A Dirac-δ function notation for source/sink terms in groundwater flow

The source/sink terms in groundwater flow are singularities that require special treatment in the numerical solution of a mathematical model. Except for the case of a point source, these singularities are not consistently defined in the governing partial differential equation or treated rigorously in the numerical solution of the governing equations. In this paper, we propose a consistent notation for handling the source/sink terms within the governing equation using the familiar Dirac-delta function notation for three-dimensional applications. We also present the domain integrals of these terms, similar to the ones that occur frequently in finite element solution of the mathematical model.