Efficient entropy stable Gauss collocation methods

Abstract

The construction of high order entropy stable collocation schemes on quadrilateral and hexahedral elements has relied on the use of Gauss-Legendre-Lobatto collocation points and their equivalence with summation-by-parts (SBP) finite difference operators. In this work, we show how to efficiently generalize the construction of semi-discretely entropy stable schemes on tensor product elements to Gauss points and generalized SBP operators. Numerical experiments suggest that the use of Gauss points significantly improves accuracy on curved meshes.