Mortar-based Entropy-Stable Discontinuous Galerkin Methods on Non-conforming Quadrilateral and Hexahedral Meshes

On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows

“…We note that the robustness, efficiency, and high order accuracy of both entropy stable DGSEM and entropy stable Gauss DG schemes have been verified in previous works [7,22,8,23,9], and will not be addressed in detail in this paper. However, the difference in robustness between the two methods has not been previously observed in the literature, and will be the focus of this work.…”

On the Entropy Projection and the Robustness of High Order Entropy Stable Discontinuous Galerkin Schemes for Under-Resolved Flows

“…These schemes began with staggered grid schemes on tensor product grids in [17], which were later extended to simplicial elements in [18]. "Modal" entropy stable DG formulations [19][20][21] have been utilized to construct a variety of new entropy stable schemes, including Gauss DG methods [22,23] and reduced order models [24]. We note that under appropriate choices of quadrature, these "modal" formulations reduce to collocation-type entropy stable schemes.…”