Solution of dam-break problem by collocation method in conjunction with hermite element

Abstract

The total and instantaneous collapse of a dam creates a negative wave upstream of the dam and a positive wave downstream of the dam. The negative wave propagates upstream along the reservoir and the positive wave propagates downstream either on a dry bed or on a water depth corresponding to the initial flow before the failure of the dam. The complete hydrodynamic equations of the shallow-water theory in one dimension are used to compute the flood wave resulting from the instantaneous collapse of a dam. A one-dimensional mathematical model has been developed based on collocation method in conjunction with quintic Hermite element to solve the system of flow equations. For the stability of the model no second-order pseudo viscosity terms are required. Moreover, no upwinding of the basis function is required. The model results obtained are compared with the test results of dam-break flood wave experiments carried out by Waterways Experiment Station (WES), U.S. Corps of Engineers ("Floods resulting from suddenly breached dams", 1960). It has been found that the model simulates most measured flood wave with reasonable accuracy. Close agreement between computed and measured stage and discharge hydrographs strongly suggests that the model is valid in routing the dam-break flood wave. The model can easily be applied to channels of arbitrary cross-sectional shapes, as well as to almost any other unsteady open channel flow problems by incorporating the appropriate initial and boundary conditions.