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

In this work we present a pressure-correction scheme for the incompressible Navier–Stokes equations combining a discontinuous Galerkin approximation for the velocity and a standard continuous Galerkin approximation for the pressure. The main interest of pressure-correction algorithms is the reduced computational cost compared to monolithic strategies. In this work we 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.