This paper describes an approach for computing transonic turbulent flows by using a high-order discontinuous Galerkin (DG) method. The method solves the RANS and k-w turbulence model equations on hybrid grids consisting of arbitrary sets of elements (triangles and quadrangles in 2D, tetrahedrons, prisms, pyramids and hexahedrons in 3D) with possibly curved faces. Oscillations of high-order solutions around shocks are controlled by means of a viscous-like term, explicitly added to the discretized equations, which acts to damp the growth of higher-order components of the solution. For steady state solutions of turbulent flow computations the DG discretized equations are integrated in time by using the backward Euler method. The code is fully parallelized and relies on METIS for grid partitioning and on PETSc for linear algebra. Numerical results of some test cases proposed within the EU ADIGMA project will demonstrate the capabilities of the method. Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.