The sampling‐based dynamic procedure as tool for higher‐order discretization

Abstract

SUMMARYAccuracy improvement is demonstrated by alternative use of a recently proposed LES formalism based on sampling operators. It is shown that the sampling-based dynamic procedure, in combination with an appropriate truncation error model, can be used as a technique to increase the numerical accuracy of a discretization. The technique is resemblant to Richardson extrapolation. The procedure is tested on a 2D lid-driven cavity at Re = 400 using a finite difference method. Promising results are obtained.

A family of dynamic finite difference schemes for large-eddy simulation

“…The schemes, inspired by the work of Winckelmans et al [12,13], Debliquy et al [14] and Knaepen et al [15], are constructed by combining Taylor expansions on two different grid resolutions, similar to Richardson Extrapolation. A first attempt of this technique has proven successful for obtaining higher accuracy in laminar flows in Fauconnier et al [16,17]. Here, we try to refine the technique for large-eddy simulation, and show the agreements with the work of Tam and Webb [7] and Kim and Lee [8].…”

“…Substitution of this coefficient into equation (17) leads to the nonlinear dynamic finite difference approximation.…”

Construction of explicit and implicit dynamic finite difference schemes and application to the large-eddy simulation of the Taylor–Green vortex

“…Obviously, the instantaneous energy spectrum is characterized by a specific shape and a filter-to-grid cutoff ratio j c =j max which can vary in time. Once these parameters are defined, it is possible to calculate the ratio c dyn k;n =c à k;n from the integral expression (51) and substitute it into the expression of the modified wavenumber (39) or (40). The behaviour of expression (51) as function of these parameters was already investigated in previous work [13].…”

“…Indeed, in earlier work of Fauconnier et al [38,39] the dynamic finite differencing technique was already successfully investigated for the laminar flow in a two-dimensional lid-driven cavity. This study demonstrated that the dynamic finite difference technique allows to increase the numerical accuracy of a wall-bounded laminar flow, by adapting the dynamic coefficients in the discretization scheme according to the specific flow solution.…”

On the use of biorthogonal interpolating wavelets for large-eddy simulation of turbulence

“…In particular, we study the simplified problem based on the unlifted wavelets. As a result from these investigations we establish an analogy between the unlifted wavelet-projected LES approach and the sampling-based formalism recently proposed in the literature [21][22][23][24].…”