A positivity preserving and well-balanced DG scheme using finite volume subcells in almost dry regions

This paper deals with a subcell finite volume strategy for a discontinuous Galerkin (DG) scheme discretizing the shallow water equations with non-constant bottom topography. Using finite volume subcells within the DG scheme is a recent shock capturing strategy decomposing elements marked by a shock indicator into a specific number of subcells on which a robust FV scheme is applied. This work newly considers the subcell approach in the context of wetting and drying shallow water flows. Here, finite volume subcells are introduced for almost dry cells in order to enable an improved resolution of the wet/dry front. Furthermore, in this work, the theory for positivity preserving and well-balanced DG schemes is extended to the DG scheme using finite volume subcells. The performance of the resulting novel approach both in the context of preserving lake at rest stationary states and for wetting and drying computations is then numerically demonstrated for challenging standard test cases in two space dimensions on unstructured triangular grids.