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Journal of Porous Media
Facteur d'impact: 1.49 Facteur d'impact sur 5 ans: 1.159 SJR: 0.504 SNIP: 0.671 CiteScore™: 1.58

ISSN Imprimer: 1091-028X
ISSN En ligne: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v4.i3.60
12 pages

A Combined Use of Direct Search Algorithms and Exterior Penalty Function Method for Groundwater Pollution Management

Ashok K. Keshari
Department of Civil Engineering, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India
Bithin Datta
Department of Civil Engineering, Indian Institute of Technology, Kanpur, Kanpur 208016, India


An optimization based numerical management model has been developed to address groundwater pollution problems cropping up at different scales. The management model consists of objective function for water supply and imposed restrictions on decision variables such as physical, operational, and managerial constraints. To simulate groundwater flow and pollutant transport processes, coupled set of discretized forms of governing partial differential equations describing two-dimensional flow through porous media and two-dimensional movement of dissolved contaminant within the porous medium with appropriate initial and boundary conditions are conflated within a single framework of the optimization model. A combined use of the Exterior Penalty Function Method (EPFM) and two direct search methods; the Hooks-Jeeves (HJ) method and the Powell's Conjugate Direction (PCD) method are employed to solve the multivariable constrained nonlinear optimization model. The optimal solutions are obtained for a number of management scenarios, each representing different porous media environment and operating situations for aquifers. The optimal solutions are also compared to investigate the relative performance of the proposed two methodologies (EPFM&HJ and EPFM&PCD) in terms of its robustness, versatility, accuracy, efficiency, ease in implementation, and computational feasibility. These methodologies avoid the repetitive use of physical system simulators and enable to handle fully embedded optimization model, although it increases the dimension. Limitations of these two methodologies are also discussed in terms of its applicability, suitability, and global optimality of solutions.

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