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Speaker: Jesse Chan, University of Texas - Austin
Title: An artificial viscosity approach to entropy stable high order DG methods
Abstract: Entropy stable discontinuous Galerkin (DG) methods improve the robustness of high order DG simulations of nonlinear conservation laws. These methods yield a semi-discrete entropy inequality, and rely on an algebraic flux differencing formulation which involves both summation-by-parts discretization matrices and entropy conservative two-point finite volume fluxes. However, explicit expressions for such two-point finite volume fluxes may not be available for all systems, or may be computationally expensive to compute.
We propose an alternative approach to constructing entropy stable DG methods using an artificial viscosity coefficient based on the local violation of a cell entropy inequality and a local entropy dissipation estimate. The resulting method yields the same global semi-discrete entropy inequality satisfied by entropy stable flux differencing DG methods. The artificial viscosity coefficients are parameter-free and locally computable over each cell. The resulting artificial viscosity preserves high order accuracy, improves linear stability, and does not result in a more restrictive maximum stable time-step size under explicit time-stepping.