extended Thiem 2D vs. steady solution for coarse graining transmissivity

The extended Thiem 2D solutions is the analytical solution of the groundwater flow equation for the coarse graining transmissivity for pumping tests. Therefore the results should coincide.

References:

• Schneider & Attinger 2008

• Zech & Attinger 2016

import numpy as np
from matplotlib import pyplot as plt

from anaflow import ext_grf_steady, ext_thiem_2d
from anaflow.tools.coarse_graining import T_CG

rad = np.geomspace(0.05, 4)  # radius from the pumping well in [0, 4]
r_ref = 2.0  # reference radius

var = 0.5  # variance of the log-transmissivity
len_scale = 10.0  # correlation length of the log-transmissivity
TG = 1e-4  # the geometric mean of the transmissivity

rate = -1e-4  # pumping rate

head1 = ext_thiem_2d(rad, r_ref, TG, var, len_scale, rate)
head2 = ext_grf_steady(
    rad, r_ref, T_CG, rate=rate, trans_gmean=TG, var=var, len_scale=len_scale
)

plt.plot(rad, head1, label="Ext Thiem 2D")
plt.plot(rad, head2, label="grf(T_CG)", linestyle="--")

plt.xlabel("r in [m]")
plt.ylabel("h in [m]")
plt.legend()
plt.tight_layout()
plt.show()