An LES Setting for DG-Based Implicit LES with Insights on Dissipation and Robustness

Abstract

We suggest a new interpretation of implicit large eddy simulation (iLES) approaches based on discontinuous Galerkin (DG) methods by analogy with the LES-PLB framework (Pope, Fluid mechanics and the environment: dynamical approaches. Springer, Berlin, 2001), where PLB stands for ‘projection onto local basis functions’. Within this framework, the DG discretization of the unfiltered compressible Navier-Stokes equations can be recognized as a Galerkin solution of a PLB-based (and hence filtered) version of the equations with extra terms originating from DG’s implicit subgrid-scale modelling. It is shown that for under-resolved simulations of isotropic turbulence at very high Reynolds numbers, energy dissipation is primarily determined by the property-jump term of the Riemann flux employed. Additionally, in order to assess how this dissipation is distributed in Fourier space, we compare energy spectra obtained from inviscid simulations of the Taylor-Green vortex with different Riemann solvers and polynomial orders. An explanation is proposed for the spectral ‘energy bump’ observed when the Lax-Friedrichs flux is employed.