An Investigation of Continuous and Discontinuous Finite-Element Discretizations on Benchmark 3D Turbulent Flows (Invited)

摘要

Two high-order finite-element solvers are used to simulate two 3D benchmark problems provided by the NASA Turbulence Modeling Resource (TMR) website. The first problem is a subsonic turbulent flow over a hemisphere-cylinder body at angles of attack of 5 and 19 degrees. The second problem is a transonic turbulent flow an ONERA M6 wing at angles of attack of 3.06 and 6.06 degrees. The first finite-element solver is based on the streamline-upwind Petrov-Galerkin (SUPG) discretization and the second one is based on the discontinuous Galerkin (DG) method. For both problems, second- and higher-order solutions are provided and a detailed mesh convergence study is presented. Also, the linear and nonlinear convergence behavior of the utilized solvers is investigated. The SUPG solver shows a very consistent non-linear convergence behavior across all grids while the DG solver struggles on the coarse grids. Both finite-element solvers demonstrate rapid convergence for high-order simulations when initialized with a second-order accurate solution. For all hemisphere-cylinder cases and the M6 wing at angle of attack of 3.06 degrees, the finite-element solvers are outperforming the FUN3D finite-volume solver in terms of accuracy per degree of freedom. For the MG wing at angle of attack of 6.06 degrees, although no reference solutions were provided by the TMR website, simulations were attempted for the finite-element solvers. For this case, no conclusions can be made about asymptotic convergence of the integrated forces due to lack of consistency between results. This was initially thought to be caused by the provided grids. However, further investigation using custom unstructured grids leads us to believe that the flow conditions, not the grids, make this case challenging.