THE IMPACT OF NUMERICAL PRECISION ON THE SOLUTION OF CONFINED AND UNCONFINED OPTIMAL HYDRAULIC CONTROL-PROBLEMS

Lineal optimization combined with groundwater flow simulation can be u sed to design groundwater control systems by defining the criteria for system performance with constraints oil hydraulic head and head diffe rence. In this investigation, a groundwater simulation and optimizatio n 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 pumpin g at each candidate well. These linear equations are then used in an o ptimization formulation which can be solved by the simplex algorithm. In a confined aquifer, the relationship between head and pumping is li near, so the response matrix is an exact representation of the hydraul ics. 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 unconf ined aquifer, the response matrix can be used as an approximation of t he true hydraulic response, and the optimization problem can be solved through iteration. In order to produce accurate results, double preci sion variables, a small con vergence criterion, and a small perturbati on value must be used.