Compressible Stokes Problem with General EOS

Abstract

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 nondecreasing function belonging to \({C}^{1}({\mathbb{R}}_{+}, \mathbb{R})\)). 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 existence of a discrete solution and convergence of this approximate solution to a solution of the continuous problem.