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

High-order entropy-stable discontinuous Galerkin (DG) methods for nonlinear conservation laws reproduce a discrete entropy inequality by combining conservative finite volume fluxes with summation-by-parts (SBP) discretization matrices. In the DG context, on tensor product (quadrilateral and hexahedral) elements, SBP matrices are typically constructed collocating at Lobatto quadrature points. Recent work has extended construction of schemes to collocation more accurate Gauss points (Chan et al. in SIAM J Sci Comput 41(5):A2938–A2966, 2019) . this work, we extend non-conforming meshes. Entropy-stable require computing numerical between surface nodes. On conforming meshes where nodes aligned, flux evaluations required only “lines” However, meshes, no longer resulting larger number evaluations. We reduce expense introducing an mortar-based treatment interfaces via face-local correction term, provide necessary conditions high-order accuracy. Numerical experiments compressible Euler equations two three dimensions confirm stability accuracy approach.