An Unconditionally Stable Pressure Correction Scheme for Barotropic Compressible Navier-Stokes Equations

European Conference on Computational Fluid Dynamics
ECCOMAS CFD 2006, Juin 2006 

L. Gastaldo, F. Babik(1), R. Herbin(2), J.-C. Latché(3).

We present in this paper a pressure correction scheme for barotropic com- pressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the continuous problem also hold for the discrete solution. The stability proof is based on two independent results for general finite volume discretizations, both interesting for their own sake: the L2-stability of the discrete advection operator provided it is consistant, in somme sense, with the mass balance and the estimate of the pressure work by means of the time derivative of the elastic potential. The proposed scheme is built in order to match these theoretical results, and combines a fractional-step time discretization of pressure-correction type to a space discretization associating low order non-conforming mixed finite elements and finite volumes. Numerical tests with a manufactured smooth solution show the convergence of the scheme.

(1) : Institut de Radioprotection et de Sûreté Nucléaire (IRSN)
(2) : Laboratoire d’Analyse, Topologie et Probabilités (LATP) (web page: http://www.latp.univ-mrs.fr/)
(3) : Institut de Radioprotection et de Sûreté Nucléaire (IRSN)