Dynamically adaptive grid based discontinuous Galerkin shallow water model

A Godunov-type numerical model, which is based on the local planar Runge–Kutta discontinuous Galerkin (RKDG2) solutions to the two dimensional (2D) shallow water equations (SWEs) on a dynamically adaptive quadrilateral grid system, is developed in this work for shallow water wave simulations, with particular application to flood inundation modeling. To be consistent with the dynamic grid adaptation, the well-balanced RKDG2 framework is reformulated to facilitate realistic flood modeling. Grid adaptation and redistribution of flow data are automated based on simple measures of local flow properties. One analytical and two diagnostic test cases are used to validate the performance of the dynamically adaptive RKDG2 model against an alternative RKDG2 code based on uniform quadrilateral meshes. The adaptive model is then assessed by further applying it to reproduce a laboratory-scale tsunami benchmark case and the historical Malpasset dam-break event. Numerical evidence indicates that the new algorithm is able to resolve the moving wave features adequately at much less computational cost than the refined uniform grid-based counterpart.