A boundary-fitted numerical model for flood routing with shock-capturing capability

SummaryThe shallow water equations (SWEs) are solved numerically in general curvilinear coordinates for predicting flood flows. Second-order accuracy is achieved both in time and space through the use of the MacCormack scheme, in conjunction with a total variation diminishing (TVD) modification. The method is highly efficient as no local characteristic transformation is needed. The possible numerical imbalance induced by the inconsistent evaluation of the flux gradient and source terms is removed by employing the non-conservative form of the SWEs. All of the flow regimes and their transitions can be modelled. Specific considerations have been given to simulating flows in practical environments. The friction-slope term is discretized semi-implicitly when the water depth is smaller than a prescribed value. The check for flooding/drying (wet/dry status of the cell) is performed at each time step. Validation tests include steady flows along a deflected wall and a converging channel, unsteady wave diffraction around a circular cylinder, and the Malpasset dam-break flood in 1959. The results indicate that the present model is able to predict accurately the shock fronts, even over initially dry beds with friction and abrupt slope changes.