approximate evaluation of convolution products - arnaud-reveillere/SAMBA GitHub Wiki

The pressurization of an aquifer of constant thickness and infinite lateral extent in response to a constant pumping rate has a (well-) known algebraic solution, known as the Theis solution.

Complexity arises for time-varying flow rates, which introduces a convolution integral into the expression for pressurization of the aquifers. Nordbotten et al. (2004) propose to approximate the solution by using a constant pumping rate which is approximately the time-varying record:

This is satisfying for monotonic pumping rates, which is not the case of a leakage flow when taking into account the brine density differences. We therefore introduce series of monotonic functions whose sum equals the total leakage rate, to be applicable to non-monotonic or non self- similar leakage rates, as presented below.