def __init__(self,
nx=100,
ny=100,
value_left=1.,
value_right=0.,
value_top=0.,
value_bottom=0.,
q=None):
"""
::param nx:: Number of cells in the x direction.
::param ny:: Number of cells in the y direction.
::param value_left:: Boundary condition on the left face.
::param value_right:: Boundary condition on the right face.
::param value_top:: Boundary condition on the top face.
::param value_bottom:: Boundary condition on the bottom face.
::param q:: Source function.
"""
#set domain dimensions
self.nx = nx
self.ny = ny
self.dx = 1. / nx
self.dy = 1. / ny
#define mesh
self.mesh = fipy.Grid2D(nx=self.nx, ny=self.ny, dx=self.dx, dy=self.dy)
#get the location of the middle of the domain
#cellcenters=np.array(self.mesh.cellCenters).T
#x=cellcenters[:, 0]
#y=cellcenters[:, 1]
x, y = self.mesh.cellCenters
x_all = x[:self.nx]
y_all = y[0:-1:self.ny]
loc1 = x_all[(self.nx - 1) / 2]
loc2 = y_all[(self.ny - 1) / 2]
self.loc = np.intersect1d(
np.where(x == loc1)[0],
np.where(y == loc2)[0])[0]
#get facecenters
X, Y = self.mesh.faceCenters
#define cell and face variables
self.phi = fipy.CellVariable(name='$T(x)$', mesh=self.mesh, value=1.)
self.C = fipy.CellVariable(name='$C(x)$', mesh=self.mesh, value=1.)
self.source = fipy.CellVariable(name='$f(x)$',
mesh=self.mesh,
value=0.)
#apply boundary conditions
#dirichet
self.phi.constrain(value_left, self.mesh.facesLeft)
self.phi.constrain(value_right, self.mesh.facesRight)
#homogeneous Neumann
self.phi.faceGrad.constrain(value_top, self.mesh.facesTop)
self.phi.faceGrad.constrain(value_bottom, self.mesh.facesBottom)
#setup the diffusion problem
self.eq = -fipy.DiffusionTerm(coeff=self.C) == self.source
def mesh_and_boundaries(params):
"""Generate a 2D grid appropriate for the parameters
"""
def fn(f, N):
'''Root solving kernel for compression factor
Determine f(N), such that $\Delta x \sum_{i=0}^N f^i = 2 \Delta x$
'''
return (1 - f**N) / (1 - f) - 2.
N = 1 + params["compression"]
compression = fsolve(fn, x0=[.5], args=(N))[0]
dx = dy = params["cellSize"]
Nx = int(params["Lx"] / dx)
Ny = int(params["Ly"] / dx)
dx_variable = [dx] * (Nx - 2) + [dx * compression**i for i in range(N)]
dy_variable = [dy] * Ny
mesh = fp.Grid2D(dx=dx_variable, dy=dy_variable)
X, Y = mesh.faceCenters
inlet = mesh.facesLeft
outlet = mesh.facesRight
walls = mesh.facesTop | mesh.facesBottom
top_right = outlet & (Y > params["Ly"] - dy)
return mesh, inlet, outlet, walls, top_right
def _eval(self, xs):
"""
Solves the advection equation for u and its derivatives for a given
source location xs.
"""
xs = view_as_column(xs)
assert xs.shape[0] == 2
nx = 50
ny = nx
dx = 0.1
dy = dx
mesh = fp.Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
vx, vy = make_V_field(mesh)
u = f(xs[:, 0], mesh, vx, vy)
du1 = df(xs[:, 0], mesh, vx, vy, 1)
du2 = df(xs[:, 0], mesh, vx, vy, 2)
d2u11 = df2(xs[:, 0], mesh, vx, vy, 1, 1)
d2u22 = df2(xs[:, 0], mesh, vx, vy, 1, 1)
d2u12 = df2(xs[:, 0], mesh, vx, vy, 1, 2)
dU = np.hstack([view_as_column(du1), view_as_column(du2)])
d2U = np.hstack([
view_as_column(d2u11),
view_as_column(d2u12),
view_as_column(d2u12),
view_as_column(d2u22)
])
d2U = d2U.reshape((d2U.shape[0], 2, 2))
state = {}
state['f'] = u #view_as_column(u)
state['f_grad'] = dU
state['f_grad_2'] = d2U
return state
def main():
"""
NAME 2DFPE.py
PURPOSE Integrate time-dependent FPE
EXECUTION python 2DFPE.py
STARTED CS 24/09/2015
"""
nx = 20
ny = nx
dx = 1.
dy = dx
L = dx * nx
mesh = fp.Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
y = np.linspace(-ny * dy * 0.5, +ny * dy * 0.5, ny,
endpoint=True)[:, np.newaxis]
X, Y = mesh.faceCenters
## phi is pdf; psi is y*pdf for convenience
phi = fp.CellVariable(mesh=mesh, value=1 / (dx * nx * dy * ny))
psi = fp.CellVariable(mesh=mesh,
value=(y * phi.value.reshape((nx, ny))).flatten())
diffCoeff = 1.
diffMatri = [[0., 0.], [0., diffCoeff]]
convCoeff = np.array([-1., +1.])
eq = fp.TransientTerm(var=phi) == fp.DiffusionTerm(
coeff=[diffMatri],
var=phi) + 0 * fp.ExponentialConvectionTerm(coeff=convCoeff, var=psi)
##---------------------------------------------------------------------------------------------------------
## BCs
phi = BC_value_at_boundary(phi, mesh)
## Evolution
timeStepDuration = 0.5 * min(dy**2 / (2. * diffCoeff), dy / (nx * dx))
steps = 10
for step in range(steps):
print np.trapz(np.trapz(phi.value.reshape([nx, ny]), dx=dx), dx=dy)
psi.value = (y * phi.value.reshape((nx, ny))).flatten()
eq.solve(var=phi, dt=timeStepDuration)
print phi.value[5]
# plot_pdf(phi.value.reshape([nx,ny]),step+1)
plt.contourf(phi.value.reshape([nx, ny]), extent=(-1, 1, -1, 1))
plt.colorbar()
plt.title("Density at timestep " + str(steps))
plt.xlabel("$x$", fontsize=18)
plt.ylabel("$\eta$", fontsize=18)
plt.savefig("fig_FPE/Imp" + str(steps) + ".png")
plt.show()
return
def forward(xs):
nx = 21
ny = nx
dx = 1. / 51
dy = dx
rho = 0.05
q0 = 1. / (np.pi * rho**2)
T = 0.3
mesh = fp.Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
time = fp.Variable()
sourceTerm_1 = fp.CellVariable(name="Source term", mesh=mesh, value=0.)
for i in range(sourceTerm_1().shape[0]):
sourceTerm_1()[i] = q0 * np.exp(-(
(mesh.cellCenters[0]()[i] - xs[0])**2 +
(mesh.cellCenters[1]()[i] - xs[1])**2) /
(2 * rho**2)) * (time() < T)
# The equation
eq = fp.TransientTerm() == fp.DiffusionTerm(
coeff=1.) + sourceTerm_1 # + sourceTerm_2
# The solution variable
phi = fp.CellVariable(name="Concentration", mesh=mesh, value=0.)
#if __name__ == '__main__':
# viewer = fp.Viewer(vars=phi, datamin=0., datamax=3.)
# viewer.plot()
x = np.arange(0, nx) / nx
y = x
data = []
dt = 0.005
steps = 60
for step in range(steps):
time.setValue(time() + dt)
eq.solve(var=phi, dt=dt)
#if __name__ == '__main__':
# viewer.plot()
#if step == 14 or step == 29 or step == 44 or step == 59:
# dl = phi()[0]
# dr = phi()[nx-1]
# ul = phi()[nx**2 - nx]
# ur = phi()[nx**2 - 1]
# print phi().shape
# data = np.hstack([data, np.array([dl, dr, ul, ur])])
#if __name__ == '__main__':
# raw_input("Transient diffusion with source term. Press <return> to proceed")
return phi().reshape(nx, nx)
def _eval_u(self, xs):
"""
Solves only the diffusion equation for u for a given
source location xs.
"""
xs = view_as_column(xs)
assert xs.shape[0] == 2
nx = 25
ny = nx
dx = 0.04
dy = dx
mesh = fp.Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
u = f(xs[:,0], mesh)
return u
def initialise_mesh(self):
if self.has_obstacles():
self.mesh = make_porous_mesh(self.rc, self.Rc, self.dx, self.L)
elif self.dim == 1:
self.mesh = fipy.Grid1D(Lx=self.L[0],
dx=self.dx[0],
origin=(-self.L[0] / 2.0, ))
elif self.dim == 2:
self.mesh = fipy.Grid2D(Lx=self.L[0],
Ly=self.L[1],
dx=self.dx[0],
dy=self.dx[1],
origin=((-self.L[0] / 2.0, ),
(-self.L[1] / 2.0, )))
def get_mesh(params):
"""Create the mesh
Args:
params: the parameter dict
Returns:
the fipy mesh
"""
return pipe(
fp.Grid2D(Lx=params["lx"],
Ly=params["lx"],
nx=params["nx"],
ny=params["nx"]),
lambda x: x - np.array(
(params["lx"] / 2., params["lx"] / 2.))[:, None],
)
def df2(xs, mesh, i, j):
"""
Evaluate the model for the 2nd derivatives at the four corners of the domain
at times ``t``.
It returns a flatten version of the system, i.e.:
y_1(t_1)
...
y_4(t_1)
...
y_1(t_4)
...
y_4(t_4)
"""
assert i == 1 or i == 2
assert j == 1 or j == 2
nx = 25
ny = nx
dx = 0.04
dy = dx
mesh = fp.Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
time = fp.Variable()
q0 = make_source_der_2(xs, mesh, time, i, j)
D = 1.
# Define the equation
eq = fp.TransientTerm() == fp.DiffusionTerm(coeff=D) + q0
# Boundary conditions
# The solution variable
phi = fp.CellVariable(name="Concentraion", mesh=mesh, value=0.)
# Solve
dt = 0.005
steps = 60
d2U = []
for step in range(steps):
eq.solve(var=phi, dt=dt)
if step == 14 or step == 29 or step == 44 or step == 59:
dl = phi()[0]
#dr = phi()[24]
ul = phi()[600]
#ur = phi()[624]
#d2U = np.hstack([d2U, np.array([dl, dr, ul, ur])])
d2U = np.hstack([d2U, np.array([dl, ul])])
return d2U
'''Root solving kernel for compression factor
Determine f(N), such that $\Delta x \sum_{i=0}^N f^i = 2 \Delta x$
'''
return (1 - f**N) / (1 - f) - 2.
N = 1 + args.compression
compression = fsolve(fn, x0=[.5], args=(N))[0]
Nx = int(Lx / dx)
Ny = int(Ly / dy)
dx_variable = [dx] * (Nx - 2) + [dx * compression**i for i in range(N+1)]
dy_variable = [dy] * Ny
mesh = fp.Grid2D(dx=dx_variable, dy=dy_variable)
volumes = fp.CellVariable(mesh=mesh, value=mesh.cellVolumes)
pressure = fp.CellVariable(mesh=mesh, name="$p$")
pressureCorrection = fp.CellVariable(mesh=mesh, name="$p'$")
xVelocity = fp.CellVariable(mesh=mesh, name="$u_x$")
yVelocity = fp.CellVariable(mesh=mesh, name="$u_y$")
velocity = fp.FaceVariable(mesh=mesh, name=r"$\vec{u}$", rank=1)
xVelocityEq = fp.DiffusionTerm(coeff=viscosity) - pressure.grad.dot([1.,0.]) + density * gravity[0]
yVelocityEq = fp.DiffusionTerm(coeff=viscosity) - pressure.grad.dot([0.,1.]) + density * gravity[1]
ap = fp.CellVariable(mesh=mesh, value=1.)
coeff = 1./ ap.arithmeticFaceValue*mesh._faceAreas * mesh._cellDistances
pressureCorrectionEq = fp.DiffusionTerm(coeff=coeff) - velocity.divergence
os.makedirs(pathStr + 'ForwardEvo/')
if (not os.path.exists(pathStr + 'ReverseEvoUnupdated/')):
os.makedirs(pathStr + 'ReverseEvoUnupdated/')
if (not os.path.exists(pathStr + 'ReverseEvoUpdated/')):
os.makedirs(pathStr + 'ReverseEvoUpdated/')
# Initialize phase-space lattice
# Nx, Dx, XMax, Np, Dp, PMax, and Mesh are Global
Nx = n1 * n2
Np = Nx
Dx = 1. / n1
Dp = Dx
XMax = Dx * Nx
PMax = Dp * Np
comm = fipy.tools.serial
Mesh = fipy.Grid2D(dx=Dx, dy=Dp, nx=2*Nx, ny=2*Np, communicator=comm)\
+ [[-XMax], [-PMax]]
fipy.dump.write(Mesh, filename=pathStr + 'mesh.gz')
# Create and save initial distribution
phi = distributionInitial()
phiInitial = fipy.CellVariable(mesh=Mesh, name=r"\LARGE $\rho_{0}(x,p)$")
phiInitial.setValue(phi.value)
del phi
if (saveResults):
fipy.tools.dump.write(phiInitial, \
filename=pathStr+'initialDistribution.gz')
# Plot initial distribution
genPlots(phiInitial, tStart, saveResults, 'initialDistribution.pdf', pathStr)
import fipy as fp
import glob
import json
import numpy as np
import os
import sys
from fipy.solvers.pysparse import LinearLUSolver as Solver
problem = '1'
domain = 'b'
nx = 200
dx = 1.0
# The first step in implementing any problem in FiPy is to define the mesh. For [Problem 1b]({{ site.baseurl }}/hackathon1/#a.-Square-Periodic) the solution domain is just a square domain with fixed boundary conditions, so a `Grid2D` object is used. No other boundary conditions are required.
mesh = fp.Grid2D(nx=nx, ny=nx, dx=dx, dy=dx)
# The next step is to define the parameters and create a solution variable.
# Constants and initial conditions:
# $c_{\alpha}$ and $c_{\beta}$ are concentrations at which the bulk free energy has minima.
# $\kappa$ is the gradient energy coefficient.
# $\varrho_s$ controls the height of the double-well barrier.
c_alpha = 0.3
c_beta = 0.7
kappa = 2.0
M = 5.0
c_0 = 0.5
epsilon = 0.01
rho_s = 5.0
def hydrology(solve_mode,
nx,
ny,
dx,
dy,
days,
ele,
phi_initial,
catchment_mask,
wt_canal_arr,
boundary_arr,
peat_type_mask,
httd,
tra_to_cut,
sto_to_cut,
diri_bc=0.0,
neumann_bc=None,
plotOpt=False,
remove_ponding_water=True,
P=0.0,
ET=0.0,
dt=1.0):
"""
INPUT:
- ele: (nx,ny) sized NumPy array. Elevation in m above c.r.p.
- Hinitial: (nx,ny) sized NumPy array. Initial water table in m above c.r.p.
- catchment mask: (nx,ny) sized NumPy array. Boolean array = True where the node is inside the computation area. False if outside.
- wt_can_arr: (nx,ny) sized NumPy array. Zero everywhere except in nodes that contain canals, where = wl of the canal.
- value_for_masked: DEPRECATED. IT IS NOW THE SAME AS diri_bc.
- diri_bc: None or float. If None, Dirichlet BC will not be implemented. If float, this number will be the BC.
- neumann_bc: None or float. If None, Neumann BC will not be implemented. If float, this is the value of grad phi.
- P: Float. Constant precipitation. mm/day.
- ET: Float. Constant evapotranspiration. mm/day.
"""
# dneg = []
track_WT_drained_area = (239, 166)
track_WT_notdrained_area = (522, 190)
ele[~catchment_mask] = 0.
ele = ele.flatten()
phi_initial = (phi_initial + 0.0 * np.zeros((ny, nx))) * catchment_mask
# phi_initial = phi_initial * catchment_mask
phi_initial = phi_initial.flatten()
if len(ele) != nx * ny or len(phi_initial) != nx * ny:
raise ValueError("ele or Hinitial are not of dim nx*ny")
mesh = fp.Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
phi = fp.CellVariable(
name='computed H', mesh=mesh, value=phi_initial,
hasOld=True) #response variable H in meters above reference level
if diri_bc != None and neumann_bc == None:
phi.constrain(diri_bc, mesh.exteriorFaces)
elif diri_bc == None and neumann_bc != None:
phi.faceGrad.constrain(neumann_bc * mesh.faceNormals,
where=mesh.exteriorFaces)
else:
raise ValueError(
"Cannot apply Dirichlet and Neumann boundary values at the same time. Contradictory values."
)
#*******omit areas outside the catchment. c is input
cmask = fp.CellVariable(mesh=mesh, value=np.ravel(catchment_mask))
cmask_not = fp.CellVariable(mesh=mesh,
value=np.array(~cmask.value, dtype=int))
# *** drain mask or canal mask
dr = np.array(wt_canal_arr, dtype=bool)
dr[np.array(wt_canal_arr, dtype=bool) * np.array(
boundary_arr, dtype=bool
)] = False # Pixels cannot be canals and boundaries at the same time. Everytime a conflict appears, boundaries win. This overwrites any canal water level info if the canal is in the boundary.
drmask = fp.CellVariable(mesh=mesh, value=np.ravel(dr))
drmask_not = fp.CellVariable(
mesh=mesh, value=np.array(~drmask.value, dtype=int)
) # Complementary of the drains mask, but with ints {0,1}
# mask away unnecesary stuff
# phi.setValue(np.ravel(H)*cmask.value)
# ele = ele * cmask.value
source = fp.CellVariable(mesh=mesh,
value=0.) # cell variable for source/sink
# CC=fp.CellVariable(mesh=mesh, value=C(phi.value-ele)) # differential water capacity
def D_value(phi, ele, tra_to_cut, cmask, drmask_not):
# Some inputs are in fipy CellVariable type
gwt = phi.value * cmask.value - ele
d = hydro_utils.peat_map_h_to_tra(
soil_type_mask=peat_type_mask, gwt=gwt,
h_to_tra_and_C_dict=httd) - tra_to_cut
# d <0 means tra_to_cut is greater than the other transmissivity, which in turn means that
# phi is below the impermeable bottom. We allow phi to have those values, but
# the transmissivity is in those points is equal to zero (as if phi was exactly at the impermeable bottom).
d[d < 0] = 1e-3 # Small non-zero value not to wreck the computation
dcell = fp.CellVariable(
mesh=mesh, value=d
) # diffusion coefficient, transmissivity. As a cell variable.
dface = fp.FaceVariable(mesh=mesh,
value=dcell.arithmeticFaceValue.value
) # THe correct Face variable.
return dface.value
def C_value(phi, ele, sto_to_cut, cmask, drmask_not):
# Some inputs are in fipy CellVariable type
gwt = phi.value * cmask.value - ele
c = hydro_utils.peat_map_h_to_sto(
soil_type_mask=peat_type_mask, gwt=gwt,
h_to_tra_and_C_dict=httd) - sto_to_cut
c[c < 0] = 1e-3 # Same reasons as for D
ccell = fp.CellVariable(
mesh=mesh, value=c
) # diffusion coefficient, transmissivity. As a cell variable.
return ccell.value
D = fp.FaceVariable(
mesh=mesh, value=D_value(phi, ele, tra_to_cut, cmask,
drmask_not)) # THe correct Face variable.
C = fp.CellVariable(
mesh=mesh, value=C_value(phi, ele, sto_to_cut, cmask,
drmask_not)) # differential water capacity
largeValue = 1e20 # value needed in implicit source term to apply internal boundaries
if plotOpt:
big_4_raster_plot(
title='Before the computation',
raster1=(
(hydro_utils.peat_map_h_to_tra(soil_type_mask=peat_type_mask,
gwt=(phi.value - ele),
h_to_tra_and_C_dict=httd) -
tra_to_cut) * cmask.value * drmask_not.value).reshape(ny, nx),
raster2=(ele.reshape(ny, nx) - wt_canal_arr) * dr * catchment_mask,
raster3=ele.reshape(ny, nx),
raster4=(ele - phi.value).reshape(ny, nx))
# for later cross-section plots
y_value = 270
# print "first cross-section plot"
# ele_with_can = copy.copy(ele).reshape(ny,nx)
# ele_with_can = ele_with_can * catchment_mask
# ele_with_can[wt_canal_arr > 0] = wt_canal_arr[wt_canal_arr > 0]
# plot_line_of_peat(ele_with_can, y_value=y_value, title="cross-section", color='green', nx=nx, ny=ny, label="ele")
# ********************************** PDE, STEADY STATE **********************************
if solve_mode == 'steadystate':
if diri_bc != None:
# diri_boundary = fp.CellVariable(mesh=mesh, value= np.ravel(diri_boundary_value(boundary_mask, ele2d, diri_bc)))
eq = 0. == (
fp.DiffusionTerm(coeff=D) + source * cmask * drmask_not -
fp.ImplicitSourceTerm(cmask_not * largeValue) +
cmask_not * largeValue * np.ravel(boundary_arr) -
fp.ImplicitSourceTerm(drmask * largeValue) +
drmask * largeValue * (np.ravel(wt_canal_arr))
# - fp.ImplicitSourceTerm(bmask_not*largeValue) + bmask_not*largeValue*(boundary_arr)
)
elif neumann_bc != None:
raise NotImplementedError("Neumann BC not implemented yet!")
cmask_face = fp.FaceVariable(mesh=mesh,
value=np.array(
cmask.arithmeticFaceValue.value,
dtype=bool))
D[cmask_face.value] = 0.
eq = 0. == (
fp.DiffusionTerm(coeff=D) + source * cmask * drmask_not -
fp.ImplicitSourceTerm(cmask_not * largeValue) +
cmask_not * largeValue * (diri_bc) -
fp.ImplicitSourceTerm(drmask * largeValue) +
drmask * largeValue * (np.ravel(wt_canal_arr))
# + fp.DiffusionTerm(coeff=largeValue * bmask_face)
# - fp.ImplicitSourceTerm((bmask_face * largeValue *neumann_bc * mesh.faceNormals).divergence)
)
elif solve_mode == 'transient':
if diri_bc != None:
# diri_boundary = fp.CellVariable(mesh=mesh, value= np.ravel(diri_boundary_value(boundary_mask, ele2d, diri_bc)))
eq = fp.TransientTerm(coeff=C) == (
fp.DiffusionTerm(coeff=D) + source * cmask * drmask_not -
fp.ImplicitSourceTerm(cmask_not * largeValue) +
cmask_not * largeValue * np.ravel(boundary_arr) -
fp.ImplicitSourceTerm(drmask * largeValue) +
drmask * largeValue * (np.ravel(wt_canal_arr))
# - fp.ImplicitSourceTerm(bmask_not*largeValue) + bmask_not*largeValue*(boundary_arr)
)
elif neumann_bc != None:
raise NotImplementedError("Neumann BC not implemented yet!")
#********************************************************
max_sweeps = 10 # inner loop.
avg_wt = []
wt_track_drained = []
wt_track_notdrained = []
cumulative_Vdp = 0.
#********Finite volume computation******************
for d in range(days):
source.setValue(
(P[d] - ET[d]) * .001 * np.ones(ny * nx)
) # source/sink. P and ET are in mm/day. The factor of 10^-3 converst to m/day. It does not matter that there are 100 x 100 m^2 in one pixel
print("(d, P - ET) = ", (d, (P[d] - ET[d])))
if plotOpt and d != 0:
# print "one more cross-section plot"
plot_line_of_peat(phi.value.reshape(ny, nx),
y_value=y_value,
title="cross-section",
color='cornflowerblue',
nx=nx,
ny=ny,
label=d)
res = 0.0
phi.updateOld()
D.setValue(D_value(phi, ele, tra_to_cut, cmask, drmask_not))
C.setValue(C_value(phi, ele, tra_to_cut, cmask, drmask_not))
for r in range(max_sweeps):
resOld = res
res = eq.sweep(var=phi, dt=dt) # solve linearization of PDE
#print "sum of Ds: ", np.sum(D.value)/1e8
#print "average wt: ", np.average(phi.value-ele)
#print 'residue diference: ', res - resOld
if abs(res - resOld) < 1e-7:
break # it has reached to the solution of the linear system
if solve_mode == 'transient': #solving in steadystate will remove water only at the very end
if remove_ponding_water:
s = np.where(
phi.value > ele, ele, phi.value
) # remove the surface water. This also removes phi in those masked values (for the plot only)
phi.setValue(s) # set new values for water table
if (D.value < 0.).any():
print("Some value in D is negative!")
# For some plots
avg_wt.append(np.average(phi.value - ele))
wt_track_drained.append(
(phi.value - ele).reshape(ny, nx)[track_WT_drained_area])
wt_track_notdrained.append(
(phi.value - ele).reshape(ny, nx)[track_WT_notdrained_area])
""" Volume of dry peat calc."""
not_peat = np.ones(shape=peat_type_mask.shape) # Not all soil is peat!
not_peat[peat_type_mask == 4] = 0 # NotPeat
not_peat[peat_type_mask == 5] = 0 # OpenWater
peat_vol_weights = utilities.PeatV_weight_calc(
np.array(~dr * catchment_mask * not_peat, dtype=int))
dry_peat_volume = utilities.PeatVolume(peat_vol_weights,
(ele - phi.value).reshape(
ny, nx))
cumulative_Vdp = cumulative_Vdp + dry_peat_volume
print("avg_wt = ", np.average(phi.value - ele))
# print "wt drained = ", (phi.value - ele).reshape(ny,nx)[track_WT_drained_area]
# print "wt not drained = ", (phi.value - ele).reshape(ny,nx)[track_WT_notdrained_area]
print("Cumulative vdp = ", cumulative_Vdp)
if solve_mode == 'steadystate': #solving in steadystate we remove water only at the very end
if remove_ponding_water:
s = np.where(
phi.value > ele, ele, phi.value
) # remove the surface water. This also removes phi in those masked values (for the plot only)
phi.setValue(s) # set new values for water table
# Areas with WT <-1.0; areas with WT >0
# plot_raster_by_value((ele-phi.value).reshape(ny,nx), title="ele-phi in the end, colour keys", bottom_value=0.5, top_value=0.01)
if plotOpt:
big_4_raster_plot(
title='After the computation',
raster1=(
(hydro_utils.peat_map_h_to_tra(soil_type_mask=peat_type_mask,
gwt=(phi.value - ele),
h_to_tra_and_C_dict=httd) -
tra_to_cut) * cmask.value * drmask_not.value).reshape(ny, nx),
raster2=(ele.reshape(ny, nx) - wt_canal_arr) * dr * catchment_mask,
raster3=ele.reshape(ny, nx),
raster4=(ele - phi.value).reshape(ny, nx))
fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(12, 9), dpi=80)
x = np.arange(-21, 1, 0.1)
axes[0, 0].plot(httd[1]['hToTra'](x), x)
axes[0, 0].set(title='hToTra', ylabel='depth')
axes[0, 1].plot(httd[1]['C'](x), x)
axes[0, 1].set(title='C')
axes[1, 0].plot()
axes[1, 0].set(title="Nothing")
axes[1, 1].plot(avg_wt)
axes[1, 1].set(title="avg_wt_over_time")
# plot surface in cross-section
ele_with_can = copy.copy(ele).reshape(ny, nx)
ele_with_can = ele_with_can * catchment_mask
ele_with_can[wt_canal_arr > 0] = wt_canal_arr[wt_canal_arr > 0]
plot_line_of_peat(ele_with_can,
y_value=y_value,
title="cross-section",
nx=nx,
ny=ny,
label="surface",
color='peru',
linewidth=2.0)
plt.show()
# change_in_canals = (ele-phi.value).reshape(ny,nx)*(drmask.value.reshape(ny,nx)) - ((ele-H)*drmask.value).reshape(ny,nx)
# resulting_phi = phi.value.reshape(ny,nx)
phi.updateOld()
return (phi.value - ele).reshape(ny, nx)
else:
class dummyTreant(object):
categories = dict()
data = dummyTreant()
data.categories['problem'] = "III-2a"
data.categories['args'] = " ".join(sys.argv)
data.categories['step'] = args.step
data.categories['sweeps'] = args.sweeps
data.categories['dx'] = args.dx
data.categories['commit'] = os.popen('git log --pretty="%H" -1').read().strip()
data.categories['diff'] = os.popen('git diff').read()
mesh = fp.Grid2D(Lx=100., dx=args.dx, Ly=100., dy=args.dx)
volumes = fp.CellVariable(mesh=mesh, value=mesh.cellVolumes)
c = fp.CellVariable(mesh=mesh, name="$c$", hasOld=True)
psi = fp.CellVariable(mesh=mesh, name=r"$\psi$", hasOld=True)
Phi = fp.CellVariable(mesh=mesh, name=r"$\Phi$", hasOld=True)
calpha = 0.3
cbeta = 0.7
kappa = 2.
rho = 5.
M = 5.
k = 0.09
epsilon = 90.
ceq = fp.TransientTerm(var=c) == fp.DiffusionTerm(coeff=M, var=psi)
def hydrology(mode,
sensor_positions,
nx,
ny,
dx,
dy,
days,
ele,
phi_initial,
catchment_mask,
wt_canal_arr,
boundary_arr,
peat_type_mask,
peat_bottom_arr,
transmissivity,
t0,
t1,
t2,
t_sapric_coef,
storage,
s0,
s1,
s2,
s_sapric_coef,
diri_bc=0.0,
plotOpt=False,
remove_ponding_water=True,
P=0.0,
ET=0.0,
dt=1.0):
"""
INPUT:
- ele: (nx,ny) sized NumPy array. Elevation in m above c.r.p.
- Hinitial: (nx,ny) sized NumPy array. Initial water table in m above c.r.p.
- catchment mask: (nx,ny) sized NumPy array. Boolean array = True where the node is inside the computation area. False if outside.
- wt_can_arr: (nx,ny) sized NumPy array. Zero everywhere except in nodes that contain canals, where = wl of the canal.
- value_for_masked: DEPRECATED. IT IS NOW THE SAME AS diri_bc.
- diri_bc: None or float. If None, Dirichlet BC will not be implemented. If float, this number will be the BC.
- neumann_bc: None or float. If None, Neumann BC will not be implemented. If float, this is the value of grad phi.
- P: Float. Constant precipitation. mm/day.
- ET: Float. Constant evapotranspiration. mm/day.
"""
# dneg = []
# track_WT_drained_area = (239,166)
# track_WT_notdrained_area = (522,190)
ele[~catchment_mask] = 0.
ele = ele.flatten()
phi_initial = (phi_initial + 0.0 * np.zeros((ny, nx))) * catchment_mask
# phi_initial = phi_initial * catchment_mask
phi_initial = phi_initial.flatten()
if len(ele) != nx * ny or len(phi_initial) != nx * ny:
raise ValueError("ele or Hinitial are not of dim nx*ny")
mesh = fp.Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
phi = fp.CellVariable(
name='computed H', mesh=mesh, value=phi_initial,
hasOld=True) #response variable H in meters above reference level
if diri_bc != None:
phi.constrain(diri_bc, mesh.exteriorFaces)
else:
raise ValueError("Dirichlet boundary conditions must have a value")
#*******omit areas outside the catchment. c is input
cmask = fp.CellVariable(mesh=mesh, value=np.ravel(catchment_mask))
cmask_not = fp.CellVariable(mesh=mesh,
value=np.array(~cmask.value, dtype=int))
# *** drain mask or canal mask
dr = np.array(wt_canal_arr, dtype=bool)
dr[np.array(wt_canal_arr, dtype=bool) * np.array(
boundary_arr, dtype=bool
)] = False # Pixels cannot be canals and boundaries at the same time. Everytime a conflict appears, boundaries win. This overwrites any canal water level info if the canal is in the boundary.
drmask = fp.CellVariable(mesh=mesh, value=np.ravel(dr))
drmask_not = fp.CellVariable(
mesh=mesh, value=np.array(~drmask.value, dtype=int)
) # Complementary of the drains mask, but with ints {0,1}
# mask away unnecesary stuff
# phi.setValue(np.ravel(H)*cmask.value)
# ele = ele * cmask.value
source = fp.CellVariable(mesh=mesh,
value=0.) # cell variable for source/sink
# CC=fp.CellVariable(mesh=mesh, value=C(phi.value-ele)) # differential water capacity
def T_value(phi, ele, cmask, peat_bottom_arr):
# Some inputs are in fipy CellVariable type
gwt = (phi.value * cmask.value - ele).reshape(ny, nx)
# T(h) - T(bottom)
T = transmissivity(gwt, t0, t1, t2, t_sapric_coef) - transmissivity(
peat_bottom_arr, t0, t1, t2, t_sapric_coef)
# d <0 means tra_to_cut is greater than the other transmissivity, which in turn means that
# phi is below the impermeable bottom. We allow phi to have those values, but
# the transmissivity is in those points is equal to zero (as if phi was exactly at the impermeable bottom).
T[T < 0] = 1e-3 # Small non-zero value not to wreck the computation
Tcell = fp.CellVariable(mesh=mesh, value=T.flatten(
)) # diffusion coefficient, transmissivity. As a cell variable.
Tface = fp.FaceVariable(mesh=mesh,
value=Tcell.arithmeticFaceValue.value
) # THe correct Face variable.
return Tface.value
def S_value(phi, ele, cmask, peat_bottom_arr):
# Some inputs are in fipy CellVariable type
gwt = (phi.value * cmask.value - ele).reshape(ny, nx)
S = storage(gwt, s0, s1, s2, s_sapric_coef) - storage(
peat_bottom_arr, s0, s1, s2, s_sapric_coef)
S[S < 0] = 1e-3 # Same reasons as for D
Scell = fp.CellVariable(mesh=mesh, value=S.flatten(
)) # diffusion coefficient, transmissivity. As a cell variable.
return Scell.value
T = fp.FaceVariable(mesh=mesh,
value=T_value(
phi, ele, cmask,
peat_bottom_arr)) # THe correct Face variable.
S = fp.CellVariable(mesh=mesh,
value=S_value(
phi, ele, cmask,
peat_bottom_arr)) # differential water capacity
largeValue = 1e20 # value needed in implicit source term to apply internal boundaries
if plotOpt:
big_4_raster_plot(
title='Before the computation',
# raster1=((hydro_utils.peat_map_h_to_tra(soil_type_mask=peat_type_mask, gwt=(phi.value - ele), h_to_tra_and_C_dict=httd) - tra_to_cut)*cmask.value *drmask_not.value ).reshape(ny,nx),
raster2=(ele.reshape(ny, nx) - wt_canal_arr) * dr * catchment_mask,
raster3=ele.reshape(ny, nx),
raster4=(ele - phi.value).reshape(ny, nx))
# for later cross-section plots
y_value = 270
"""
###### PDE ######
"""
if mode == 'steadystate':
temp = 0.
elif mode == 'transient':
temp = fp.TransientTerm(coeff=S)
if diri_bc != None:
# diri_boundary = fp.CellVariable(mesh=mesh, value= np.ravel(diri_boundary_value(boundary_mask, ele2d, diri_bc))
eq = temp == (
fp.DiffusionTerm(coeff=T) + source * cmask * drmask_not -
fp.ImplicitSourceTerm(cmask_not * largeValue) +
cmask_not * largeValue * np.ravel(boundary_arr) -
fp.ImplicitSourceTerm(drmask * largeValue) + drmask * largeValue *
(np.ravel(wt_canal_arr))
# - fp.ImplicitSourceTerm(bmask_not*largeValue) + bmask_not*largeValue*(boundary_arr)
)
#********************************************************
max_sweeps = 10 # inner loop.
avg_wt = []
# wt_track_drained = []
# wt_track_notdrained = []
cumulative_Vdp = 0.
#********Finite volume computation******************
for d in range(days):
if type(P) == type(ele): # assume it is a numpy array
source.setValue(
(P[d] - ET[d]) * .001 * np.ones(ny * nx)
) # source/sink, in mm/day. The factor of 10^-3 takes into account that there are 100 x 100 m^2 in one pixel
# print("(d,P) = ", (d, (P[d]-ET[d])* 10.))
else:
source.setValue((P - ET) * 10. * np.ones(ny * nx))
# print("(d,P) = ", (d, (P-ET)* 10.))
if plotOpt and d != 0:
# print "one more cross-section plot"
plot_line_of_peat(phi.value.reshape(ny, nx),
y_value=y_value,
title="cross-section",
color='cornflowerblue',
nx=nx,
ny=ny,
label=d)
res = 0.0
phi.updateOld()
T.setValue(T_value(phi, ele, cmask, peat_bottom_arr))
S.setValue(S_value(phi, ele, cmask, peat_bottom_arr))
for r in range(max_sweeps):
resOld = res
res = eq.sweep(var=phi, dt=dt) # solve linearization of PDE
#print "sum of Ds: ", np.sum(D.value)/1e8
#print "average wt: ", np.average(phi.value-ele)
#print 'residue diference: ', res - resOld
if abs(res - resOld) < 1e-7:
break # it has reached to the solution of the linear system
if remove_ponding_water:
s = np.where(
phi.value > ele, ele, phi.value
) # remove the surface water. This also removes phi in those masked values (for the plot only)
phi.setValue(s) # set new values for water table
if (T.value < 0.).any():
print("Some value in D is negative!")
# For some plots
avg_wt.append(np.average(phi.value - ele))
# wt_track_drained.append((phi.value - ele).reshape(ny,nx)[track_WT_drained_area])
# wt_track_notdrained.append((phi.value - ele).reshape(ny,nx)[track_WT_notdrained_area])
""" Volume of dry peat calc."""
not_peat = np.ones(shape=peat_type_mask.shape) # Not all soil is peat!
not_peat[peat_type_mask == 4] = 0 # NotPeat
not_peat[peat_type_mask == 5] = 0 # OpenWater
peat_vol_weights = utilities.PeatV_weight_calc(
np.array(~dr * catchment_mask * not_peat, dtype=int))
dry_peat_volume = utilities.PeatVolume(peat_vol_weights,
(ele - phi.value).reshape(
ny, nx))
cumulative_Vdp = cumulative_Vdp + dry_peat_volume
if plotOpt:
big_4_raster_plot(
title='After the computation',
# raster1=((hydro_utils.peat_map_h_to_tra(soil_type_mask=peat_type_mask, gwt=(phi.value - ele), h_to_tra_and_C_dict=httd) - tra_to_cut)*cmask.value *drmask_not.value ).reshape(ny,nx),
raster2=(ele.reshape(ny, nx) - wt_canal_arr) * dr * catchment_mask,
raster3=ele.reshape(ny, nx),
raster4=(ele - phi.value).reshape(ny, nx))
# fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(12,9), dpi=80)
# x = np.arange(-21,1,0.1)
# axes[0,0].plot(httd[1]['hToTra'](x),x)
# axes[0,0].set(title='hToTra', ylabel='depth')
# axes[0,1].plot(httd[1]['C'](x),x)
# axes[0,1].set(title='C')
# axes[1,0].plot()
# axes[1,0].set(title="Nothing")
# axes[1,1].plot(avg_wt)
# axes[1,1].set(title="avg_wt_over_time")
# # plot surface in cross-section
# ele_with_can = copy.copy(ele).reshape(ny,nx)
# ele_with_can = ele_with_can * catchment_mask
# ele_with_can[wt_canal_arr > 0] = wt_canal_arr[wt_canal_arr > 0]
# plot_line_of_peat(ele_with_can, y_value=y_value, title="cross-section", nx=nx, ny=ny, label="surface", color='peru', linewidth=2.0)
# plt.show()
# change_in_canals = (ele-phi.value).reshape(ny,nx)*(drmask.value.reshape(ny,nx)) - ((ele-H)*drmask.value).reshape(ny,nx)
# resulting_phi = phi.value.reshape(ny,nx)
wtd = (phi.value - ele).reshape(ny, nx)
wtd_sensors = [wtd[i] for i in sensor_positions]
return np.array(wtd_sensors)
# This example solves a diffusion problem and demonstrates the use of
# applying boundary condition patches.
try:
import fipy
except ImportError:
raise ImportError('Problem with FiPy Installation')
from PyAMGSolver import PyAMGSolver
nx = 20
ny = nx
dx = 1.0
dy = dx
L = dx * nx
mesh = fipy.Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
phi = fipy.CellVariable(name="solution variable", mesh=mesh, value=0.)
# Apply Dirichlet boundary conditions (else Neumann by default)
valueTopLeft = 0
valueBottomRight = 1
x, y = mesh.getFaceCenters()
facesTopLeft = ((mesh.getFacesLeft() & (y > L / 2)) | (mesh.getFacesTop() &
(x < L / 2)))
facesBottomRight = ((mesh.getFacesRight() & (y < L / 2)) |
(mesh.getFacesBottom() & (x > L / 2)))
BCs = (fipy.FixedValue(faces=facesTopLeft, value=valueTopLeft),
fipy.FixedValue(faces=facesBottomRight, value=valueBottomRight))
# set solver
# solver = LinearLUSolver(tolerance = 1.e-6, iterations = 100)
MGSetupOpts = {'max_coarse': 10}
import fipy as fp
import glob
import json
import numpy as np
import os
import sys
from fipy.solvers.pysparse import LinearLUSolver as Solver
problem = '1'
domain = 'c'
nx = 100
dx = 1.0
# The first step in implementing any problem in FiPy is to define the mesh. In this case, the T-shaped domain is constructed out of two rectangular `Grid2D` objects. No other boundary conditions are required.
mesh = fp.Grid2D(Lx=20., Ly=100.0, dx=dx, dy=dx) + (
fp.Grid2D(Ly=20.0, Lx=100.0, dx=dx, dy=dx) + [[-40], [100]])
# The next step is to define the parameters and create a solution variable.
# Constants and initial conditions:
# $c_{\alpha}$ and $c_{\beta}$ are concentrations at which the bulk free energy has minima.
# $\kappa$ is the gradient energy coefficient.
# $\varrho_s$ controls the height of the double-well barrier.
c_alpha = 0.3
c_beta = 0.7
kappa = 2.0
M = 5.0
c_0 = 0.5
epsilon = 0.01
rho_s = 5.0
