def RichardsModel(psi, t, dz, n, p, vg, qTfun, qBot, psiTop, psiBot):
# Basic properties:
C = vg.CFun(psi, p)
# initialize vectors:
q = np.zeros(n + 1)
# # Upper boundary
# if qTop == []: # Fixed value
# KTop = vg.KFun(np.zeros(1) + psiTop, p)
# q[n] = -KTop * ((psiTop - psi[n - 1]) / dz * 2 + 1)
# else: # Fixed flux
# q[n] = qTop
# if t>10:
# q[n] = qTfun(10)
# else:
# q[n] = qTfun(t)
if t > 160920:
q[n] = qTfun(160920)
else:
q[n] = qTfun(t)
# Lower boundary
if qBot == []:
if psiBot == []:
# Free drainage: fixed flux: fixed gradient
KBot = vg.KFun(np.zeros(1) + psi[0], p)
q[0] = -KBot
else:
# Type 1 boundary: Fixed gradient
KBot = vg.KFun(np.zeros(1) + psiBot, p)
q[0] = -KBot * ((psi[0] - psiBot) / dz * 2 + 1.0)
else:
# Type 2 boundary
q[0] = qBot
# Internal nodes
i = np.arange(0, n - 1)
Knodes = vg.KFun(psi, p)
Kmid = (Knodes[i + 1] + Knodes[i]) / 2.0
j = np.arange(1, n)
q[j] = -Kmid * ((psi[i + 1] - psi[i]) / dz + 1.0)
if q[n] != 0:
if q[n] < q[n - 1]: # because here q is a negative value
print('Water accumulated at the top, time = ', t / 60, 'min(s)')
KTop = vg.KFun(psiTop, p)
dhdz = (psiTop - psi[n - 1]) * 2 / dz + 1
q[n] = -KTop * dhdz
# Continuity
i = np.arange(0, n)
dpsidt = (-(q[i + 1] - q[i]) / dz) / C
return dpsidt
def PlotProps(pars):
import numpy as np
import pylab as pl
import vanGenuchten as vg
psi = np.linspace(-10, 2, 200)
pl.figure
pl.subplot(3, 1, 1)
pl.plot(psi, vg.thetaFun(psi, pars))
pl.ylabel(r'$\theta(\psi) [-]$')
pl.subplot(3, 1, 2)
pl.plot(psi, vg.CFun(psi, pars))
pl.ylabel(r'$C(\psi) [1/m]$')
pl.subplot(3, 1, 3)
pl.plot(psi, vg.KFun(psi, pars))
pl.xlabel(r'$\psi [m]$')
pl.ylabel(r'$K(\psi) [m/d]$')
if q[n] != 0:
if q[n] < q[n - 1]: # because here q is a negative value
print('Water accumulated at the top, time = ', t / 60, 'min(s)')
KTop = vg.KFun(psiTop, p)
dhdz = (psiTop - psi[n - 1]) * 2 / dz + 1
q[n] = -KTop * dhdz
# Continuity
i = np.arange(0, n)
dpsidt = (-(q[i + 1] - q[i]) / dz) / C
return dpsidt
psi = np.linspace(-10, 5)
theta = vg.thetaFun(psi, p)
C = vg.CFun(psi, p)
K = vg.KFun(psi, p)
pl.figure()
pl.rcParams['figure.figsize'] = (5.0, 10.0)
pl.subplot(311)
pl.plot(psi, theta)
pl.ylabel(r'$\theta$', fontsize=20)
pl.subplot(312)
pl.plot(psi, C)
pl.ylabel(r'$C$', fontsize=20)
pl.subplot(313)
pl.plot(psi, K)
pl.ylabel(r'$K$', fontsize=20)
pl.xlabel(r'$\psi$', fontsize=20)