Finite Analytic Solution of Flow over spillways

In this study, two‐dimensional irrotational gravity flows over a spill‐way with a free surface are investigated numerically and compared to available experimental measurements. The difficulty of the present problem lies in that both the free surface elevation and flow rate are unknowns, even when the reservoir and spillway crest heights are given. In order to solve the problem, the boundary‐fitted coordinate system is adopted to map the complex domain into a rectangular domain with uniform meshes. The finite analytic method is used to obtain the numerical solution. In the finite analytic method, the local analytic solution of the governing equation in an element is obtained and used to formulate the algebraic representation of the governing equation. The discharge coefficient is deduced by a scan method according to the variational principle for variable domains. The prediction is made for the Waterways Experimental Station spillway, where extensive data are available for comparison. The numerical results agree well with experimental data on discharge coefficients and free surface elevation.