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Pollutant transport by shallow water flows on non-flat topography is presented and numerically solved using a finite volume scheme. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bathymetric gradients that may form in the approximate solution. The scheme is non-oscillatory and possesses conservation property that conserves the pollutant mass during the transport process. Numerical results are presented for three test examples which demonstrate the accuracy and robustness of the scheme and its applicability in predicting pollutant transport by shallow water flows. In this paper, we also apply the developed scheme for a pollutant transport event in the Strait of Gibraltar. The scheme is efficient, robust and may be used for practical pollutant transport phenomena.

SUMMARYWe discuss the application of a finite volume method to morphodynamic models on unstructured triangular meshes. The model is based on coupling the shallow water equations for the hydrodynamics with a sediment transport equation for the morphodynamics. The finite volume method is formulated for the quasi-steady approach and the coupled approach. In the first approach, the steady hydrodynamic state is calculated first and the corresponding water velocity is used in the sediment transport equation to be solved subsequently. The second approach solves the coupled hydrodynamics and sediment transport system within the same time step. The gradient fluxes are discretized using a modified Roe's scheme incorporating the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of source terms. We also describe an adaptive procedure in the finite volume method by monitoring the bed-load in the computational domain during its transport process. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bed gradients that may form in the approximate solution. Numerical results are shown for a test problem in the evolution of an initially hump-shaped bed in a squared channel. For the considered morphodynamical regimes, the obtained results point out that the coupled approach performs better than the quasi-steady approach only when the bed-load rapidly interacts with the hydrodynamics.

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