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The impact of numerical precision on the solution of confined and unconfined optimal hydraulic control problems

TitleThe impact of numerical precision on the solution of confined and unconfined optimal hydraulic control problems
Publication TypeJournal Article
Year of Publication1996
AuthorsRiefler R.G, Ahlfeld D. P.
JournalHazardous Waste and Hazardous Materials
Volume13
Issue2
Start Page167
Pagination167-176
Date Published06/1996
ISSN0882-5696
Abstract

Lineal optimization combined with groundwater flow simulation can be used to design groundwater control systems by defining the criteria for system performance with constraints oil 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 con vergence criterion, and a small perturbation value must be used.
 

URLhttps://doi.org/10.1089/hwm.1996.13.167
DOI10.1089/hwm.1996.13.167