Large eddy simulations using truncated Navier–Stokes equations with the automatic filtering criterion

Abstract

We propose a large eddy simulation (LES) technique based on the previously developed Trancated Navier–Stokes (TNS) method. In TNS, the Navier–Stokes equations are solved through a sequence of direct numerical simulation runs and a periodic processing of small scales to provide the necessary dissipation. In the simplest case, the processing is accomplished by filtering the turbulent fields with a properly chosen filter. In the previous work, the period for processing was selected in advance for each case using heuristic arguments validated by trial and error. In this work, we develop a criterion that automates the selection of a time instant in simulations when the processing occurs. The criterion is based on the relationship between the energy of the flow field and the energy of the same field filtered with the chosen filter. The procedure is tested in LES of the turbulent channel flow performed at various Reynolds numbers and in domains of different sizes for which Direct Numerical Simulations (DNS) and experimental data are available for comparisons.

Keywords:

• large eddy simulations
• truncated Navier–Stokes equations
• explicit filtering
• automatic filtering criterion

Acknowledgements

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

Notes

^aThe total number of time steps until convergence to statistically steady state.

^bThe observed frequency of the filtering operation (every N _T time steps).

^cΔz ₁ ⁺ is the distance between the first grid point and the boundary.

^d N = N _x × N _y × N _z in TNS and baseline DNS rescaled to the same domain size.

^aFor HiDNS2, Δz ⁺ = Δz _max ⁺; for all other cases Δz ⁺ is the distance between the first grid point and the boundary.