Radial well aquifer benchmark (Water Module)

This testcase demonstrates a situation where a well is pumping up ground water. A characteristic ground water level curve will form over time.

Formulas

Stationary lowering of the ground water table in a closed water transmissive layer can be described by the following formula

$\varphi (r)-{\varphi }_0=\frac{Q_0}{2\pi \cdot kD}\ln \left(\frac{r}{R}\right)$

where:

$phi(0)$: stable water level at the considered stable water table edge

$phi(r)$: water level between the considered stable water table edge and the well

$phi(rw)$: water level in the well

$kD$: transmissivity of the aquifer in m² / day

$r$: distance to the well

$R$: distance of the considered stable water table edge to the well

$Q_0$: amount of water pumped out in m³ / day

Setup

We use the following setup in our tests. The grid size used is 51 by 51, with a configurable cell size of $dx$ in meters. There is one underground outlet, which pumps water away continuously with a default amount per second.

The outlet is placed on the cells x = 25 and y = 25 as an inlet with a negative inlet . Inlet Q is set to $\frac{-Q_0}{3600*24}$

References

Water Module

Tutorials

Overview

Theory

Benchmarks