  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.
