An Enriched Spectral Element Wall-Model for Wall-Modeled Large-Eddy Simulations

We developed an enrichment wall-model for the spectral element method (SEM) for wall-modeled large-eddy simulations (WMLES) of turbulent flows. Ordinarily, higher-order methods, such as SEM, require significant mesh refinement near the wall in order resolve the turbulent boundary layer without log-layer mismatch or spurious oscillations due to the large gradients in the boundary layer. To avoid this issue, as is done in traditional WMLES, we take the velocity at matching points away from the wall and fit it with an analytical wall function to compute the shear stress on the wall and apply it to the flow at the boundary. Then, in order to increase the fidelity of the model, we incorporate the wall function as an enrichment term in the solution representation. This allows the near wall behavior to be captured without unphysical oscillations or mismatches at the wall and improves the accuracy of the overall solution. We discuss the procedure for integrating the enrichment wall-model in the SEM and its implementation in the SEM CFD solver Nek5000. The method is demonstrated in the context of RANS and WMLES for canonical wall-bounded turbulent flows.