The method first replaces the differential equations of ground-water flow by finite-difference approximations that include unknown sink/source terms. The resulting system of algebraic linear equations has a rectangular matrix of coefficients. This system, together with linear inequalities relating sink/source terms, heads or both, and together with an objective function, forms a linear programming (LP) model. The method is applied to small-scale models of confined and unconfined saturated flow for steady-state and transient cases. The steady-state LP models are solved using available computer codes. For the transient confined model, the Crank-Nicolson scheme is used, and a single LP problem is solved covering all of the time steps. For the transient unconfined model, a predictor technique is used, and a LP problem is solved at each corrector step. The optimal solutions are consistent with the results of traditional analyses.
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Aguado et al. (1974) studied this question.