme is both accurate and stable for all Mach flows.
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Dates et versions

hal-00776629 , version 1 (15-01-2013)
hal-00776629 , version 2 (22-03-2015)
hal-00776629 , version 3 (26-11-2015)
hal-00776629 , version 4 (15-08-2016)

Identifiants

  • HAL Id : hal-00776629 , version 3

Citer

Stéphane Dellacherie, Jonathan Jung, Pascal Omnes, Pierre-Arnaud Raviart. Construction of modified Godunov type schemes accurate at any Mach number for the compressible Euler system. 2015. ⟨hal-00776629v3⟩
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