Free surface flows are frequently encountered in hydraulic engineering problems including water jets, weirs and around gates. An iterative solution to the incompressible two-dimensional vertical steady Navier-Stokes equations, comprising momentum and continuity equations, is used to solve for the priori unknown free surface, the velocity and the pressure fields. The entire water body is covered by a unstructured finite element grid which is locally refined. The dynamic boundary condition is imposed for the free surface where the pressure vanishes. This procedure is done continuously until the normal velocities components vanish. To overcome numerical errors and oscillations encountering in convection terms, the SUPG (streamline upwinding Petrov-Galerkin) method is applied. The solution method is tested for different discharges onto a standard spillway geometries. The results shows good agreement with available experimental data.

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