Wall modeling via function enrichment: Extension to detached-eddy simulation

We extend the approach of wall modeling via function enrichment to detached-eddy simulation. The wall model aims at using coarse cells in the near-wall region by modeling the velocity profile in the viscous sublayer and log-layer. In our approach however, unlike other wall models, the full Navier–Stokes equations are still discretely satisfied, including the pressure gradient and convective term. This is achieved by enriching the elements of the high-order discontinuous Galerkin method with the law-of-the-wall. As a result, the Galerkin method can “choose” the optimal solution among the polynomial and enrichment shape functions. The detached-eddy simulation methodology provides a suitable turbulence model for the coarse near-wall cells. The approach is applied to wall-modeled LES of turbulent channel flow in a wide range of Reynolds numbers. Flow over periodic hills shows the superiority compared to an equilibrium wall model under separated flow conditions.