An H-Box Method For Shallow Water Equations Including Barriers

The shallow water equations provide the basic modeling equations for a number of coastal flooding hazards, such as tsunamis and storm surge. In realistic scenarios, there are often structures important to these flows that have a large extent but small width, including sea walls, berms, and harbor barriers. Explicit time stepping schemes, most often used for the shallow water equations, can then suffer from time step restrictions due to the CFL condition. In this article, we introduce an approach that side-steps these issues by allowing a barrier to have zero-width and to cut a cell arbitrarily without suffering from CFL restrictions. This is done by supplementing existing Riemann solvers and leveraging h-box and large time stepping methods. These methods preserve the properties of the Riemann solver and add negligible cost to the original solvers.