Nonhydrostatic Dam Break Flows. I: Physical Equations and Numerical Schemes

Abstract

Modeling of dam break flows is frequently required in civil and environmental engineering because of the risk associated with this catastrophic flow. Typically, model predictions are conducted using the Saint-Venant hydrostatic theory, which can lead to unrealistic predictions. The prediction of the amplitude of nonhydrostatic waves generated during dam break flows is an important engineering problem given the risk of overtopping of flow in manmade canals or the increasing of flooding areas in natural watercourses. The weakly nondispersive and fully nonlinear Serre equations are a suitable choice for modeling these flows, but there is a lack of a systematic assessment of this system of equations for dam break flow modeling reported in the literature. In this paper, the Serre equations are applied to dam break flows over horizontal rigid bottoms, whereas in the second part of this research, the nonhydrostatic dam break waves over erodible beds are considered. Here, a high resolution finite volume model is developed where a suitable time stepping scheme is systematically investigated. The impact of the vertical pressure distribution shape, nonlinear terms in the equations, and the enhancement of the linear frequency dispersion are examined in detail. The model is successfully tested against the experimental data, a solitary wave propagation test, and the three-dimensional (3D) simulations. The results obtained from finite volume method are further compared with those obtained from finite element and finite difference methods available in the literature.