Wall modeling via function enrichment within a high-order DG method for RANS simulations of incompressible flow

Abstract: We present a novel approach to wall modeling for RANS within the discontinuous Galerkin method. Wall functions are not used to prescribe boundary conditions as usual but they are built into the function space of the numerical method as a local enrichment, in addition to the standard polynomial component. The Galerkin method then automatically finds the optimal solution among all shape functions available. This idea is fully consistent and gives the wall model vast flexibility in separated boundary layers or high adverse pressure gradients. The wall model is implemented in a high-order discontinuous Galerkin solver for incompressible flow complemented by the Spalart-Allmaras closure model. As benchmark examples we present turbulent channel flow starting from $Re_{\tau}=180$ and up to $Re_{\tau}=100{,}000$ as well as flow past periodic hills at Reynolds numbers based on the hill height of $Re_H=10{,}595$ and $Re_{H}=19{,}000$.