Wall-modeled large-eddy simulation based on spectral-element discretization

TL;DR

This paper evaluates the use of spectral-element methods for wall-modeled large-eddy simulations, demonstrating effective turbulence modeling and high accuracy in complex flow cases despite some numerical challenges.

Contribution

It introduces algebraic wall modeling into SEM-based LES, compares SGS models, and assesses SEM's performance for turbulent flows on coarse grids.

Findings

Vreman SGS model provides good stability and resolution.

SEM achieves state-of-the-art accuracy in turbulent flow simulations.

Coarse grid challenges include derivative jumps and boundary condition issues.

Abstract

This article analyses the simulation methodology for wall-modeled large-eddy simulations using solvers based on the spectral-element method (SEM). To that end, algebraic wall modeling is implemented in the popular SEM solver Nek5000. It is combined with explicit subgrid-scale (SGS) modeling, which is shown to perform better than the high-frequency filtering traditionally used with the SEM. In particular, the Vreman model exhibits a good balance in terms stabilizing the simulations, yet retaining good resolution of the turbulent scales. Some difficulties associated with SEM simulations on relatively coarse grids are also revealed: jumps in derivatives across element boundaries, lack of convergence for weakly formulated boundary conditions, and the necessity for the SGS model as a damper for high-frequency modes. In spite of these, state-of-the-art accuracy is achieved for turbulent channel flow and flat-plate turbulent boundary layer flow cases, proving the SEM to be a an excellent numerical framework for massively-parallel high-order WMLES.