On the role of spectral properties of viscous flux discretization for flow simulations on marginally resolved grids

TL;DR

This paper examines how the spectral properties of viscous flux discretization affect turbulent flow simulations on coarse grids, demonstrating that an $oldsymbol{ ext{α}}$-damping method yields more accurate solutions and better convergence to DNS.

Contribution

It introduces a compact $oldsymbol{ ext{α}}$-damping discretization method with improved spectral properties for viscous fluxes, enhancing accuracy in turbulent flow simulations on marginally resolved grids.

Findings

The $oldsymbol{ ext{α}}$-damping method outperforms other discretizations at high wavenumbers.

The proposed method converges to DNS solutions at lower grid resolutions.

Better spectral properties lead to more accurate turbulent flow simulations.

Abstract

In this note, the importance of spectral properties of viscous flux discretization in solving compressible Navier-Stokes equations for turbulent flow simulations is discussed. We studied six different methods, divided into two different classes, with poor and better representation of spectral properties at high wavenumbers. Both theoretical and numerical results have revealed that the method with better properties at high wavenumbers, denoted as $\alpha$-damping type discretization, produced superior solutions compared to the other class of methods. The proposed compact $\alpha$-damping method converged towards the direct numerical simulation (DNS) solution at lower grid resolution compared with the other class of methods and is, therefore, a better candidate for high fidelity large-eddy simulations (LES) and DNS studies.