A Second-Order WENO-based Finite Volume Method for Flooding Simulations using Shallow Water Equations with Enhanced Bathymetry Resolution

Inland waterways provide an environmentally friendly and often more cost-efficient method of transporting goods across Europe. However, according to the UNECE, these waterways are under-exploited, and they plan on expanding the transportation network to increase their attractiveness. The reliability of waterways is key to promoting their use; therefore, flood control and accurate predictions are of utmost importance.

Subgrid methods for the shallow water equations (SWEs) are ideal for modeling inland flooding. These methods use two superimposed meshes: a coarse mesh, where the equations are solved, and an underlying subgrid mesh, where bathymetry data are stored to enhance water volume calculations, friction evaluation, and the accuracy of wet and dry fronts. The subgrid method was pioneered by Casulli [1]; however, the method presented here is explicit and shock-capturing, similar to the more recent approach by Sander et al. [2]. The method by Sanders relies on a cartesian grid, which limits geometric flexibility to handle accurately details of the terrain. In this work, we present a new subgrid method for solving SWEs on an unstructured simplex mesh with an underlying unstructured subgrid mesh, offering increased flexibility. The model solves the SWEs using a Godunov-type method with an intercell approximate Riemann solver, making it shock-capturing. It employs a second-order spatial WENO-type finite volume method, based on slope-limiting techniques introduced by [3]. This flexibility and spatial accuracy make the method ideal for modeling floods near rivers and channels, where it effectively resolves high velocities. At the workshop, we will discuss the model's concepts and showcase several smaller proof-of-concept examples.