Explicit algebraic influence coefficients: one-dimensional aquifer model

Abstract

Explicit algebraic expressions of influence coefficients of an aquifer system are addressed. The methodology is straightforwardly exemplified using a one-dimensional (1D) semi-confined homogeneous aquifer model. It consists of the integration of the governing equation from two different viewpoints. On the one hand, the analytical solution to the governing equation is presented under an integral form involving the appropriate Green function. On the other hand, equations resulting from a finite difference discretization are processed to deduce a fully explicit algebraic expression of the nodal hydraulic head. This latter, arranged after the previously developed continuum solution, helps with deriving an explicit algebraic expression of influence coefficients corresponding to the studied aquifer model. Finally, the study is extended to an inhomogeneous aquifer model.