Scale Separation for Implicit Large Eddy Simulation

Introduction

Unlike standard large eddy simulation (LES) (for a review of LES for incompressible and compressible turbulence refer e.g. to [18, 7]), implicit LES (ILES) does not require an explicitly computed sub-grid scale (SGS) closure, but rather employs an inherent, usually nonlinear, regularization mechanism due to the nonlinear truncation error of the convective-flux discretization scheme as implicit SGS model. As finite-volume discretizations imply a top-hat filtered solution, regularized finitevolume reconstruction schemes were among the first ILES approaches, such as the flux-corrected transport (FCT) method [4], the piecewise parabolic method (PPM) [5]. Although ILES is attractive due to its relative simplicity, numerical robustness and easy implementation, it often exhibits inferior performance to explicit LES [8] if the discretization scheme is not constructed properly. Some schemes, such as PPM, FCT, MUSCL [16] and WENO [3] methods, work reasonably well for ILES by being able to recover a Kolmogorov-range for high-Reynolds-number turbulence up to k _max /2, where k _max is the Nyquist wavenumber of the underlying grid [9, 10, 21]. These promising results have led to further efforts on the physically-consistent design of discretization schemes for ILES. Physical consistency implies the correct and resolution-independent reproduction of the subgrid-scale (SGS) energy transfer mechanism of isotropic turbulence. Based on this notion the adaptive local deconvolution method (ALDM) has been developed [1, 11]. Approaches for decreasing excessive model dissipation for the solenoidal velocity field include the low-Mach number switch of [22], and the dilatation switch and shock sensor of [15].