Truncated Navier–Stokes equations with the automatic filtering criterion: Reynolds stress and energy budgets

Abstract

A large eddy simulation (LES) technique has been previously developed using the combination of the truncated Navier–Stokes (TNS) methodology with the automatic filtering criterion. Numerical experiments were conducted to validate this model by comparing the computed low-order statistics in fully developed channel flows at low-to-moderate friction Reynolds numbers with the benchmark data. In this work, we show that in wall-resolved LES, the results are independent of the value of the filtering criterion as long as it falls into previously derived guideline range. Further, we analyze Reynolds stress and energy budgets in the simulations performed with this model. The analysis leads to better understanding of filtering effects on the energy transport and suggests how the filtering can be modified to manipulate the energy content in specific areas of the flow. Such selective filtering procedures improve results in marginally resolved LES and can be applied to transitional flows.

Keywords:

• large eddy simulations
• truncated Navier–Stokes equations
• automatic filtering criterion
• Reynolds stress budgets
• energy budgets

Acknowledgments

The numerical simulations in this work were performed at the University of Southern California High Performance Computing Center's (HPCC) Linux cluster (www.usc.edu/hpcc). One of the authors (JAD) has been partially supported by the ONR contract number N000140611073 (contract monitor Dr. Ron Joslin).