Explicit filtering and exact reconstruction of the sub-filter stresses in large eddy simulation

Abstract

Explicit filtering has the effect of reducing numerical or aliasing errors near the grid scale in large eddy simulation (LES). We use a differential filter, namely the inverse Helmholtz operator, which is readily applied to unstructured meshes. The filter is invertible, which allows the sub-filter scale (SFS) stresses to be exactly reconstructed in terms of the filtered solution. Unlike eddy viscosity models, the method of filtering and reconstruction avoids making any physical assumptions and is therefore valid in any flow regime. The sub-grid scale (SGS) stresses are not recoverable by reconstruction, but the second-order finite element method used here is an adequate source of numerical dissipation in lieu of an SGS model. Results for incompressible turbulent channel flow at Re τ = 180 are presented which show that explicit filtering and exact SFS reconstruction is a significant improvement over the standard LES approach of implicit filtering and eddy-viscosity SGS modelling.

Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence

“…We aim to utilize the dissipative behavior of this framework to prevent Gibbs oscillations which arise due to the use of central schemes in governing laws with dominating hyperbolic behavior. Relaxation filtering has been used with success for the large eddy simulation of homogeneous isotropic turbulence [47] and represents a computationally inexpensive approach to subgrid scale modeling [48]. Various filters have also been utilized for the relaxation filtering methodology [49,50] and the choice of free filtering parameters is crucial for this method.…”

Subgrid-scale stresses and scalar fluxes constructed by the multi-scale turnover Lagrangian map

“…54 and more recently Ref. 55). From this reconstructed velocity field, one may calculate the approximate τ ij , although its expression is not derived explicitly.…”

Explicit and implicit LES closures for Burgers turbulence

“…Therefore, it has been concluded that a mesh should be finer than the smallest eddy that one hopes to resolve when using explicit filtering. Further details on how the explicit filtering has the effect of reducing numerical errors near the grid cut-off scale can be found in a recent work of Bull and Jameson (2016).…”

“…Therefore the understanding of how the filter shape affects LES results is of paramount importance in constructing efficient and consistent LES closure models (De Stefano and Vasilyev 2002). Various low-pass filtering procedures have been reported in LES literature (Schumann 1975;Jordan and Ragab 1996;Najjar and Tafti 1996;Vasilyev, Lund, and Moin 1998;Sagaut and Grohens 1999;Mullen and Fischer 1999;Pruett and Adams 2000;Brandt 2006;Berland et al 2011;San, Staples, and Iliescu 2015;Bull and Jameson 2016). Although the filter design process is well established in digital image processing (Oppenheim, Schafer, and Buck 1989;Jahne 1997), there is a limited number of studies that focuses on filter design in LES (e.g., see San (2016) and references therein).…”