Implementation of the transition model for high order discontinuous Galerkin method with hybrid discretization strategy

The γ-Re_θt⌢ transition model has been applied within the framework of high order discontinuous Galerkin (DG) discretization of Reynolds-averaged Navier-Stokes (RANS) equations. A hybrid discretization strategy that takes advantage of all available information from DG method is suggested for the implementation of the transition model. Some techniques for the spatial and temporal discretization are utilized to enhance the effectiveness of the method. The resulting approaches achieve high accuracy of transition prediction and meanwhile do not increase notable computational challenge when compared to DG discretization of fully coupled RANS/transition system. We carry out both steady and unsteady transitional simulations to examine the performance of the designed method. Numerical results have demonstrated that the present approaches are capable of capturing the transition flow characteristics as well as improving transition prediction accuracy with high order DG schemes.