Solutions to the Laplace equation are required in many branches of groundeater hydrology. The most difficult class of problems involve generating solutions to the Laplace equation when the domain is bounded by a free-surface. In this case, solutions can be generated by finite difference and finite element methods. However, due to the computational requirements of these methods, they are not often incorporated into "practical' comdels of sub-catchment hydrology. This paper illustrates an alternative method to finite difference/finite element methods for generating solutions to saturated and partially-saturated porous edia flow problems with a free surface, The solution strategy is based on approximating the boundary conditions with orthonormal sequence expansions and developing approximating the boundary conditions with orthonormal sequence expansions and developing appropriate recurrence relations for the coefficients of the expansion, In practice the research, this method was limited to problems with simple domains. However, we show that with some modifications, the solution method can also be applied domains. Hwever, we show that with that the method is computatinally very efficient and rapid solutions can be generated on basic PC computers. Several examples will be discussed.
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