Finite element numerical simulation of transient free surface flows

In this paper, consideration is given to the numerical solution of the transient flow in prismatic open channels. In this study the flow is supposed unidirectional in a low slope channel. The Mathematical model consists of a system of two partial differential equations, hyperbolic, resolved numerically by the finite element method. To define the interpolation functions in the integral form of the weighted residuals, the Galerkin method was used. In applications, different prismatic sections are examined. The transient regimes are due to valve maneuvers downstream of the channel, the upstream end being connected to a constant reservoir. In these conditions, transient regime represents an evolution of flow from initial steady state to a final steady state. These two regimes are assumed uniform at constant flow defined by the Manning formula. The results concern the evolution of hydraulic parameters in different sections of the channel, following downstream maneuver. Two cases of maneuvers are considered; the case of an opening and the case of a closure. This study allowed analyzing the propagation and reflection of surface waves on both ends of the channel. Particularly, the numerical results show that when the width of the channel bed is very small (the triangular section) the fluctuations of depths are quickly damped.