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

Abstract

A high-resolution, unstructured grid, finite-volume algorithm is developed for unsteady, two-dimensional, shallow-water flow and scalar transport over arbitrary topography with wetting and drying. The algorithm uses a grid of triangular cells to facilitate grid generation and localized refinement when modeling natural waterways. The algorithm uses Roe’s approximate Riemann solver to compute fluxes, a multidimensional limiter for second-order spatial accuracy, and predictor–corrector time stepping for second-order temporal accuracy. The novel aspect of the algorithm is a robust and efficient procedure to consistently track fluid volume and the free surface elevation in partially submerged cells. This leads to perfect conservation of both fluid and dissolved mass, preservation of stationarity, and near elimination of artificial concentration and dilution of scalars at stationary or moving wet/dry interfaces. Multi-dimensional slope limiters, variable reconstruction, and flux evaluation schemes are optimized in the algorithm on the basis of accuracy per computational effort.