Accuracy considerations of mixed explicit implicit schemes for embedded boundary meshes

Abstract

We consider a mixed explicit implicit finite volume scheme for solving the advection equation on a Cartesian cut cell mesh: the scheme couples an implicit time stepping scheme on cut cells with an explicit time stepping scheme on cells away from the cut cells by means of flux bounding. We examine the accuracy of the resulting mixed scheme to see if a second-order explicit and a second-order implicit scheme result in a second-order mixed scheme.