Singular Integral Operators Method in Unsteady Spillway Flows

A classical open channel hydraulics problem is the determination of the free-surface profile of an unsteady flow over a spillway flow. Thus, by using the Singular Integral Operators Method (S.I.O.M.) then the above problem can be solved by applying numerical evaluation. When a flow rate Q is known, then the velocities and the elevations are computed on the free surface of the spillway flow. For the numerical evaluation of the singular integral equations are used both constant and linear elements. An application is finally given to the determination of the free-surface profile of a special spillway and comparing the numerical results with corresponding results by the Boundary Integral Equation Method (B.I.E.M.).