SUMMARYThe one-dimensional Saint Venant equations for shallow-water ows are used to simulate the ood wave resulting from the sudden opening (or closure) of a gate or collapse of a dam. An iterative explicit characteristics-based ÿnite-di erence method, based on the explicit ÿnite analytic method, is proposed to discretize the dynamic equation, and the conservative control volume method is used for the discretization of the continuity equation. Surge and dam-break ows in a horizontal, rectangular and frictionless channel were ÿrst considered, under such conditions the analytic solutions exist. For the surge simulation, numerical results of the proposed scheme are nearly identical to those obtained from the Preissmann scheme. For the dam-break simulations addressing three ratios of tailwater depth to water depth in the reservoir, the proposed scheme, as compared with the analytic solutions, yields better results than those obtained by the MacCormack scheme, the Gabutti scheme, and Jha et al.'s ux splitting scheme (J. Hydraul. Res. 1996; 34(5):605-621). As the depth ratio approaches zero, the accuracy of the proposed scheme is still satisfactory, even with the dry-bed condition. Investigations then were made for more realistic dam-break ow waves propogating in a sloped and frictional channel. Lacking analytic solutions, the simulating results from the proposed scheme as well as those from Chen's scheme (J. Hydraul. Div. 1980; 106(HY4):535-556) were compared with the laboratory data collected in 1960 -1961 at the United States Army Engineer Waterways Experiments Station (WES). An assumed initial ow was required for the computer-simulated condition in Chen's model. However, this is not the case in the proposed model, i.e., a real dry-bed condition was set as the initial condition in the downstream channel of the dam. The consistency between the two simulated results is obvious compared with the experimental data.

A depth‐averaged two‐dimensional model has been developed in the curvilinear co‐ordinate system for free‐surface flow problems. The non‐linear convective terms of the momentum equations are discretized based on the explicit–finite–analytic method with second‐order accuracy in space and first‐order accuracy in time. The other terms of the momentum equations, as well as the mass conservation equation, are discretized by the finite difference method. The discretized governing equations are solved in turn, and iteration in each time step is adopted to guarantee the numerical convergence. The new model has been applied to various flow situations, even for the cases with the presence of sub‐critical and supercritical flows simultaneously or sequentially. Comparisons between the numerical results and the experimental data show that the proposed model is robust with satisfactory accuracy. Copyright © 2000 John Wiley & Sons, Ltd.