A divergence-conforming hybridized discontinuous Galerkin method for the incompressible Reynolds-averaged Navier-Stokes equations |
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Authors: | Eric L. Peters John A. Evans |
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Affiliation: | Ann and H.J. Smead Aerospace Engineering Sciences, University of Colorado at Boulder, Boulder, Colorado |
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Abstract: | We present a hybridized discontinuous Galerkin (HDG) method for the incompressible Reynolds-averaged Navier-Stokes equations coupled with the Spalart-Allmaras one-equation turbulence model. The method extends upon an HDG method recently introduced by Rhebergen and Wells for the incompressible Navier-Stokes equations. With a special choice of velocity and pressure spaces for both element and trace degrees of freedom (DOFs), the method returns pointwise 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 HDG methods, static condensation can be employed to remove the element DOFs and thus dramatically reduce the global number of DOFs. Numerical results illustrate the effectiveness of the proposed methodology. |
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Keywords: | divergence conforming discretizations hybridized discontinuous Galerkin methods incompressible flow Reynolds-averaged Navier-Stokes (RANS) Spalart-Allmaras turbulence model static condensation |
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