This paper addresses a class of physical problems which can be set under the form of the Navier-Stokes equations, supplemented by the balance equation of an independent unknown field z, the fluid density being given as a nonlinear function of this latter. In particular, governing equations of some reactive low Mach number flows enter this framework. Two fractional steps schemes are built for the solution of this system. They combine a particular finite volume discretization of the balance of z, which L1 and L2 stability is proven, with a non-conforming finite element pressure correction method for the solution of the Navier-Stokes equations. Numerical experiments show that these schemes are almost optimally convergent in time and space and remarkably stable, in view of the strong non-linearity of the problems at hand.
(1) : IRSN, BP3-13115 St. Paul-lez-Durance, France
(2) : Laboratoire d’Analyse, Topologie, Probabilité, UMR 6632, CMI
Université de Provence, 39 rue F. Joliot-Curie, 13453 Marseille cedex 13, France