Iterative explicit simulation of 1D surges and dam‐break flows

Abstract

AbstractThe one‐dimensional Saint Venant equations for shallow‐water flows are used to simulate the flood wave resulting from the sudden opening (or closure) of a gate or collapse of a dam. An iterative explicit characteristics‐based finite‐difference method, based on the explicit finite 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 flows in a horizontal, rectangular and frictionless channel were first 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 flux 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 flow 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 flow 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. Copyright © 2002 John Wiley & Sons, Ltd.