Solution Enrichment Wall-Modeled LES in the Spectral Element Method Framework*

We developed an enriched wall-model for the spectral element method (SEM) based 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 to resolve the turbulent boundary layer without 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 them with an analytical wall function to compute the shear stress on the wall and apply

it to the flow. To increase the fidelity of the model beyond the traditional method, we incorporate the wall function as an

enrichment term in the solution representation. This improves the accuracy of the model and allows for the solution to

be physically relevant up to the wall, unlike with shear-stress wall models. We discuss the procedure for integrating the

enrichment term in a SEM and its implementation in the SEM CFD solver Nek5000. The method is demonstrated in the

context of WMLES for canonical wall-bounded turbulent flows.