A Divergence-Conforming Hybridized Discontinuous Galerkin Method for the Incompressible Reynolds Averaged Navier-Stokes Equations

Abstract

We introduce a hybridized discontinuous Galerkin method for the incompressible Reynolds Averaged Navier-Stokes equations coupled with the Spalart-Allmaras one equation turbulence model. With a special choice of velocity and pressure spaces for both element and trace degrees of freedom, we arrive at a method which returns point-wise divergence-free mean velocity fields and properly balances momentum and energy. We further examine the use of different polynomial degrees and meshes to see how the order of the scalar eddy viscosity affects the convergence of the mean velocity and pressure fields, specifically for the method of manufactured solutions. As is standard with hybridized discontinuous Galerkin methods, static condensation can be employed to remove the element degrees of freedom and thus dramatically reduce the global number of degrees of freedom. Numerical results illustrate the effectiveness of the proposed methodology.

References in corpus (1)

• An explicit divergence-free DG method for incompressible flow

Cited by in corpus (5)

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• Design and analysis of an exactly divergence-free hybridized discontinuous Galerkin method for incompressible flows on meshes with quadrilateral cells
• A Divergence-Free and $H(div)$-Conforming Embedded-Hybridized DG Method for the Incompressible Resistive MHD equations