This paper develops a robust and efficient PDE-constrained optimal control model for multicomponent pollutions in porous media, which takes into account nonlinear multi-component contamination flows of groundwater. The objective of the pollution optimal control is to identify the optimal injection rates from the top part boundary of domain, which can minimize the least squares error between the concentrations that are simulated and the allowable observed concentrations at observation sites, combining with the affection of costs associated with reducing emissions at injection locations. To discrete the constrained governing system of nonlinear multi-component flows, the splitting improved upwind finite difference scheme is developed for multicomponent PDEs system involving nonlinear chemical reactions of multicomponent pollutants and the pollutant injected rates on the upper part boundary. We employ the differential evolution (DE) optimization algorithm to solve the optimization. We numerically demonstrate the effectiveness of our model by analyzing the flow simulation on a simple geometric aquifer and identifying the optimal injection rates by minimizing the concentration derivation and the abatement costs. We also investigate the simulation of the contamination flow in a more realistic-shaped aquifer, which further validates our model's robustness and efficacy. The developed PDE-constrained control model and algorithm can be applied to applications of groundwater pollution control.

中文翻译：

---

开发多孔介质中多组分污染流的 PDE 约束最优控制


本文开发了一种稳健高效的 PDE 约束多组分污染最优控制模型，该模型考虑了地下水的非线性多组分污染流。污染最优控制的目标是确定从域的顶部边界开始的最佳注入速率，这可以最小化模拟的浓度与观测点允许的观测浓度之间的最小二乘误差，并结合与减少注入点排放相关的成本影响。为了离散非线性多组分流的约束控制系统，针对多组分污染物的非线性化学反应和上部边界的污染物注入速率的多组分偏微分方程系统，开发了一种分裂改进的逆风有限差分方案。我们采用差分进化 （DE） 优化算法来解决优化问题。我们通过分析简单几何含水层上的流动模拟，并通过最小化浓度推导和减排成本来确定最佳注入速率，以数值方式证明了我们模型的有效性。我们还研究了更逼真形状的含水层中污染流的模拟，这进一步验证了我们模型的稳健性和有效性。所开发的偏微分方程约束控制模型和算法可应用于地下水污染控制应用。