Variational Multiscale SGS modeling for LES using high-order Discontinuous Galerkin method.

High-order methods for the simulation of turbulent flows have gained significant attention for their attractive numerical dissipative and dispersive properties. Among others, the Discontinuous Galerkin (DG) method has been the focus of active research. One of the main challenges of using DG methods for Large Eddy Simulations (LES) is the solution stabilization on underresolved meshes. Recently, an entropy-bounded scheme has been proposed for the solution stabilization in the context of Implicit LES (ILES). In contrast, the Variational Multiscale (VMS) formulation exploits the flexibility and
modal separation of the high-order DG-methods in the formulation of physical subgrid scale (SGS) models. VMS applies standard SGS models to a selected number of resolved modes using the polynomial modal expansion. The purpose of this study is to examine the spectral properties of ILES and VMS LES. Specifically,  by considering compressible isotropic turbulence, statistical properties and effects of both methods on the energy transfer between scales will be investigated.