On the All-Speed Roe-type Scheme for Large Eddy Simulation of Homogeneous Decaying Turbulence

TL;DR

This paper analyzes and improves the Roe scheme for large eddy simulation of homogeneous decaying turbulence, reducing numerical dissipation to better capture turbulence spectra even on coarse grids.

Contribution

The paper introduces a novel all-speed LES-Roe scheme that minimizes dissipation and enhances turbulence simulation accuracy compared to traditional Roe schemes.

Findings

The parts , , and have minimal impact on LES results.

Large numerical dissipation mainly originates from and , exceeding SGS dissipation.

The improved scheme achieves accurate LES results on coarse grids.

Abstract

As the representative of the shock-capturing scheme, the Roe scheme fails to LES because important turbulent characteristics cannot be reproduced such as the famous k-5/3 spectral law owing to large numerical dissipation. In this paper, the Roe scheme is divided into five parts: , , , , and , which means basic upwind dissipation, pressure-difference-driven and velocity-difference-driven modification of the interface fluxes and pressure, respectively. Then, the role of each part on LES is investigated by homogeneous decaying turbulence. The results show that the parts , , and have little effect on LES. It is important especially for because it is necessary for computation stability. The large numerical dissipation is due to and , and each of them has much larger dissipation than SGS dissipation. According to these understanding, an improved all-speed LES-Roe scheme is proposed, which can give enough good LES results for even coarse grid resolution with usually adopted reconstruction.