Numerical assessments of a parametric implicit large eddy simulation model

Abstract

This study proposes a parametric implicit large eddy simulation (LES) strategy for the simulation of incompressible turbulence given by the Taylor–Green vortex. Our proposed scheme is derived from the dispersion-relation-preserving (DRP) philosophy to provide a specified numerical dissipation through a free modeling parameter. The specification of this dissipation control parameter represents a unique formulation for computing inviscid fluxes within the finite volume method. It is shown that the specification of a zero dissipation recovers the classical central DRP scheme. For comparison, we also evaluate multiple closure strategies from both implicit and explicit LES techniques through the use of various statistical quantities such as kinetic energy spectrum and energy dissipation rate. Some of the closure strategies examined, in addition to our scheme, include the use of established linear and nonlinear state reconstruction methods for implicit LES as well as the use of relaxation filtering utilized for explicit closure. In particular, it is seen that the proposed method embeds an identical low-pass spatial filtering through a state-reconstruction compared to our choice of the relaxation filter. In addition, consistency with the finite volume framework ensures more controllable dissipation. Our assessments indicate that the proposed numerical formulation obtains excellent reconstructions for statistical measures utilizing coarser grids and represents a viable approach for computationally efficient user-defined upwind based dissipation in implicit LES.