BOUNDARY INTEGRAL EQUATION——INVERSE METHOD FOR FREE SURFACE GRAVITY FLOWS
摘要
The principal purpose of this paper is to develop a new method for 2-dimensional gravity-influenced free surface potential flows passing arbitrary curvilinear solid boundaries. Using Muskhelishvili's theory, and by substitution, we can obtain a system of nonsingular boundary-integral equations in the physical plane. The integral equations are solved by an iterative method in which the length of streamline of the boundary is taken as an independent variable, and the velocity potential on boundary as the function to be solved. The difficulties encountered in applying the analytical function theory have been overcome. The analytical theory has found new applications. Theoretical research and numerical calculations indicate that the method is superior to the existing numerical ones in good and fast convergence and small calculating quantity. The free jets flowing through a spillway flip bucket and flows from sluice gates are calculated. The numerical results agree well with those measured.