The paper On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows of Jesse Chan, Andrés M. Rueda-Ramírez, Gregor J. Gassner, Tim Warburton, and me has been published in Frontiers in Physics.
High order entropy stable schemes provide improved robustness for computational simulations of fluid flows. However, additional stabilization and positivity preserving limiting can still be required for variable-density flows with under-resolved features. We demonstrate numerically that entropy stable DG methods which incorporate an “entropy projection” are less likely to require additional limiting to retain positivity for certain types of flows. We conclude by investigating potential explanations for this observed improvement in robustness.