An adaptive simplex cut-cell method for high-order discontinuous Galerkin discretizations of multi-material and multi-physics problems

Abstract

In this paper we present a new approach for high-order discretizations of multi-material and multi-physics problems on non-geometry-conforming meshes. The approach consists of a discontinuous Galerkin (DG) discretization, a simplex cut-cell technique, and an outputbased adaptive scheme. With the cut-cell technique, the interface definition is completely separate from the mesh generation process, and no assumption is made on the interface shape (other than Lipschitz continuity). We demonstrate our solution strategy through several numerical examples, including a conjugate heat transfer problem.