Finite element analysis of free surface flow through gates

Two-dimensional finite element analyses of two types of gate-(i) a conduit gate with pressure flow upstream of the gate and free surface flow downstream of the gate and (ii) a sluice gate with free surfaces both upstream and downstream of the gate-are done using ideal fluid theory. The conduit gate problem is solved using both phi- and psi-formulations. Various methods of satisfying the boundary conditions were tested for both formulations. The psi-formulation developed in the present study is found to converge faster for flows with Froude numbers less than 4, which are common in sluice gates. The results obtained from the present study are compared with results from analytical and experimental techniques available in the literature. The psi-formulation developed in the present study is then used to solve the spillway gate problem, for which no analytical solution is available.