simpeg.flow.richards.empirical.Vangenuchten_k.derivM

Vangenuchten_k.derivM(u)

derivative with respect to m

import sympy as sy

alpha, u, n, I, Ks, theta_r, theta_s = sy.symbols(
    'alpha u n I Ks theta_r theta_s', real=True
)

m = 1.0 - 1.0/n
theta_e = 1.0 / ((1.0 + sy.functions.Abs(alpha * u) ** n) ** m)

f_n = Ks * theta_e ** I * (
    (1.0 - (1.0 - theta_e ** (1.0 / m)) ** m) ** 2
)

f_n = (
    (
        theta_s - theta_r
    ) /
    (
        (1.0 + abs(alpha * u)**n) ** (1.0 - 1.0 / n)
    ) +
    theta_r
)