The large eddy simulation (LES) equations of turbulent flows are formally derived by applying a low-pass filter to the Navier–Stokes equations. As a result the subgrid-scale (SGS) stress tensor strongly depends on the assumed filter shape, which causes a SGS model to be filter dependent. In particular, depending on the choice of the filter the corresponding SGS model should satisfy very different requirements in terms of large scale dynamics and kinetic energy budget. This paper is an attempt to systematically study the effect of the filter shape on the subgrid scale model and its subsequent effect on LES. For the sake of simplicity, we consider numerical simulation of a one-dimensional homogeneous flow, governed by the viscous Burgers equation. Large eddy simulations of the solution of the Burgers problem are performed using subgrid scale models obtained by filtering data from direct numerical simulations. Diagnostics include temporal evolution of energy and dissipation as well as energy spectra. It is demonstrated both theoretically and numerically that the assumed filter shape can have a significant effect on LES in terms of spectral content and physical interpretation of the solution. The results are generalized for LES of three-dimensional turbulent flows and specific recommendations for the use of filters and corresponding SGS models are made.

The stochastic coherent adaptive large eddy simulation (SCALES) methodology is a novel approach to the numerical simulation of turbulence, where a dynamic grid adaptation strategy based on wavelet threshold filtering is utilized to solve for the most ‘energetic’ eddies. The effect of the less energetic unresolved motions is simulated by a model. Previous studies have demonstrated excellent predictive properties of the SCALES approach for decaying homogeneous turbulence. In this paper the applicability of the method is further explored for statistically steady turbulent flows by considering linearly forced homogeneous turbulence at moderate Reynolds number. A local dynamic subgrid-scale eddy viscosity model based on the definition of the kinetic energy associated with the unresolved motions is used as closure model. The governing equations for the wavelet filtered velocity field, along with the additional evolution equation for the subgrid-scale kinetic energy, are numerically solved by means of a dynamically adaptive wavelet collocation method. It is demonstrated that adaptive simulations closely match results from a reference pseudo-spectral fully de-aliased direct numerical simulation, by using only about 1% of the corresponding computational nodes. In contrast to classical non-adaptive large eddy simulation, the agreement with direct solution holds for the mean flow statistics as well as in terms of energy and enstrophy spectra up to the dissipative wavenumbers range.

The ability of wavelet multi-resolution analysis to detect and track the energy-containing motions that govern the dynamics of a fluid flow offers a unique hierarchical framework for modelling and simulating turbulence. In this paper, the role of the wavelet thresholding level in wavelet-based modelling and simulation of turbulent flows is systematically examined. The thresholding level controls the relative importance of resolved energetic structures and residual unresolved background flow and, thus, the achieved turbulence resolution. A fully adaptive eddy capturing approach is developed that allows variable-fidelity numerical simulations of turbulence to be performed. The new method is based on wavelet filtering with time-varying thresholding. The thresholding level automatically adapts to the desired turbulence resolution during the simulation. The filtered governing equations supplemented by a localized dynamic energy-based closure model are solved numerically using the adaptive wavelet collocation method. The approach is successfully tested in the numerical simulation of both linearly forced and freely decaying homogeneous turbulence.

A wavelet-based adaptive approach, called wavelet-based adaptive unsteady Reynolds-averaged Navier–Stokes (WA-URANS), is proposed to solve the URANS equations for the computation of wall-bounded in...