Water flow function

\[\frac{2\pi T_u\left(H_u-H_l\right)}{\ln\left(\frac{r}{r_w}\right)\left[1+\frac{2LT_u}{\ln\left(\frac{r}{r_w}\right)r_w^2K_w}+\frac{T_u}{T_l}\right]},\]

\(0.05\leq r_w\leq 0.15,\quad 100\leq r\leq 50000,\quad 63070\leq T_u\leq 115600,\quad 990 \leq H_u \leq 1110, \quad 63.1 \leq T_l \leq 116, \quad 700 \leq H_l \leq 820, \quad 1120 \leq L \leq 1680,\quad \text{and}\quad 9855 \leq K_w \leq 12045.\)

Usage

import matplotlib.pyplot as plt
import numpy as np

from smt.problems import WaterFlow

ndim = 8
problem = WaterFlow(ndim=ndim)

num = 100
x = np.ones((num, ndim))
for i in range(ndim):
    x[:, i] = 0.5 * (problem.xlimits[i, 0] + problem.xlimits[i, 1])
x[:, 0] = np.linspace(0.05, 0.15, num)
y = problem(x)

yd = np.empty((num, ndim))
for i in range(ndim):
    yd[:, i] = problem(x, kx=i).flatten()

print(y.shape)
print(yd.shape)

plt.plot(x[:, 0], y[:, 0])
plt.xlabel("x")
plt.ylabel("y")
plt.show()

(100, 1)
(100, 8)

Options

List of options

Option	Default	Acceptable values	Acceptable types	Description
ndim	1	None	[‘int’]
return_complex	False	None	[‘bool’]
name	WaterFlow	None	[‘str’]
use_FD	False	None	[‘bool’]