Application of hypersingular equations to free-surface seepage problems

Abstract

In this paper, the Laplace problem with a free surface is solved by using the hypersingular equation. In the conventional boundary element method, only singular integral equation was used. The boundary of free surface can be determined by trial and error after initial guess and iterations. By introducing the hypersingular equation, the convergence rate of free surface can be accelerated. It is found that the result by using a higher-order singularity approach for the kernel is more accurate than introducing a higher-order element for the boundary density. Finally, numerical examples were demonstrated to show the validity of the present method.