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extended Thiem 2D vs. steady solution for apparent transmissivity from Neuman
Both, the extended Thiem and the Neuman solution, represent an effective steady drawdown in a heterogeneous aquifer. In both cases the heterogeneity is represented by two point statistics, characterized by mean, variance and length scale of the log transmissivity field. Therefore these approaches should lead to similar results.
import numpy as np from matplotlib import pyplot as plt from anaflow import ext_thiem_2d, neuman2004_steady rad = np.geomspace(0.05, 4) # radius from the pumping well in [0, 4] r_ref = 30.0 # 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 = neuman2004_steady(rad, r_ref, TG, var, len_scale, rate) plt.plot(rad, head1, label="extended Thiem 2D") plt.plot(rad, head2, label="Steady Neuman 2004", linestyle="--") plt.xlabel("r in [m]") plt.ylabel("h in [m]") plt.legend() plt.tight_layout() plt.show()
Total running time of the script: ( 0 minutes 0.465 seconds)