Implicit Large Eddy Simulations for NACA0012 Airfoils Using Compressible and Incompressible Discontinuous Galerkin Solvers

We present implicit Large Eddy Simulations for NACA0012 airfoils at various Reynolds numbers (Re = 1 × 10⁴, Re = 1 × 10⁵ and Re = 1 × 10⁶) and Angles of Attack (0^∘≤ AoA ≤ 10^∘) using two discontinuous Galerkin formulations. On the one hand, we use a compressible solver based on a nodal DGSEM formulation and supplemented with a stabilising split-form formulation (Pirozzoli) and Roe interface fluxes. On the other hand, we use an incompressible DG-Fourier formulation that uses the interior penalty parameter to provide localised dissipation. Both solvers enable high order computations by varying the polynomial order inside mesh elements, which are here set to P = 3 and P = 4. We provide results of aerodynamic coefficients and pressure distributions using both solvers to show how they are able to provide under-resolved flows that agree well with experimental data and well established solvers (Xfoil or Ansys-Fluent).