A high order discontinuous Galerkin method for compressible turbulent flows

An implicit high order accurate Discontinuous Galerkin method for the numerical solution of the compressible Favre-Reynolds Averaged Navier-Stokes equations is presented. The method is characterized by a highly compact discretization support even for higher order approximations and this feature can be exploited in the development of implicit integration schemes. Turbulence effects are accounted for by means of the low-Reynolds k-omega turbulence model. A non-standard implementation of the model, whereby the logarithm of omega rather than w itself is used as unknown, has been found very useful to enhance the stability of the method especially for the higher (third and fourth) order approximations. We present computational results of the transitional flow over a flat plate and of the turbulent flow through a turbine vane with wall heat transfer.