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simpeg/simpegFLOW/Richards/Empirical.py
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rowanc1 0084a278b5 derivative tests
2014-02-25 16:54:29 -08:00

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from SimPEG import Model, Utils, np
class RichardsModel(object):
"""docstring for RichardsModel"""
mesh = None #: SimPEG mesh
@property
def thetaModel(self):
"""Model for moisture content"""
return self._thetaModel
@property
def kModel(self):
"""Model for hydraulic conductivity"""
return self._kModel
def __init__(self, mesh, thetaModel, kModel):
self.mesh = mesh
assert isinstance(thetaModel, Model.BaseNonLinearModel)
assert isinstance(kModel, Model.BaseNonLinearModel)
self._thetaModel = thetaModel
self._kModel = kModel
def theta(self, u, m):
return self.thetaModel.transform(u, m)
def thetaDerivM(self, u, m):
return self.thetaModel.transformDerivM(u, m)
def thetaDerivU(self, u, m):
return self.thetaModel.transformDerivU(u, m)
def k(self, u, m):
return self.kModel.transform(u, m)
def kDerivM(self, u, m):
return self.kModel.transformDerivM(u, m)
def kDerivU(self, u, m):
return self.kModel.transformDerivU(u, m)
def _ModelProperty(name, model, doc=None, default=None):
def fget(self):
if getattr(self, model, None) is not None:
MOD = getattr(self, model)
return getattr(MOD, name, default)
return default
def fset(self, value):
if getattr(self, model, None) is not None:
MOD = getattr(self, model)
setattr(MOD, name, value)
return property(fget, fset=fset, doc=doc)
class HaverkampParams(object):
"""Holds some default parameterizations for the Haverkamp model."""
def __init__(self): pass
@property
def celia1990(self):
"""
Parameters used in:
Celia, Michael A., Efthimios T. Bouloutas, and Rebecca L. Zarba.
"A general mass-conservative numerical solution for the unsaturated flow equation."
Water Resources Research 26.7 (1990): 1483-1496.
"""
return {'alpha':1.611e+06, 'beta':3.96,
'theta_r':0.075, 'theta_s':0.287,
'Ks':np.log(9.44e-03), 'A':1.175e+06,
'gamma':4.74}
class _haverkamp_theta(Model.BaseNonLinearModel):
theta_s = 0.430
theta_r = 0.078
alpha = 0.036
beta = 3.960
def __init__(self, mesh, **kwargs):
Model.BaseNonLinearModel.__init__(self, mesh)
Utils.setKwargs(self, **kwargs)
def setModel(self, m):
self._currentModel = m
def transform(self, u, m):
self.setModel(m)
f = (self.alpha*(self.theta_s - self.theta_r )/
(self.alpha + abs(u)**self.beta) + self.theta_r)
f[u >= 0] = self.theta_s
return f
def transformDerivM(self, u, m):
self.setModel(m)
def transformDerivU(self, u, m):
self.setModel(m)
g = (self.alpha*((self.theta_s - self.theta_r)/
(self.alpha + abs(u)**self.beta)**2)
*(-self.beta*abs(u)**(self.beta-1)*np.sign(u)))
g[u >= 0] = 0
g = Utils.sdiag(g)
return g
class _haverkamp_k(Model.BaseNonLinearModel):
A = 1.175e+06
gamma = 4.74
Ks = np.log(24.96)
def __init__(self, mesh, **kwargs):
Model.BaseNonLinearModel.__init__(self, mesh)
Utils.setKwargs(self, **kwargs)
def setModel(self, m):
self._currentModel = m
#TODO: Fix me!
self.Ks = m
def transform(self, u, m):
self.setModel(m)
f = np.exp(self.Ks)*self.A/(self.A+abs(u)**self.gamma)
if type(self.Ks) is np.ndarray and self.Ks.size > 1:
f[u >= 0] = np.exp(self.Ks[u >= 0])
else:
f[u >= 0] = np.exp(self.Ks)
return f
def transformDerivM(self, u, m):
self.setModel(m)
#A
# dA = np.exp(self.Ks)/(self.A+abs(u)**self.gamma) - np.exp(self.Ks)*self.A/(self.A+abs(u)**self.gamma)**2
#gamma
# dgamma = -(self.A*np.exp(self.Ks)*np.log(abs(u))*abs(u)**self.gamma)/(self.A + abs(u)**self.gamma)**2
# This assumes that the the model is Ks
return Utils.sdiag(self.transform(u, m))
def transformDerivU(self, u, m):
self.setModel(m)
g = -(np.exp(self.Ks)*self.A*self.gamma*abs(u)**(self.gamma-1)*np.sign(u))/((self.A+abs(u)**self.gamma)**2)
g[u >= 0] = 0
g = Utils.sdiag(g)
return g
class Haverkamp(RichardsModel):
"""Haverkamp Model"""
alpha = _ModelProperty('alpha', 'thetaModel', default=1.6110e+06)
beta = _ModelProperty('beta', 'thetaModel', default=3.96)
theta_r = _ModelProperty('theta_r', 'thetaModel', default=0.075)
theta_s = _ModelProperty('theta_s', 'thetaModel', default=0.287)
Ks = _ModelProperty('Ks', 'kModel', default=np.log(24.96))
A = _ModelProperty('A', 'kModel', default=1.1750e+06)
gamma = _ModelProperty('gamma', 'kModel', default=4.74)
def __init__(self, mesh, **kwargs):
RichardsModel.__init__(self, mesh,
_haverkamp_theta(mesh),
_haverkamp_k(mesh))
Utils.setKwargs(self, **kwargs)
# class Haverkamp(object):
# """docstring for Haverkamp"""
# empiricalModelName = "VanGenuchten"
# theta_s = 0.430
# theta_r = 0.078
# alpha = 0.036
# beta = 3.960
# A = 1.175e+06
# gamma = 4.74
# Ks = np.log(24.96)
# def __init__(self, **kwargs):
# Utils.setKwargs(self, **kwargs)
# def setModel(self, m):
# self.Ks = m
# def moistureContent(self, h):
# f = (self.alpha*(self.theta_s - self.theta_r )/
# (self.alpha + abs(h)**self.beta) + self.theta_r)
# f[h > 0] = self.theta_s
# return f
# def moistureContentDeriv(self, h):
# g = (self.alpha*((self.theta_s - self.theta_r)/
# (self.alpha + abs(h)**self.beta)**2)
# *(-self.beta*abs(h)**(self.beta-1)*np.sign(h)));
# g[h >= 0] = 0
# g = Utils.sdiag(g)
# return g
# def hydraulicConductivity(self, h):
# f = np.exp(self.Ks)*self.A/(self.A+abs(h)**self.gamma)
# if type(self.Ks) is np.ndarray and self.Ks.size > 1:
# f[h >= 0] = np.exp(self.Ks[h >= 0])
# else:
# f[h >= 0] = np.exp(self.Ks)
# return f
# def hydraulicConductivityModelDeriv(self, h):
# #A
# # dA = np.exp(self.Ks)/(self.A+abs(h)**self.gamma) - np.exp(self.Ks)*self.A/(self.A+abs(h)**self.gamma)**2;
# #gamma
# # dgamma = -(self.A*np.exp(self.Ks)*np.log(abs(h))*abs(h)**self.gamma)/(self.A + abs(h)**self.gamma)**2;
# return Utils.sdiag(self.hydraulicConductivity(h)) # This assumes that the the model is Ks
# def hydraulicConductivityDeriv(self, h):
# g = -(np.exp(self.Ks)*self.A*self.gamma*abs(h)**(self.gamma-1)*np.sign(h))/((self.A+abs(h)**self.gamma)**2)
# g[h >= 0] = 0
# g = Utils.sdiag(g)
# return g
# class VanGenuchten(object):
# """
# .. math::
# \\theta(h) = \\frac{\\alpha (\\theta_s - \\theta_r)}{\\alpha + |h|^\\beta} + \\theta_r
# Where parameters alpha, beta, gamma, A are constants in the media;
# theta_r and theta_s are the residual and saturated moisture
# contents; and K_s is the saturated hydraulic conductivity.
# Celia1990
# """
# empiricalModelName = "VanGenuchten"
# theta_s = 0.430
# theta_r = 0.078
# alpha = 0.036
# n = 1.560
# beta = 3.960
# I = 0.500
# Ks = np.log(24.96)
# def __init__(self, **kwargs):
# Utils.setKwargs(self, **kwargs)
# def setModel(self, m):
# self.Ks = m
# def moistureContent(self, h):
# m = 1 - 1.0/self.n;
# f = (( self.theta_s - self.theta_r )/
# ((1+abs(self.alpha*h)**self.n)**m) + self.theta_r)
# f[h > 0] = self.theta_s
# return f
# def moistureContentDeriv(self, h):
# g = -self.alpha*self.n*abs(self.alpha*h)**(self.n - 1)*np.sign(self.alpha*h)*(1./self.n - 1)*(self.theta_r - self.theta_s)*(abs(self.alpha*h)**self.n + 1)**(1./self.n - 2)
# g[h > 0] = 0
# g = Utils.sdiag(g)
# return g
# def hydraulicConductivity(self, h):
# alpha = self.alpha
# I = self.I
# n = self.n
# Ks = self.Ks
# m = 1.0 - 1.0/n
# theta_e = 1.0/((1.0+abs(alpha*h)**n)**m)
# f = np.exp(Ks)*theta_e**I* ( ( 1.0 - ( 1.0 - theta_e**(1.0/m) )**m )**2 )
# if type(self.Ks) is np.ndarray and self.Ks.size > 1:
# f[h >= 0] = np.exp(self.Ks[h >= 0])
# else:
# f[h >= 0] = np.exp(self.Ks)
# return f
# def hydraulicConductivityModelDeriv(self, h):
# #alpha
# # dA = I*h*n*np.exp(Ks)*abs(alpha*h)**(n - 1)*np.sign(alpha*h)*(1.0/n - 1)*((abs(alpha*h)**n + 1)**(1.0/n - 1))**(I - 1)*((1 - 1.0/((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1)**2*(abs(alpha*h)**n + 1)**(1.0/n - 2) - (2*h*n*np.exp(Ks)*abs(alpha*h)**(n - 1)*np.sign(alpha*h)*(1.0/n - 1)*((abs(alpha*h)**n + 1)**(1.0/n - 1))**I*((1 - 1.0/((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1)*(abs(alpha*h)**n + 1)**(1.0/n - 2))/(((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1) + 1)*(1 - 1.0/((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1.0/n));
# #n
# # dn = 2*np.exp(Ks)*((np.log(1 - 1.0/((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))*(1 - 1.0/((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n))/n**2 + ((1.0/n - 1)*(((np.log(abs(alpha*h)**n + 1)*(abs(alpha*h)**n + 1)**(1.0/n - 1))/n**2 - abs(alpha*h)**n*np.log(abs(alpha*h))*(1.0/n - 1)*(abs(alpha*h)**n + 1)**(1.0/n - 2))/((1.0/n - 1)*((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1) + 1)) - np.log((abs(alpha*h)**n + 1)**(1.0/n - 1))/(n**2*(1.0/n - 1)**2*((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))))/(1 - 1.0/((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1.0/n))*((abs(alpha*h)**n + 1)**(1.0/n - 1))**I*((1 - 1.0/((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1) - I*np.exp(Ks)*((np.log(abs(alpha*h)**n + 1)*(abs(alpha*h)**n + 1)**(1.0/n - 1))/n**2 - abs(alpha*h)**n*np.log(abs(alpha*h))*(1.0/n - 1)*(abs(alpha*h)**n + 1)**(1.0/n - 2))*((abs(alpha*h)**n + 1)**(1.0/n - 1))**(I - 1)*((1 - 1.0/((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1)**2;
# #I
# # dI = np.exp(Ks)*np.log((abs(alpha*h)**n + 1)**(1.0/n - 1))*((abs(alpha*h)**n + 1)**(1.0/n - 1))**I*((1 - 1.0/((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1)**2;
# return Utils.sdiag(self.hydraulicConductivity(h)) # This assumes that the the model is Ks
# def hydraulicConductivityDeriv(self, h):
# alpha = self.alpha
# I = self.I
# n = self.n
# Ks = self.Ks
# m = 1.0 - 1.0/n
# g = I*alpha*n*np.exp(Ks)*abs(alpha*h)**(n - 1.0)*np.sign(alpha*h)*(1.0/n - 1.0)*((abs(alpha*h)**n + 1)**(1.0/n - 1))**(I - 1)*((1 - 1.0/((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1)**2*(abs(alpha*h)**n + 1)**(1.0/n - 2) - (2*alpha*n*np.exp(Ks)*abs(alpha*h)**(n - 1)*np.sign(alpha*h)*(1.0/n - 1)*((abs(alpha*h)**n + 1)**(1.0/n - 1))**I*((1 - 1.0/((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1)*(abs(alpha*h)**n + 1)**(1.0/n - 2))/(((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1) + 1)*(1 - 1.0/((abs(alpha*h)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1.0/n))
# g[h >= 0] = 0
# g = Utils.sdiag(g)
# return g
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