BEM numerical simulation of spillway flows

Abstract

The study of gravity-free surface flows presents difficulties, such as the nonlinearity of the dynamic boundary condition in the free surface, and also the fact that the location of this surface is not known a priori. Traditionally, this phenomenon has been investigated by physical models, but the progress of computer science and numeric methods has allowed more and more the successful use of mathematical models to simulate this type of flow. This work presents a boundary element method (BEM) numerical simulation of spillway flows with discontinuous linear elements. The solution procedure involves an iterative process in the determination of the free surface. The Newton-Raphson method is adopted together with the use of pseudo-nodes on the free surface and an empiric step factor (or damping factor) which controls the stability and the rate of convergence. An example of WES standard spillway shape is presented. The obtained results are compared with experimental data and they check the efficiency and good precision of the adopted method.