Robust wetting and drying with discontinuous Galerkin flood model on unstructured triangular meshes

Godunov-based finite volume (FV) methods are widely employed to numerically solve the Shallow-Water Equations (SWEs) with application to simulate flood inundation over irregular geometries and real-field, where unstructured triangular meshing is favored. Second-order extensions have been devised, mostly on the MUSCL reconstruction and the discontinuous Galerkin (DG) approaches. In this paper, we introduce a novel second-order Runge–Kutta discontinuous Galerkin (RKDG) solver for flood modeling, specifically addressing positivity preservation and wetting and drying on unstructured triangular meshes. To enhance the RKDG model, we adapt and refine positivity-preserving and wetting and drying techniques originally developed for the MUSCL-based finite volume (FV) scheme, ensuring its effective integration within the RKDG framework. Two analytical test problems are considered first to validate the proposed model and assess its performance in comparison with the MUSCL formulation. The performance of the model is further explored in real flooding scenarios involving irregular topographies. Our findings indicate that the added complexity of the RKDG model is justified, as it delivers higher-quality results even on very coarse meshes. This reveals that there is a promise in deploying RKDG-based flood models in real-scale applications, in particular when field data are sparse or of limited resolution.