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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi(r) - \phi_0 = \frac {Q_0}{2\pi\cdot kD} \ln{\left ( \frac{r}{R} \right )}}

where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle phi(0)} : stable water level at the considered stable water table edge

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle phi(r)} : water level between the considered stable water table edge and the well

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle phi(rw)} : water level in the well

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle kD} : transmissivity of the aquifer in m² / day

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} : distance to the well

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R} : distance of the considered stable water table edge to the well

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{-Q_0}{3600*24}}

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

The simulation is run for 64 days with 0 rainfall, which is configured in the weather's rain attribute as: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [64 \cdot 24 \cdot 3600, 0]}

References

Water Module

Tutorials

Overview

Theory

Benchmarks