Discontinuous Galerkin solution of the Reynolds Averaged Navier-Stokes and k-omega turbulence model equations

Discontinuous Galerkin methods, originally developed in the advective case, have been successively extended to advection-diffusion problems, and are now used in very diverse applications. We here consider the numerical solution of the compressible Reynolds-averaged Navier–Stokes and k–omega turbulence model equations by means of DG space discretization and implicit time integration. Detailed description of the DG discretization of the viscous part of the equations and of several implementation details of the k–omega turbulence model are given. To assess the performance of the proposed methodology we present the results obtained in the computation of the turbulent flow over a flat plate and of the turbulent unsteady wake developing behind a turbine blade.