An explicit filtering method for large eddy simulation of compressible flows

TLDR

The authors present a filter‑based LES method that achieves sub‑grid‑scale modeling solely through filtering procedures. They develop a mathematically consistent sub‑grid model by combining primary filtering, approximate deconvolution, and regularization into an equivalent low‑pass filter, and apply it to compressible Navier–Stokes equations for two supersonic channel flows, examining filter cut‑off, differentiation schemes, and grid refinement against DNS data. The LES results for Mach 1.5 and 3.0 at Reynolds 3000 and 6000 show that the effects of filter cut‑off, differentiation scheme, and grid refinement are consistent with filter characteristics, and all simulations converge uniformly to the DNS solutions.

Abstract

A method for large eddy simulation (LES) is presented in which the sub-grid-scale modeling is achieved by filtering procedures alone. The procedure derives from a deconvolution model, and provides a mathematically consistent approximation of unresolved terms arising from any type of nonlinearity. The formal steps of primary filtering to obtain LES equations, approximate deconvolution to construct the subgrid model term and regularization are combined into an equivalent filter. This filter should be an almost perfect low pass filter below a cut-off wavenumber and then fall off smoothly. The procedure has been applied to a pressure-velocity-entropy formulation of the Navier–Stokes equations for compressible flow to perform LES of two fully developed, turbulent, supersonic channel flows and has been assessed by comparison against direct numerical simulation (DNS) data. Mach numbers are 1.5 and 3.0, and Reynolds numbers are 3000 and 6000, respectively. Effects of filter cut-off location, choice of differentiation scheme (a fifth-order compact upwind formula and a symmetric sixth-order compact formula were used), and grid refinement are examined. The effects are consistent with, and are readily understood by reference to, filtering characteristics of the differentiation and the LES filter. All simulations demonstrate a uniform convergence towards their respective DNS solutions.