Numerical approximation of the general compressible Stokes problem

A Fettah (1) , Thierry Gallouët (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

In this paper, we propose a discretization for the compressible Stokes problem with an equation of state of the form p = ϕ(ρ) (where p stands for the pressure, ρ for the density and ϕ is a superlinear nondecreasing function from R to R). This scheme is based on Crouzeix-Raviart approximation spaces. The discretization of the momentum balance is obtained by the usual finite element technique. The discrete mass balance is obtained by a finite volume scheme, with an upwinding of the density, and two additional terms. We prove the existence of a discrete solution and the convergence of this approximate solution to a solution of the continuous problem.

Mots clés: Compressible Stokes Equations; Numerical Scheme

Domaines: Analyse classique [math.CA]

A Fettah, Thierry Gallouët. Numerical approximation of the general compressible Stokes problem. IMA Journal of Numerical Analysis, 2013, 33 (3), pp.922 - 951. ⟨10.1093/imanum/drs024⟩. ⟨hal-01116755⟩