A new finite volume method for flux-gradient and source-term balancing in shallow water equations

We present a new finite volume method for flux-gradient and source-term balancing in the numerical solution of shallow water equations on nonflat topography. The method consists of a predictor stage for discretization of gradient terms and a corrector stage for treatment of source terms. The numerical fluxes at the interfaces of each triangle are reconstructed using an upwind scheme along with slope limiters to obtain high accuracy in the method. Using a three-sided decomposition, the source terms are balanced in the corrector stage. The proposed method is implemented on unstructured meshes and verifies the exact conservation property (C-property). We also discuss a mesh adaptive procedure by monitoring the water depth in the computational domain. Several standard test examples are used to verify high accuracy, exact C-property and good resolution properties for smooth and discontinuous solutions.