A 2D shallow water flow model with 1D internal boundary condition for subgrid-scale topography

In this work, a dynamic internal boundary condition is used as subgrid model in a two-dimensional (2D) model based on the shallow water equations in order to model narrow regions in the domain. In this way, computational savings are sought, since it is not necessary to discretize these regions with cells of reduced size. The new internal boundary condition simplifies other works where 1D–2D coupled models were presented, since the 1D model is a subgrid for the 2D mesh, so the coupling between both models is simple and direct. The coupling is performed using mass conservation, simplifying the calculation in the transfer between both models. Test cases are studied to validate the implemented boundary condition, and a mountain catchment as a realistic case. The results obtained with a fully 2D mesh and a 2D mesh with rills in narrow regions are very similar, with a large reduction in computational cost when using rills, both in test cases and in the realistic case. Thus, the use of the implemented internal boundary condition is an effective tool to study regions with narrow regions by reducing the computational cost with little loss of accuracy in the results.