A multiscale approach to hybrid RANS/LES wall modeling within a high‐order discontinuous Galerkin scheme using function enrichment

Wall modeling is the key technology for making industrial high-Reynolds-number flows accessible to computational analysis. In this work, we present an innovative multiscale approach to hybrid RANS/LES wall modeling, which overcomes the problem of the RANS/LES transition and enables coarse meshes near the boundary. In a layer near the wall, the Navier-Stokes equations are 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. Additional problem-tailored shape functions, which are constructed using a wall-law as an enrichment function, automatically compute the ensemble-averaged flow where the coarseness of the LES filter width does not allow for the resolution of the energetic scales. An algebraic mixing length RANS model acts on the RANS degrees of freedom only, which effectively prevents the typical issue of a log-layer mismatch in attached boundary layers. The wall model is fully consistent, no terms of the Navier-Stokes equations are neglected, and spatial refinement gradually yields wall-resolved LES with exact boundary conditions. This approach has been implemented in a high-performance discontinuous Galerkin framework and is validated using turbulent channel flow as well as flow over periodic hills. These numerical tests show the outstanding characteristics of the wall model regarding grid independence and achieve a speed-up by two orders of magnitude compared to wall-resolved LES.

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