Dec 12 – 16, 2022
Europe/Paris timezone

An asymptotic preserving scheme for the full Euler equations in the low Mach limit

Dec 14, 2022, 9:45 AM
Amphithéâtre Schwartz (IMT)

Amphithéâtre Schwartz


Université Paul Sabatier, 118 Route de Narbonne, 31000 Toulouse France




This work is in collaboration with Marie-Hélène Vignal, Institut de Mathéma-
tiques de Toulouse, UT3-Paul Sabatier.

In this work, we develop and study an asymptotic preserving (AP) scheme for
the compressible Euler system in the low Mach number regime. For subsonic
flows, the acoustic waves are very fast compared to the velocity of the fluid,
we are in an incompressible regime. From a numerical point of view, when
the Mach number tends to zero, classical explicit schemes present two major
drawbacks : they loose consistency and impose a very restrictive constraint on
the time step to guaranty the stability of the scheme since they have to follow
the fast acoustic waves.

We propose a new linear asymptotic stable scheme, with a CFL condition inde-
pendent of the Mach number, and asymptotically consistent, that is it degener-
ates into a consistent discretization of the incompressible model when the Mach

number is sufficiently small.
This type of scheme has been widely studied in the literature, in particular
for the isentropic case [5, 4, 3, 6] but also for the full Euler system [2, 1] with
various methods. In this work we propose an AP scheme based on an IMEX
(Implict-Explicit) discretization in time and cell-centered finite volume in space.
I will present our AP scheme, its extension to order 2 and the MOOD procedure
used to reduce the oscillations (classical problem of high order schemes). Finally,
I will finish my presentation with some results on the Navier-Stokes equations.

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