Constructing robust high order entropy stable discontinuous Galerkin methods

High order methods are known to be unstable when applied to nonlinear conservation laws whose solutions exhibit shocks and turbulence. Entropy stable schemes address this instability by ensuring that physically relevant solutions satisfy a semi-discrete entropy inequality independently of numerical resolution or solution regularization and shock capturing. In this talk, we will review different approaches for constructing robust entropy stable discontinuous Galerkin methods and discuss the impact of different discretization choices on robustness for under-resolved compressible flows.