Wall modeling via function enrichment: Extension to detached-eddy simulation

Abstract

We extend the approach of wall modeling via function enrichment to detached-eddy simulation. The wall model aims at using coarse cells in the near-wall region by modeling the velocity profile in the viscous sublayer and log-layer. However, unlike other wall models, the full Navier-Stokes equations are still discretely fulfilled, including the pressure gradient and convective term. This is achieved by enriching the elements of the high-order discontinuous Galerkin method with the law-of-the-wall. As a result, the Galerkin method can "choose" the optimal solution among the polynomial and enrichment shape functions. The detached-eddy simulation methodology provides a suitable turbulence model for the coarse near-wall cells. The approach is applied to wallmodeled LES of turbulent channel flow in a wide range of Reynolds numbers. Flow over periodic hills shows the superiority compared to an equilibrium wall model under separated flow conditions.

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

“…Wall modeling via function enrichment has been introduced by Krank and Wall and represents a highly efficient discretization method problem tailored for turbulent boundary layers. The topic of near‐wall subgrid modeling in the hybrid RANS/LES context has recently been addressed by extending the wall‐function‐enriched RANS solver based on the Spalart‐Allmaras model to DES . While that work allows the use of comparably coarse grids in wall‐normal direction in the inner layer as compared to classical DES, the issue of the RANS‐LES transition persisted.…”

“…A complete review of wall modeling approaches and RANS/LES methods would be beyond the scope of this article, so we refer to a series of review articles in this field . Within the high‐order DG method, detached‐eddy simulation (DES) models, a hybrid RANS/implicit large eddy simulation (ILES) model, and wall‐stress models based on equilibrium wall functions have been developed.…”

“…The scale separation allows appropriate turbulence modeling for each of the scales, a RANS turbulence model for the RANS equation and an LES turbulence model for the LES scale, exactly as they are derived through the three‐level hybrid RANS/LES filter. We note that this is a fundamental difference to the application of function enrichment in DES, where the domain is clearly separated into the inner RANS region and the outer LES region, with a “gray area” in between, since the RANS eddy viscosity acts on the polynomial velocity component as well in that study; these differences are detailed in the subsequent section.…”

“…The multiscale wall model is further compared to two of the classical hybrid RANS/LES wall models, the original DES approach by Spalart et al, which was recently applied with wall modeling via function enrichment in the work of Krank et al (in the delayed‐DES (DDES) variant), and the method of blending subgrid models through a weighted sum by Baggett . Both models follow the idea of two spatially separated zones, a RANS layer and an LES bulk flow, with a transition region in between.…”

“…It is this difference that avoids nonphysical velocity fluctuations, such as described by Baggett, within the present method. A direct qualitative and quantitative comparison of DES using function enrichment and the present multiscale wall model will be presented in Section 5.1.…”