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 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.

Two-Dimensional Evaluation of ATHAM-Fluidity, a Nonhydrostatic Atmospheric Model Using Mixed Continuous/Discontinuous Finite Elements and Anisotropic Grid Optimization

“…Note that in the present formulation, only acoustic waves are treated semiimplicitly, with gravity waves being treated explicitly [semi-implicit treatment of gravity waves has been adopted, for example, in Smolarkiewicz et al (2014)]. The reader is referred to Botti and Di Pietro (2011) for the implementation and stability of pressure-correction methods combined with DG.…”

“…This class of methods is known to perform well in both low-Mach and high-Mach number regimes (although this latter may not be relevant for atmospheric applications), while relaxing the severe time step restriction typically fixed by fast-propagating acoustic waves in density-based solvers [for which a continuity equation is solved explicitly, as in Giraldo and Restelli (2008) and Kopera and Giraldo (2014)]. In this context, using a mixed FEM formulation with the velocity possessing more or equal degrees of freedom than the pressure is essential to prevent the formation of spurious numerical pressure modes (Cotter et al 2009a;Botti and Di Pietro 2011).…”

AView: An Image-based Clinical Computational Tool for Intracranial Aneurysm Flow Visualization and Clinical Management

“…2 In addition, it embeds an open-source Computational Fluid Dynamics (CFD) solver (Gnuid, https://github.com/lorbot/Gnuid). 3,4 A schematic of AView general architecture is provided in Fig. 1.…”

“…The Gnuid component is the executable for the Gnuid Mixed Discontinuous-Continuous Galerkin open-source incompressible Navier-Stokes solver. 4 The solver relies on the libMesh library which in turn relies on the PETSc numerical library for solving parallel sparse linear systems, the METIS partitioning library and MPI for message passing. The implemented bundle is completely self-contained, in that it ships with all components illustrated in the Fig.…”

Cell centered Galerkin methods for diffusive problems

“…In our case, the velocity-pressure coupling is stabilized by penalizing the pressure jumps across interfaces with a weight proportional to the meshsize; see, e.g., [19]. As regards the convective term, we use the non-dissipative trilinear form recently proposed by Di Pietro and Ern [22], which has proven suitable to convection-dominated regimes; see also Botti and Di Pietro [9] for the application to a dG discretization of the advection step in the context of a pressure-correction time-integration scheme. Since the convergence analysis is similar as for the dG method of [22], the proofs of the results that hold a fortiori are sometimes omitted to leave room to specific issues related to the ccG method.…”