A simple and efficient unstructured finite volume scheme for solving the shallow water equations in overland flow applications

Abstract

This paper presents the decoupled hydrological discretization (DHD) scheme for solving the shallow water equations in hydrological applications involving surface runoff in rural and urban basins. The name of the scheme is motivated by the fact that the three equations which form the two-dimensional shallow water system are discretized independently from each other and thus, the numerical scheme is decoupled in a mathematical sense. Its main advantages compared to other classic finite volume schemes for the shallow water equations are its simplicity to code and the lower computational cost per time step. The validation of the scheme is presented in five test cases involving overland flow and rainfall-runoff transformation over topographies of different complexity. The scheme is compared to the finite volume scheme of Roe (1986), to the simple inertia formulation, and to the diffusive wave model. The test cases show that the DHD scheme is able to compute subcritical and supercritical flows in rural and urban environments, and that in overland flow applications it gives similar results to the second-order scheme of Roe with a lower computational cost. The results obtained with the simple inertia and diffusive wave models are very similar to those obtained with the DHD scheme in rural basins in which the bed friction and topography dominate the flow hydrodynamics but they deteriorate in typical urban configurations in which the presence of supercritical flow conditions and small-scale patterns boost the relevance of the inertial terms in the momentum equations.