An explicit filtering method for large eddy simulation of compressible flows

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.

Computation of the Self-Similarity Region of a Turbulent Round Jet Using Large-Eddy Simulation

“…The selective filtering is applied explicitly every second iteration to remove the grid-to-grid oscillations without affecting the resolved scales, but also to provide the effects of the subgrid energydissipating scales. The LES approach based on explicit filtering has been successfully used by different authors for various flows [8,11,12,13]. It has been shown in particular that the filtering does not artificially decrease the effective flow Reynolds number unlike subgrid models based on eddy-viscosity [9].…”

Study of Some Key Issues for Applying LES to Real Engineering Problems

“…Low order filters can also obtain good results. It is similar to the strategy used by Mathew et al (Mathew et al 2003). A one-dimensional filter given by Vasilyev et al (Vasilyev et al 1998) is defined as:…”

A High-Order Compact Finite-Difference Scheme for Large-Eddy Simulation of Active Flow Control

“…Mathew et al [27] have shown that filtering provides a mathematically consistent approximation of unresolved terms arising from any type of nonlinearity. Filtering regularizes the solution, and generates virtual subgrid model terms that are equivalent to those of approximate deconvolution.…”

“…Equation (27) illustrates that Fourier components of the filtered function φ m are related to those of the original function by…”