Multiwavelet-based mesh adaptivity with Discontinuous Galerkin schemes: Exploring 2D shallow water problems

Abstract

In Gerhard et al. (2015a) a new class of adaptive Discontinuous Galerkin schemes has been introduced for shallow water equations, including the particular necessary properties, such as well-balancing and wetting-drying treatments. The adaptivity strategy is based on multiresolution analysis using multiwavelets in order to encode information across different mesh resolution levels. In this work, we follow-up on the previous proof-of-concept to thoroughly explore the performance, capabilities and weaknesses of the adaptive numerical scheme in the two-dimensional shallow water setting, under complex and realistic problems. To do so, we simulate three well-known and frequently used experimental benchmark tests in the context of flood modelling, ranging from laboratory to field scale. The real and complex topographies result in complex flow fields which pose a greater challenge to the adaptive numerical scheme and are computationally more ambitious, thus requiring a parallelised version of the aforementioned scheme. The benchmark tests allow to examine in depth the resulting adaptive meshes and the hydrodynamic performance of the scheme. We show that the scheme presented by Gerhard et al. (2015a) is accurate, i.e., allows to capture simultaneously large and very small flow structures, is robust, i.e., local grid refinement is controlled by just one parmeter that is auotmatically chosen and is more efficient in terms of the adaptive meshes than other shallow-water adaptive schemes achieving higher resolution with less cells.