Identification of multiple unknown point sources occurring in the 2D transport equation: application to groundwater pollution source identification

Abstract

Accessing quality water is of crucial importance to both society and the environment. Deterioration in water quality through groundwater pollution presents a substantial risk to human health, plant and animal life, and detrimental effects on the local economy. To ensure groundwater quality, there is need to identify locations of unknown groundwater pollution sources. In this paper, the locations of groundwater contaminant sources have been identified using inverse problem technique. The work in this paper concerns the inverse source problem in the Advection Dispersion Reaction Equation (ADRE) with an emphasis on groundwater pollution source identification. Mathematically, inverse source problem involves the reconstruction of the source function in the ADRE from the boundary and interior measurements. An inverse source problem technique for identifying the unknown groundwater pollution source utilizing only the boundary and interior measurements is developed. The finite volume discretization method is employed on the adjoint ADRE to provide the data. The data from the finite volume method results into Volterra integral equation which after discretizing transforms into an ill-posed inverse problem. Tikhonov regularization method is used to achieve stability on the ill-posed problem. The results indicates that our proposed inverse problem is accurate with the data.