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

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. The governing Partial Differential Equations are discretized using a procedure similar to the linear conforming Finite Element Galerkin scheme, with a different flux formulation and a special flux treatment that requires Delaunay triangulation but entire solution monotonicity. A simple mesh adjustment is suggested, that attains the Delaunay condition for all the triangle sides without changing the original nodes location and also maintains the internal boundaries. The original governing system is solved applying a fractional time step procedure, that solves consecutively a convective prediction system and a diffusive correction system. The non linear components of the problem are concentrated in the prediction step, while the correction step leads to the solution of a linear system of the order of the number of computational cells. A semi-analytical procedure is applied for the solution of the prediction step. The discretized formulation of the governing equations allows to handle also wetting and drying processes without any additional specific treatment. Local energy dissipations, mainly the effect of vertical walls and hydraulic jumps, can be easily included in the model.Several numerical experiments have been carried out in order to test (1) the stability of the proposed model with regard to the size of the Courant number and to the mesh irregularity, (2) its computational performance, (3) the convergence order by means of mesh refinement. The model results are also compared with the results obtained by a fully dynamic model. Finally, the application to a real field case with a Venturi channel is presented.

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