Analytical Simulations for Spill Point Source Localization Using Inverse Problems in Closed Form

Abstract

This work delves into the realm of inverse problems in the context of aquatic pollution. Specifically, it presents a novel analytical approach for pinpointing the origins of leaks in underwater pipelines, circumventing the need for data regularization and auxiliary partial differential equation solving. This method streamlines the process, significantly reducing processing time compared to traditional numerical approaches. The approach involves identifying local concentration maxima in a known distribution, tracing streamlines connecting them, and utilizing parametric equations to describe these streamlines. Points of intersection between these parametric curves and the submerged pipe network define potential leak origins. Validation of these origins is achieved through simulations, using the same concentration distribution to compute the source term. This method not only minimizes computational time but also remains effective in scenarios with uncertain experimental data. The results demonstrate that this approach outperforms traditional techniques in terms of processing time, making it particularly advantageous in decision-making processes related to leak containment and environmental recovery in underwater environments. This analytical method offers a valuable tool for efficient and accurate leak source localization, enhancing environmental protection efforts.

Keywords

• differential equations
• inverse problems
• analytical methods
• low processing time
• aquatic pollution