An unconditionnally stable pressure correction scheme for compressible barotropic Navier-Stokes equations
For computational fluid dynamics researchers, this provides a provably stable numerical scheme for compressible flows, though it is an incremental improvement over existing pressure correction methods.
The paper presents a pressure correction scheme for barotropic compressible Navier-Stokes equations that is unconditionally stable, preserving energy and maximum-principle-based a priori estimates at the discrete level. Numerical tests with an exact smooth solution demonstrate convergence.
We present in this paper a pressure correction scheme for barotropic compressible 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 $L^2$-stability of the discrete advection operator provided it is consistent, in some 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 an exact smooth solution show the convergence of the scheme.