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 $\frac{-Q_0}{3600*24}$

UNDERGROUND is set to true (1.0) to place the outlet below the surface.

An aquifer can be added to configure the kD value used in the test.

The simulation is run for 64 days with 0 rainfall, which is configured in the weather's rain attribute as: $[64\cdot 24\cdot 3600,0]$

References

Water Module

Tutorials

Overview

Theory

Benchmarks