A Discontinuous Galerkin Method for the RANS Equations Under ProjectX

Eric Liu, Massachusetts Institute of Technology

As part of the ProjectX team, I have worked on extending the capabilities of the ProjectX software package to the Reynolds-averaged Navier--Stokes (RANS) Equations in 2D and 3D. As a point of notice, ProjectX is a research initiative at MIT, the group of which has authored a CFD code implementing a Discontinuous Galerkin (DG) Finite Element method. ProjectX is particularly interested in obtaining higher-order solutions for PDEs arising from flow problems. Its objectives revolve around solver automation through output-based mesh adaptation via error estimation through the adjoint problem. I have been implementing a RANS-solution capability (built on a pre-existing Navier-Stokes solver) using the one-parameter Spalart-Allmaras (SA) turbulence model. Part of the investigation is to observe whether RANS simulations benefit from the use of higher-order solution methods, and whether we can achieve a sufficiently robust adaptation algorithm for the highly anisotropic meshes characteristic of RANS cases. Wall-distances are calculated using a Newton-optimization loop initialized by a kd-tree based point search. Utilizing the work of T. Oliver, the SA source terms are discretized in a dual-consistent fashion, which is necessary for mesh adaptation. We are working toward demonstrating possibly the first higher-order, adaptive RANS solution techniques in 3D, but are currently only able to show results for 2D problems. Future challenges include improving our parallel performance (e.g., balancing domain decomposition by constraints (BDDC) preconditioners for DG) and providing a more robust mesh adaptation capability, especially in 3D (e.g., using cut-cells).

Abstract Author(s): Eric Liu