Towards Discontinuous Galerkin Solution of the 3D RANS Equations

Eric Liu, Massachusetts Institute of Technology

The Discontinuous Galerkin (DG) Finite Element method (and higher-order methods in general) have recently been the topic of increased research efforts. Due to the prevalence of CFD-based design in the aerospace industry, the AIAA has hosted several "Drag Prediction Workshops" (DPWs) in the past decade to assess the state-of-the-art in CFD when applied to representative problems of turbulent flow over aerodynamic bodies. From their efforts, we see that while conditions are improving, there is still significant scatter in the numerical predictions made by current CFD codes. We believe that higher-order DG methods are clear candidates for this problem requiring high accuracy on complex geometries. Furthermore, the DG discretization of the Reynolds-Averaged Navier-Stokes (RANS) equations with associated turbulence model remains a difficult problem due to the presence of very stiff source terms and highly anisotropic mesh elements.

In the present work, we extended ProjectX to support the 3D RANS equations using the Spalart-Allmaras (SA) turbulence model for closure. This included the development of a kd-tree based routine for calculating wall-distances. ProjectX is an ongoing solver development effort working on applying a DG method to equations relevant to aerodynamic flows. Here we are largely building on an existing 2D RANS-SA capability born through the work of T. Oliver who also advanced theory on the treatment of source terms. Preliminary results for an extruded flat plate are shown. The goal is to run the solver on
the DPW cases, eventually with output-based adaptation.

Abstract Author(s): Eric Liu