A second order conservative time-staggered scheme for all speed flow

Overview & Synopsis

A time-staggered scheme for variable density flow is presented. The compressible Navier-Stokes equations are used by this pressure correction scheme which is implemented in the collocated finitevolumes open-source computational fluid dynamics solver code saturne. The Helmholtz equation is solved for the pressure increment, taking the thermodynamic pressure into account and avoiding the acoustic time step limitation. The internal energy equation is used to compute the temperature and a numerical analysis providing conditions ensuring the positivity of the thermodynamic variables is proposed. The scheme accuracy is first verified on a 0-D pressure cooker system. Then, a discontinuous shock problem shows its capability to reproduce shocks correctly and finally, the scheme is validated on a natural convection numerical reference case.