An exact source-term balancing scheme on the finite element solution of shallow water equations

Abstract

In this paper, a numerical model is presented based on a semi-discrete Streamline Upwind Petrov–Galerkin scheme for solving the two-dimensional shallow water equations with arbitrary bed topography and wetting–drying fronts. The present finite element method is implemented for moving-boundary problems on fixed numerical meshes. In order to satisfy the C-property for both still water and dry regions, a new exact source-term balancing method is presented within the finite element framework. The formulation is stabilized using two different stabilization terms, and a discontinuity-capturing scheme is used to simulate steep wave fronts. The second-order scheme is applied for both temporal and spatial discretization. The proposed mathematical balancing method is verified through well-known test cases including the traditional dam break problem, evolution of a dam break wave over an obstacle, and oscillation of a bead of water in a parabolically-shaped basin.