A moment limiter for the discontinuous Galerkin method on unstructured tetrahedral meshes

Abstract

We propose a moment limiter for the second order discontinuous Galerkin method on unstructured meshes of tetrahedra. We provide a systematic way for reconstructing and limiting the solution moments from the cell averages. Our analysis, which is based on the linear advection equation, reveals a restriction on the time step and local intervals in which each moment must belong such that a local maximum principle is satisfied. The time step restriction is based on a new measure of cell size that is approximately twice as large as the radius of the inscribed sphere that is typically used. Finally, we discuss limiting across reflecting boundaries for the Euler equations. The efficacy of our limiting algorithm is demonstrated with a number of test problems.