A multiscale approach to hybrid RANS/LES wall modeling within a high-order discontinuous Galerkin scheme using function enrichment
For computational fluid dynamics practitioners, this provides a more accurate and efficient wall modeling technique for turbulent flows, particularly in separated flow regimes.
This work presents a novel hybrid RANS/LES wall modeling approach using function enrichment within a high-order discontinuous Galerkin scheme, which eliminates the RANS-LES transition problem and log-layer mismatch. The method achieves grid independence, outperforms equilibrium wall models in separated flows, and reduces computational cost by two orders of magnitude compared to wall-resolved LES.
We present a novel approach to hybrid RANS/LES wall modeling based on function enrichment, which overcomes the common problem of the RANS-LES transition and enables coarse meshes near the boundary. While the concept of function enrichment as an efficient discretization technique for turbulent boundary layers has been proposed in an earlier article by Krank & Wall (J. Comput. Phys. 316 (2016) 94-116), the contribution of this work is a rigorous derivation of a new multiscale turbulence modeling approach and a corresponding discontinuous Galerkin discretization scheme. In the near-wall area, the Navier-Stokes equations are explicitly solved for an LES and a RANS component in one single equation. This is done by providing the Galerkin method with an independent set of shape functions for each of these two methods; the standard high-order polynomial basis resolves turbulent eddies where the mesh is sufficiently fine and the enrichment automatically computes the ensemble-averaged flow if the LES mesh is too coarse. As a result of the derivation, the RANS model is consistently applied solely to the RANS degrees of freedom, which effectively prevents the typical issue of a log-layer mismatch in attached boundary layers. As the full Navier-Stokes equations are solved in the boundary layer, spatial refinement gradually yields wall-resolved LES with exact boundary conditions. Numerical tests show the outstanding characteristics of the wall model regarding grid independence, superiority compared to equilibrium wall models in separated flows, and achieve a speed-up by two orders of magnitude compared to wall-resolved LES.