A Riemann coupled edge (RCE) 1D–2D finite volume inundation and solute transport model

A novel 1D–2D shallow water model based on the resolution of the Riemann problem at the coupled grid edges is presented in this work. Both the 1D and the 2D shallow water models are implemented in a finite volume framework using approximate Roe’s solvers that are able to deal correctly with wet/dry fronts. After an appropriate geometric link between the models, it is possible to define local Riemann problems at each coupled interface and estimate the contributions that update the cell solutions from the interfaces. The solute transport equation is also incorporated into the proposed procedure. The numerical results achieved by the 1D–2D coupled model are compared against a complete 2D model, which is considered the reference solution. The computational time is also examined.