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

TL;DR

This paper introduces an extension of wall modeling via function enrichment to detached-eddy simulation, enabling accurate near-wall flow modeling with coarse meshes while fulfilling the full Navier-Stokes equations.

Contribution

It presents a novel wall modeling approach that combines function enrichment with high-order discontinuous Galerkin methods within detached-eddy simulation, improving accuracy in separated flows.

Findings

Effective in turbulent channel flow across Reynolds numbers

Superiority over equilibrium wall models in separated flow

Enables coarse near-wall cell modeling with full Navier-Stokes compliance

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 wall-modeled 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.