Staggered discretizations, pressure correction schemes and all speed barotropic flows

Laura Gastaldo (1) , Raphaele Herbin (2) , Walid Kheriji (1, 2) , Céline Lapuerta (3) , Jean-Claude Latché (1)

1 IRSN - Institut de Radioprotection et de Sûreté Nucléaire
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités
3 IRSN/DPAM/SEMIC/LIMSI - Laboratoire d'études de l'Incendie et de développement de Méthodes pour la Simulation et les Incertitudes

We present in this paper a class of schemes for the solution of the barotropic Navier- Stokes equations. These schemes work on general meshes, preserve the stability properties of the continuous problem, irrespectively of the space and time steps, and boil down, when the Mach number vanishes, to discretizations which are standard (and stable) in the incompressible framework. Finally, we show that they are able to capture solutions with shocks to the Euler equations

Mots clés: Barotropic Navier-Stokes; Staggered discretizations

Domaines: Analyse numérique [math.NA]

Laura Gastaldo, Raphaele Herbin, Walid Kheriji, Céline Lapuerta, Jean-Claude Latché. Staggered discretizations, pressure correction schemes and all speed barotropic flows. FVC6, International Symposium, Jun 2011, Prague, Czech Republic. pp.839-855, ⟨10.1007/978-3-642-20671-9_86⟩. ⟨hal-00576246⟩