Un algorithme pour la simulation du transport convectif et de la propagation acoustique à tout nombre de Mach

Abstract

A pressure-correction algorithm is presented for compressible fluid flow regimes. It is well-suited to si- mulate flows at all levels of Mach number with smooth and discontinuous flow field changes, by providing a precise representation of convective transport and acoustic propagation. The co-located finite volume space discretization is used with the AUSM flux splitting. It is demonstrated that two ingredients are essential for obtaining good quality solutions : the presence of an inertia term in the transporting velo- city expression ; a velocity difference diffusive term in the face pressure expression, with a correct Mach number scaling to recover the hydrodynamic and acoustic low Mach number limits. To meet these two requirements, a new flux scheme, named MIAU, for Momentum Interpolation with Advection Upstream splitting is proposed.