p-multigrid Discontinuous Galerkin method for compressible turbulent flows

Discontinuous Galerkin (DG) methods are very well suited for the construction of very high-order approximations of the Euler and Navier-Stokes equations on unstructured and possibly non conforming grids, but are rather demanding in terms of computational resources. In order to improve the computational efficiency of this class of methods, a high-order DG approximation of the Reynolds Average Navier-Stokes and k-ω turbulence model equations coupled with a p-multigrid solution strategy is here considered. In particular a line smoother will be used to alleviate the effect of stretched grids on the convergence rate. The effectiveness of the proposed approach is demonstrated in the computation of turbulent test cases.