On the Entropy Projection and the Robustness of High Order Entropy Stable Discontinuous Galerkin Schemes for Under-Resolved Flows
Jesse Chan, Hendrik Ranocha, Andrés M. Rueda-Ramírez, Gregor J. Gassner, Tim Warburton
Abstract
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 Discontinuous Galerkin (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.
Topics & Concepts
Robustness (evolution)Discontinuous Galerkin methodLimitingEntropy (arrow of time)MathematicsApplied mathematicsStatistical physicsMathematical optimizationComputer scienceFinite element methodPhysicsThermodynamicsEngineeringGeneBiochemistryChemistryMechanical engineeringComputational Fluid Dynamics and AerodynamicsFluid Dynamics and Turbulent FlowsModel Reduction and Neural Networks