added another example

docs/source/tutorial_02_extended_theis.rst

@@ -0,0 +1,33 @@
+Tutorial 2: compare the extended theis solution
+===============================================
+
+We provide an extended theis solution, that incorporates the effectes of a
+heterogeneous transmissivity field on a pumping test.
+
+In the following this extended solution is compared to the standard theis
+solution for well flow. You can nicely see, that the extended solution represents
+a transition between the theis solutions for the geometric- and harmonic-mean
+transmissivity.
+
+.. code-block:: python
+
+    import numpy as np
+    from matplotlib import pyplot as plt
+    from anaflow import theis
+
+
+    time = [10, 100, 1000]
+    rad = np.geomspace(0.1, 10)
+
+    head = theis(rad=rad, time=time, T=1e-4, S=1e-4, Qw=-1e-4)
+
+    for i, step in enumerate(time):
+        plt.plot(rad, head[i], label="Theis(t={})".format(step))
+
+    plt.legend()
+    plt.show()
+
+
+.. image:: pics/02_call_ext_theis.png
+   :width: 400px
+   :align: center

docs/source/tutorials.rst

@@ -9,3 +9,4 @@ explore its whole beauty and power.
    :maxdepth: 1
 
    tutorial_01_call.rst
+   tutorial_02_extended_theis.rst

examples/02_call_ext_theis.py

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+# -*- coding: utf-8 -*-
+import numpy as np
+from matplotlib import pyplot as plt
+from anaflow import theis, ext_theis2D
+
+
+time = [10, 600, 36000]      # 10s, 10min, 10h
+rad = np.geomspace(0.05, 4)  # radius from the pumping well in [0, 4]
+var = 0.5                    # variance of the transmissivity
+corr = 10.0                  # correlation length of the transmissivity
+TG = 1e-4                    # the geometric mean of the transmissivity
+TH = TG*np.exp(-var/2.0)     # the harmonic mean of the transmissivity
+S = 1e-4                     # storativity
+Qw = -1e-4                   # pumping rate
+
+head_TG = theis(rad=rad, time=time, T=TG, S=S, Qw=Qw)
+head_TH = theis(rad=rad, time=time, T=TH, S=S, Qw=Qw)
+head_ef = ext_theis2D(rad=rad, time=time, TG=TG, sig2=var, corr=corr, S=S, Qw=Qw)
+
+for i, step in enumerate(time):
+    if i == 0:
+        label_TG = "Theis($T_G$)"
+        label_TH = "Theis($T_H$)"
+        label_ef = "extended Theis"
+    else:
+        label_TG = label_TH = label_ef = None
+    plt.plot(rad, head_TG[i], label=label_TG, color="C"+str(i), linestyle="--")
+    plt.plot(rad, head_TH[i], label=label_TH, color="C"+str(i), linestyle=":")
+    plt.plot(rad, head_ef[i], label=label_ef, color="C"+str(i))
+
+plt.xlabel("r in [m]")
+plt.ylabel("h in [m]")
+plt.legend()
+plt.show()