Multicomponent Optimal Control of Contamination Flows in Porous Media And Applications

Abstract

This thesis develops advanced PDE-constrained optimization frameworks for the control and remediation of multicomponent groundwater contamination in porous media. First, a robust optimal control model is formulated to describe nonlinear multicomponent contaminant transport governed by advection, diffusion, and chemical reactions. Environmental and economic objectives are simultaneously considered through concentration matching and abatement cost minimization. A splitting-based improved upwind finite difference scheme is developed to ensure stable and accurate numerical solutions, while a Differential Evolution (DE) algorithm is employed to determine optimal control strategies. Numerical experiments demonstrate effective contaminant reduction in both idealized and realistic aquifer systems.

Next, a parallel DE-PDE optimization framework is developed to address the substantial computational demands of large-scale PDE-constrained optimization. Using the Message Passing Interface (MPI), population evaluations are distributed across multiple processors, enabling efficient parallel solution of the contaminant transport PDEs within the optimization loop. The proposed parallel strategy significantly reduces computational time while maintaining solution quality and convergence performance.

Finally, a multi-control optimization framework is proposed that integrates concentration matching, pollutant reduction, and pumping-related operational costs within a unified objective function. This formulation balances environmental effectiveness with economic feasibility and supports practical remediation decision-making. Numerical studies on rectangular and L-shaped aquifers demonstrate that the proposed framework produces cost-effective remediation strategies, while the parallel DE-PDE implementation further enhances computational efficiency and scalability.