Unstructured Grid Finite Volume Algorithm for Shallow-Water Flow and Transport with Wetting and Drying

Two high-resolution, unstructured grid, finite volume algorithms are developed for unsteady, two-dimensional, shallow-water flow and scalar transport over arbitrary topography with wetting and drying. The algorithms either use grids of triangular cells (which facilitates grid generation and localized refinement when modeling natural waterways) or quadrilateral cells. The algorithms use Roe's approximate Riemann solver to compute fluxes, a multi-dimensional limiter for second-order spatial accuracy, and predictor-corrector time stepping for second-order temporal accuracy. A robust and novel procedure is introduced to consistently track fluid volume and the free surface elevation in partially submerged cells, which leads to excellent flow and scalar transport predictions in the presence of a stationary or moving wet/dry interface. The two algorithms are found to perfectly conserve both fluid and dissolved mass, preserve stationarity, and nearly eliminate artificial concentration and dilution of scalars at wet/dry interfaces