Groundwater pollution source identification using the backward beam equation method

The reliable assessment of hazards or risks arising from water contamination problems and the design of efficient and effective techniques to mitigate them require the capability to predict the behavior of chemical contaminants in flowing water. Most attempts at quantifying contaminant transport have relied on a solution of some form of a well-known governing equation referred to as advection-dispersion-reaction equation. In this paper, the method of Backward Beam Equation (BBE) is studied and enhanced to solve the Advection-Dispersion Equation (ADE) within a contaminant source identification context. Even though the BBE has been applied successfully to parabolic problems before, it has never been applied to solving the ADE. The BBE employed in this work is capable of finding the history of a groundwater contaminant plume from measurements of its current spatial distribution. For the examples presented in this work, the method solves the heterogeneous case with better accuracy than the homogeneous case. It also backtracks the bimodal concentration plume more accurately than the unimodal one. With a modification to the method, rendering it a hybrid between a marching and a jury method, we were also able to make the computational time requirements manageable.