NUMERICAL COMPUTATION OF CRITICAL FLOW OVER A SPILLWAY BY MEANS OF MINIMIZATION OF VIOLATION OF NEGATIVE CURVATURE CONDITION

A new method for the computation of two-dimensional critical flows over spillways is presented. The premise of the method is that at a critical value of the discharge coefficient that free boundary has no upstream waves. For the chosen spillway geometry without a toe section this requirement is equivalent to negative curvature of the free boundary. The method consists of two levels: at the inner level the corresponding free boundary value problem is solved for a fixed value of Q and at the outer level a critical value of Q is sought by minimization of the oscillation of the free boundary. An invaluable part of the method is the sensitivity anlaysis of the finite element stiffness matrix. The correctness of the numerical results is proved by scrutinizing the convergence rate by mesh refinement. Good agreement of the computed results with experimental data is achieved.