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A mathematical optimal control method is developed to identify a hydraulic conductivity distribution in a density dependent flow field. Using a variational method, the adjoint partial differential equations are obtained for the density-dependent state equations used for the saline aquifer water flow. The adjoint equations are numerically solved in through a finite difference method. The developed method is applied to identify the hydraulic conductivity distribution through the numerical solution of an optimal control problem. To demonstrate the effectiveness of the optimal control method, three numerical experiments are conducted with artificial observation data. The results indicate that the developed method has the potential to accurately identify the hydraulic conductivity distribution in a saline water aquifer flow system.
A mathematical optimal control method is developed to identify a hydraulic conductivity distribution in a density dependent flow field. The adjoint partial differential equations are for the density-dependent state equations used for the saline aquifer water flow. are numerically solved in a finite difference method. The developed method is applied to identify the hydraulic conductivity distribution through the numerical solution of an optimal control problem. The results indicate that the developed method has the potential to accurately identify the hydraulic conductivity distribution in a saline water aquifer flow system.