Finite-Element Modeling of Floodplain Flow

A new methodology for a robust solution of the diffusive shallow water equations is proposed. The methodology splits the unknowns of the momentum and continuity equations into one kinematic and one parabolic component. The kinematic component is solved using the slope of the water level surface computed in the previous time-step and a zero-order approximation of the water head inside the mass-balance area around each node of the mesh. The parabolic component is found by applying a standard finite-element Galerkin procedure, where the source terms can be computed from the solution of the previous kinematic problem. A simple 1D case, with a known analytical solution, is used to test the accuracy of the model. A second test is performed by comparing, in a more complex case, the flow rates computed by the model with the flow rates directly estimated from the computed water heads. An application to a real 2D case of flood flow on a river floodplain shows the practical advantages of the methodology.