Integral Equation Formulation for Ground-Water Flow

Abstract

Advantages of boundary integral equation methods (BIEM) for the analysis of two-dimensional flows through porous media are numerous. The data required and the number of unknowns are significantly fewer than for other general, numerical methods such as finite differences of finite element methods. A BIEM based on the Cauchy integral equation is developed. This formulation has the advantage that the equation used for any unknown is a Fredholm equation of the second kind which results in well-conditioned equations and allows nodes to be closely spaced in the region of singularities. The method is extended to the analysis of multizone, anisotropic flows. Computational algorithms for solution of the equations by a simple iterative method and by direct solution of the full set of simultaneous linear equations are developed.