Navier-Stokes solution using hybridizable discontinuous Galerkin methods

Abstract

We are concerned with the numerical solution of the Navier-Stokes and Reynolds-averaged Navier-Stokes equations using hybridizable discontinuous Galerkin (HDG) meth- ods recently introduced in Ref. [36]. These methods are computationally more efficient and accurate than other discontinuous Galerkin methods. They are thus well-suited for solving many CFD problems. However, the HDG methods can not directly deal with viscous com- pressible flows with shock waves. We thus propose to add an artificial viscosity term to the Navier-Stokes equations. Moreover, in order to render the Spalart-Allmaras (SA) tur- bulence model easier to integrate using HDG methods, we propose a simple modification of the SA model. The modification is effective only in regions where the eddy viscosity is smaller than the molecular viscosity. Therefore, it does not affect the numerical prediction of flow quantities as compared to the original SA model. Numerical results are presented to demonstrate the proposed approach.