extended Thiem 3D vs. steady solution for coarse graining conductivity

The extended Thiem 3D solutions is the analytical solution of the groundwater flow equation for the coarse graining conductivity for pumping tests. Therefore the results should coincide.

Reference: Zech et. al. 2012

import numpy as np
from matplotlib import pyplot as plt

from anaflow import ext_grf_steady, ext_thiem_3d
from anaflow.tools.coarse_graining import K_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
KG = 1e-4  # the geometric mean of the transmissivity
anis = 0.7  # aniso ratio

rate = -1e-4  # pumping rate

head1 = ext_thiem_3d(rad, r_ref, KG, var, len_scale, anis, 1, rate)
head2 = ext_grf_steady(
    rad,
    r_ref,
    K_CG,
    rate=rate,
    cond_gmean=KG,
    var=var,
    len_scale=len_scale,
    anis=anis,
)

plt.plot(rad, head1, label="Ext Thiem 3D")
plt.plot(rad, head2, label="grf(K_CG)", linestyle="--")

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