Numerical evaluation of Theis and Hantush-Jacob well functions

This paper presents a new approach where a numerical quadrature scheme is applied to compute special functions described by integrals, appearing in many groundwater hydrology and pollution problems. The basic idea is to apply a smoothing procedure to the singular integrand and a non-linear coordinate transformation in the quadrature domain. Techniques for lowering the degree of singularity of integrand functions have been successfully applied in physics and computational mechanics, and the self-adaptive co-ordinate transformation used in this work is a well-established procedure in general boundary element integrals quadrature. The main advantage of this joint technique is that it can be directly used to other related functions without further approximations and the user can choose freely the degree of accuracy. Tables included in this paper show the improvement of several orders of magnitude when both techniques are applied simultaneously.