Impact of wall modeling on kinetic energy stability for the compressible Navier-Stokes equations

TL;DR

This paper investigates how different wall models affect the stability of high-order simulations of turbulent flows, revealing a trade-off between accuracy and stability for common wall models.

Contribution

It introduces a kinetic energy stability estimate to analyze wall model boundary conditions, comparing equilibrium stress and dynamic slip models.

Findings

Equilibrium stress wall model is accurate but unstable.

Dynamic slip wall model is stable but less accurate.

Stability results extend to discrete numerical methods.

Abstract

Affordable, high order simulations of turbulent flows on unstructured grids for very high Reynolds number flows require wall models for efficiency. However, different wall models have different accuracy and stability properties. Here, we develop a kinetic energy stability estimate to investigate stability of wall model boundary conditions. Using this norm, two wall models are studied, a popular equilibrium stress wall model, which is found to be unstable and the dynamic slip wall model which is found to be stable. These results are extended to the discrete case using the Summation by parts (SBP) property of the discontinuous Galerkin method. Numerical tests show that while the equilibrium stress wall model is accurate but unstable, the dynamic slip wall model is inaccurate but stable.