A pressure-correction scheme for convection-dominated incompressible flows with discontinuous velocity and continuous pressure

Lorenzo Botti (1) , Daniele Antonio Di Pietro (2)

1 Department of Industrial Engineering
2 IFPEN - IFP Energies nouvelles

In this work we present a pressure-correction scheme for the incompressible Navier-Stokes equations combining a discontinuous Galerkin approximation for the velocity with a standard continuous Galerkin approximation for the pressure. The main interest of pressure-correction algorithms is the reduced computational cost compared to fully coupled schemes. The aim of the present work is to show how a proper discretization of the decoupled momentum equation can render this method suitable to simulate high Reynolds regimes. The proposed spatial velocity-pressure approximation is LBB stable for equal polynomial orders and it allows adaptive $p$-refinement for velocity and global $p$-refinement for pressure. The method is validated against a large set of classical two- and three-dimensional test cases covering a wide range of Reynolds numbers, in which it proves effective both in terms of accuracy and computational cost.

Mots clés: Incompressible Navier-Stokes equations; Discontinuous Galerkin; Pressure-correction

Domaines: Analyse numérique [math.NA]

Lorenzo Botti, Daniele Antonio Di Pietro. A pressure-correction scheme for convection-dominated incompressible flows with discontinuous velocity and continuous pressure. Journal of Computational Physics, 2010, 230 (3), pp.572-585. ⟨10.1016/j.jcp.2010.10.004⟩. ⟨hal-00458293v2⟩