Study of free-surface seepage problems using hypersingular equations

Abstract

Free‐surface boundary is not only unknown in a priori but also the boundary conditions are overspecified. In this paper, the Laplace problem with overspecified boundary conditions on the free surface is solved by using the hypersingular equation instead of singular equation used conventionally in boundary element method. The free surface can be determined using an iterative procedure starting from an initial guess. By introducing the hypersingular equation, the convergence rate of free surface can be accelerated. Finally, numerical examples including rectangular dams and canals were demonstrated and were compared with others to show the validity of the present method.