Collocation Finite-Element Simulation of Dam-Break Flows

Abstract

The one-dimensional hydrodynamic equations based on shallow-water theory are used to compute the flood wave resulting from the total instantaneous collapse of a dam. The collocation method is used in conjunction with quintic Hermite elements to solve the system of flow equations. Quintic Hermite elements are used to provide the high resolution required in the solution of discontinuities, thereby producing satisfactorily stable solutions. The model can simulate both subcritical and supercritical flows in different parts of the channel or in a sequence in time. The model is stable, although there are no second-order pseudoviscosity terms in it. No upwinding of the basis function is required. Linear stability analysis reveals the selective damping of short wavelengths and excellent phase accuracy of the model and insensitivity to parameter variation. The computed results are compared with the test results of the U.S. Corps of Engineers, Waterways Experiment Station. Close agreement between computed and measured stage and discharge hydrographs strongly suggests that the model is valid in routing dam-break flood waves.