Abstract
ABSTRACT
Linear optimization combined with groundwater flow simulation can be used to design groundwater control systems by defining the criteria for system performance with constraints on hydraulic head and head difference. In this investigation, a groundwater simulation and optimization code, MODLP, is used to investigate numerical precision issues when solving these problems under confined and unconfined conditions. MODLP perturbs the pump rate at each candidate well to develop a system of linear response equations relating head at each constraint with pumping at each candidate well. These linear equations are then used in an optimization formulation which can be solved by the simplex algorithm. In a confined aquifer, the relationship between head and pumping is linear, so the response matrix is an exact representation of the hydraulics. Due to the mathematical manipulations involved in calculating the response matrix, however, a large perturbation value must be used to maintain accuracy, when using single precision variables. In an unconfined aquifer, the response matrix can be used as an approximation of the true hydraulic response, and the optimization problem can be solved through iteration. In order to produce accurate results, double precision variables, a small convergence criterion, and a small perturbation value must be used.
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