Green’s function-based integral approaches to head fluctuations in a coastal leaky confined aquifer system

In developing boundary integral methods, converting the governing differential equation into its integral form by way of Green’s functions is a major requirement. This however requires that there exists in the first place a fundamental solution associated with the adjoint operator of the governing differential equation. In the work presented herein, we explore three methods of arriving at Green’s functions for the case of the equation governing head fluctuations in a confined leaky aquifer located inland from the sea. The first method or model-1 is based on the Green’s function of the 1-D Laplace operator, while the second (model-2) and more intuitive approach incorporates the leakance as well as the 1-D Laplace operator into the auxiliary equation. The third (model-3) formulates the auxiliary equation based on the time-dependent Green’s function. While each of these models is consistent and mathematically correct, numerical verifications do show that model-1 and model-2 despite their easier formulation produce results that are quite dependable. On the other hand, model-3 compensates for its more elaborate and rigorous derivations, by giving accurate results with larger time steps.