Entropy behavior for underresolved discontinuous Galerkin discretizations of the Navier-Stokes equations

Abstract

High-order methods are emerging as a crucial tool for aerodynamics. One application is for solving large eddy simulations (LES). The use of the discontinuous Galerkin (DG) discretization in particular has attractive properties for these simulations. The stabilization methods used for high-order DG for underresolved Navier Stokes perform some compensation for subgrid scale effects, like subgrid-scale modeling in explict LES. In this work, the mathematical formulation of the finite element method is used to create a new technique for quantifying the artificial generation of entropy due to stabilization in a common DG formulation, in order to clarify the necessity of explicit subgrid modeling and give insight into future modeling strategies for LES performed using high-order finite element methods.