Mesh-Resolved Airfoil Simulations Using Finite Volume and Discontinuous Galerkin Solvers

Abstract

A traditional second-order accurate finite volume unstructured mesh solver and a high-order discontinuous Galerkin solver are used to simulate turbulent flow over a NACA 0012 airfoil. Using a family of standardized high-density grids, mesh-resolved solutions are obtained. The flow is simulated by solving the Reynolds-averaged Navier–Stokes equations closed by the negative Spalart–Allmaras turbulence model. The flow conditions for this case are , , and . Lift, drag, pitching moment, pressure, and skin friction coefficients are provided for multiple grids and discretization orders and are compared against other simulation results from well known solvers. The current simulations give very similar results to these benchmark solvers, pointing toward fully mesh-resolved simulations and providing verification evidence of correct and consistent implementation of these discretizations. Results obtained using the high-order discontinuous Galerkin discretizations show higher accuracy using fewer degrees of freedom compared to the finite volume discretization and the benchmark results. Also, it is shown for the discontinuous Galerkin simulations that refinement converges quicker to the mesh-resolved solutions compared to refinement.