Application of Modal Filtering in Discontinuous Spectral Element Method for Simulation of Compressible Channel Flow at Different Reynolds Numbers

TL;DR

This paper evaluates a modal filtering approach within the discontinuous spectral element method for simulating compressible channel flows at various Reynolds numbers, showing promising accuracy in predicting key turbulent statistics.

Contribution

It introduces and assesses a novel modal filtering technique in DSEM for compressible flows, demonstrating its effectiveness in turbulence simulation at different Reynolds numbers.

Findings

Maximum 2.16% error in friction Reynolds number prediction

Promising average velocity profile results compared to DNS

Filter parameters need tuning for accurate rms statistics

Abstract

Large-eddy simulation of incompressible turbulent flow has been extensively investigated; hence, a variety of models suited for different numerical schemes have been developed. In the case of compressible flow, the modeling is more challenging due to the numerous terms that arise in the filtered Navier-Stokes equations. Recently, modal explicit filtering was implemented in the discontinuous spectral element method (DSEM) to mimic the effects of sub-filtered scales for compressible flows. The method is computationally inexpensive since it is implemented in the DSEM code using a well-established math library. It has been successfully applied to simulations of compressible decaying isotropic turbulence and turbulent channel flow. In this study, channel flows with three different friction Reynolds numbers are simulated using explicit modal filtering in DSEM to assess the performance of the new method by comparing turbulent statistics and friction Reynolds numbers to those from DNS. The model predicts the friction Reynolds number with a maximum of 2.16% error with respect to DNS. Although the model generates promising results for the average velocity profile compared to DNS, it requires adjustment of filter strength and frequency to predict rms statistics accurately.