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

Abstract : 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.
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Journal of Computational Physics, Elsevier, 2010, 230 (3), pp.572-585. 〈10.1016/j.jcp.2010.10.004〉
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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, Elsevier, 2010, 230 (3), pp.572-585. 〈10.1016/j.jcp.2010.10.004〉. 〈hal-00458293v2〉

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