In this work, a numerical approach using finite element method is proposed for the integration of the nonlinear differential equation of the side weir flow in rectangular channel. After recalling the ordinary differential equation governing the problem, the numerical modeling is given by use of the Galerkin weighting residual method. The problem being of Cauchy with initial value, the element matrix obtained was rewritten in recurrence formula. The non-linearity of the latter is treated by an iterative technique for the variables; flow depth and lateral outflow. The performances of the numerical approach are confronted with experimental measurements available in the literature according to different flow regimes. The results obtained show a good agreement with the experimental observations.


Side weir, Numerical model, Finite elements, weighted residuals, Galerkin’s method.

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