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Copy pathgenerate-total-dofs.py
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generate-total-dofs.py
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1/1:
def T(v, e):
return e/cv
1/2: from math import cos
1/3:
def rho(x):
cos(x)
1/4:
def rho_u(x):
cos(1.1*x)
1/5: rho0 = 3.487882614709243
1/6:
def rho(x):
rho0*cos(x)
1/7:
def rho_u(x):
rho0*cos(1.1*x)
1/8:
def u(x):
rho_u(x) / rho(x)
1/9: u(.1)
1/10:
def rho(x):
return rho0*cos(x)
1/11:
def rho_u(x):
return rho0*cos(1.1*x)
1/12:
def u(x):
return rho_u(x) / rho(x)
1/13: u(.1)
1/14: u(1.1)
1/15: rho(1.1)
1/16: rho(.1)
1/17:
def rho_et(x):
return 26.74394130735463*cos(1.2*x)
1/18:
def e(x):
return rho_et(x) / rho - 0.5*u(x)*u(x)
1/19: e(.1)
1/20:
def e(x):
return rho_et(x) / rho(x) - 0.5*u(x)*u(x)
1/21: e(.1)
1/22: e(1.1)
1/23:
gamma = 1.4
molar_mass = 29e-3
R = 8.3145
R_specific = R / molar_mass
cp = gamma * R_specific / (gamma - 1)
cv = cp / gamma
1/24:
def T(x):
return e(x) / cv
1/25: T(.1)
1/26: T(1.1)
1/27:
def c(x):
return sqrt(gamma * R_specific * T(x))
1/28: from math import sqrt
1/29: c(.1)
1/30: c(1.1)
1/31: u(.1)
1/32: u(1.1)
1/33: rho0
2/1: 461.40 + 92.20 - 351.80
3/1: height_brick = .4*2
3/2: height_side_ref = .1*2
3/3: height_hot_plenum = 1*.8
3/4: height_bottom_reflector = .3 + .2 + .3 + .216 + .412
3/5: cum = height_brick + height_side_ref + height_hot_plenum + height_bottom_reflector
3/6: cum
3/7: height_pebble_bed = 20 * .550
3/8: cum = cum + height_pebble_bed
3/9: cum
3/10: cavity = 1*.760
3/11: cum = cum + cavity
3/12: cum
4/1: 496.54 / 9
4/2: individ = 496.54 / 9
4/3: individ
4/4: individ * 2
5/1: .4 * 12
5/2: .2 * 12
5/3: 6. / 52
5/4: _ * 12
6/1: 250 + 125 + 100 + 120
7/1: 118000 * .02
7/2: 163000 * .08
8/1: dr_fgm = 500.
8/2: dr_gfa = 1061.
8/3: s_fgm = 410.
8/4: s_gfa = 861.
8/5: dr_fgx = dr_fgm / dr_gfa
8/6: s_fgx = s_fgm / s_fga
8/7: s_fgx = s_fgm / s_gfa
8/8: dr_fgx
8/9: (500 + 52.) / (1061. + 100.)
8/10: (410. + 42) / (861. + 100)
8/11: 19. / 31
8/12: 106. / 13.1
8/13: _ - 8.
8/14: _ * 60
9/1: from math import *
9/2: 1.1*sin(1.1*0.6)
9/3: 1.1*sin(1.1*-0.6)
9/4: 1.1*sin(1.1*-0.9)
9/5: 1.1*sin(1.1*-1.2)
9/6: 1.1*sin(0)
9/7: 1.9999999999999998 + -3.348857074341554
9/8: _ / 2.
9/9:
def rho(x):
return 1.1*sin(1.1*x)
9/10:
def vel(x):
return 1.1*cos(1.1*x)
9/11:
def rhou(x):
return rho(x) * vel(x)
9/12: rhou(-0.6)
9/13: vel(-0.6)
9/14: 2 * _ - 2.
9/15: rho(-0.6)
9/16: 2 * _ - 2.
9/17: rho_ghost = _
9/18: vel_ghost = 2 * vel(-0.6) - 2.
9/19: rho_ghost
9/20: vel_ghost
9/21: rho_elem = 2
9/22: vel_elem = 2
9/23: rhou_elem = rho_elem * vel_elem
9/24: rhou_ghost = rho_ghost * vel_ghost
9/25: rhou_elem
9/26: rhou_ghost
9/27: (rhou_elem + rhou_ghost) / 2.
10/1: (1.94444 + 2.5) / 2
11/1:
from math import sqrt
def error(numeric):
square = (numeric - 1./3.)**2
return sqrt(square)
11/2: error(1)
11/3:
def numerical_eval(r):
return r**2
11/4:
def run_sim(nx):
h = 1. / nx
integral = 0
for elem_id in range(nx):
centroid = elem_id * h + h / 2
integral = integral + numerical_eval(centroid) * h
print(error(integral))
11/5: run_sim(1)
11/6: 1./3. - 1./4.
11/7: run_sim(2)
11/8:
r0 = run_sim(1)
r1 = run_sim(2)
r1 / r0
11/9:
def run_sim(nx):
h = 1. / nx
integral = 0
for elem_id in range(nx):
centroid = elem_id * h + h / 2
integral = integral + numerical_eval(centroid) * h
return error(integral))
11/10:
def run_sim(nx):
h = 1. / nx
integral = 0
for elem_id in range(nx):
centroid = elem_id * h + h / 2
integral = integral + numerical_eval(centroid) * h
return error(integral)
11/11: run_sim(1)
11/12: run_sim(2)
11/13:
r0 = run_sim(1)
r1 = run_sim(2)
r1 / r0
11/14:
r0 = run_sim(1)
r1 = run_sim(2)
r0 / r1
11/15: r2 = run_sim(4)
11/16: r1 / r2
12/1: from math import sin, cos
12/2: sin(1.4)
12/3: cos(1.3)
12/4: cos(0)
12/5: cos(-1.3)
12/6: sin(-1.4)
12/7: cos(1.4)
13/1:
def top_flux(x):
return 1.1*cos(1.3*x)*cos(1.4)
13/2: face_coords = [-0.984375 , -0.953125 , -0.921875 , -0.890625 , -0.859375 , -0.828125 , -0.796875 , -0.765625 , -0.734375 , -0.703125 , -0.671875 , -0.640625 , -0.609375 , -0.578125 , -0.546875 , -0.515625 , -0.484375 , -0.453125 , -0.421875 , -0.390625 , -0.359375 , -0.328125 , -0.296875 , -0.265625 , -0.234375 , -0.203125 , -0.171875 , -0.140625 , -0.109375 , -0.078125 , -0.046875 , -0.015625 , 0.015625 , 0.046875 , 0.078125 , 0.109375 , 0.140625 , 0.171875 , 0.203125 , 0.234375 , 0.265625 , 0.296875 , 0.328125 , 0.359375 , 0.390625 , 0.421875 , 0.453125 , 0.484375 , 0.515625 , 0.546875 , 0.578125 , 0.609375 , 0.640625 , 0.671875 , 0.703125 , 0.734375 , 0.765625 , 0.796875 , 0.828125 , 0.859375 , 0.890625 , 0.921875 , 0.953125 , 0.984375]
13/3:
for coord in face_coords:
print(top_flux(coord))
13/4: from math import sin, cos
13/5:
for coord in face_coords:
print(top_flux(coord))
13/6:
def v(x, y):
return cos(1.3*x)*cos(1.4*y)
13/7: v(0.5, 1)
14/1: import numpy as np
14/2: import sympy as sp
14/3: def mmsf(x):
14/4:
def mmsf(x):
return -np.sin(x)
14/5:
def run_test(nx):
x = np.linspace(0, 1, nx)
14/6:
def run_test(nx):
x = np.linspace(0, 1, nx)
u = mmsf(x)
14/7: run_test(4)
14/8: x
14/9:
def run_test(nx):
x = np.linspace(0, 1, nx)
u = mmsf(x)
return x
14/10: x = run_test(4)
14/11: x
14/12:
class Elem():
def __init__(self, centroid):
self.centroid = centroid
14/13:
class FaceInfo:
def __init__(self, elem, neighbor=None):
self.elem = elem
self.neighbor = neighbor
14/14:
class Elem():
def __init__(self, left_node, right_node):
self.left_node = left_node
self.right_node = right_node
self.centroid = (left_node.x() + right_node.x()) / 2
14/15:
class Elem():
def __init__(self, left_node, right_node):
self.left_node = left_node
self.right_node = right_node
self.centroid = (left_node.x() + right_node.x()) / 2
def centroid(self):
return self.centroid
14/16:
class Node():
def __init__(self, x):
self.x = x
def x(self):
return self.x
15/1:
def ux(x, y):
return -sin(x)*cos(y)
15/2: from math import sin, cos
15/3:
def uy(x, y):
return cos(x)*sin(y)
15/4: ux(0.25)
15/5: ux(0.25, 0)
15/6: uy(0.25, 0)
15/7: ux(.25, .25)
15/8: uy(.25, .25)
15/9: ux(.125, .125)
15/10: uy(.125, .125)
15/11: ux(.375,.125)
15/12: uy(.375,.125)
15/13: ux(.625,.875)
15/14: uy(.625,.875)
15/15: .375 * 4
18/1:
from fipy.tools import numerix
from fipy.tools import inline
from fipy.variables.cellVariable import CellVariable
from fipy import *
class _FacesToCells(CellVariable):
r"""surface integral of `self.faceVariable`, :math:`\phi_f`
.. math:: \int_S \phi_f\,dS \approx \frac{\sum_f \phi_f A_f}{V_P}
Returns
-------
integral : CellVariable
volume-weighted sum
"""
def __init__(self, faceVariable, mesh = None):
if not mesh:
mesh = faceVariable.mesh
CellVariable.__init__(self, mesh, hasOld = 0, elementshape=faceVariable.shape[:-1])
self.faceVariable = self._requires(faceVariable)
def _calcValue(self):
if inline.doInline and self.faceVariable.rank < 2:
return self._calcValueInline()
else:
return self._calcValueNoInline()
def _calcValueInline(self):
NCells = self.mesh.numberOfCells
ids = self.mesh.cellFaceIDs
val = self._array.copy()
inline._runInline("""
int i;
for(i = 0; i < numberOfCells; i++)
{
int j;
value[i] = 0.;
float counter = 0;
for(j = 0; j < numberOfCellFaces; j++)
{
// cellFaceIDs can be masked, which caused subtle and
// unreproducible problems on OS X (who knows why not elsewhere)
long id = ids[i + j * numberOfCells];
if (id >= 0) {
value[i] += orientations[i + j * numberOfCells] * faceVariable[id];
counter += 1.'
}
}
value[i] = value[i] / counter;
}
""",
numberOfCellFaces = self.mesh._maxFacesPerCell,
numberOfCells = NCells,
faceVariable = self.faceVariable.numericValue,
ids = numerix.array(ids),
value = val,
orientations = numerix.array(self.mesh._cellToFaceOrientations),
cellVolume = numerix.array(self.mesh.cellVolumes))
return self._makeValue(value = val)
def _calcValueNoInline(self):
ids = self.mesh.cellFaceIDs
contributions = numerix.take(self.faceVariable, ids, axis=-1)
# FIXME: numerix.MA.filled casts away dimensions
s = (numerix.newaxis,) * (len(contributions.shape) - 2) + (slice(0, None, None),) + (slice(0, None, None),)
faceContributions = contributions
return numerix.tensordot(numerix.ones(faceContributions.shape[-2], 'd'),
numerix.MA.filled(faceContributions, 0.), (0, -2)) / self.mesh.cellFaceIDs.shape[0]
def custom_interpolation(variable, query_points):
f_int = interpolate.CloughTocher2DInterpolator(list(zip(variable.mesh.cellCenters.value[0],
variable.mesh.cellCenters.value[1])),
variable.value)
return f_int(query_points[0], query_points[1])
18/2:
import matplotlib.pyplot as plt
query_x = np.linspace(0., max(mesh.cellCenters[0]), 30)
query_y = query_x * 0 + 0.1
query_points = np.vstack([query_x, query_y])
new_p = custom_interpolation(pressure, query_points)
plt.plot(query_x, new_u)
plt.xlabel('x $[m]$')
plt.xlabel('u $[m/s]$')
plt.grid()
18/3:
from fipy import *
from fipy.variables.faceGradVariable import _FaceGradVariable
import numpy as np
D = 0.2
N = 20
dL = D / N
viscosity = 0.1
U = 1.0
Dp = 1000000.
#0.8 for pressure and 0.5 for velocity are typical relaxation values for SIMPLE
pressureRelaxation = 0.8
velocityRelaxation = 0.5
sweeps = 70
mesh = Grid2D(Lx=D*4, Ly=D, dx=dL, dy=dL)
pressure = CellVariable(mesh=mesh, name='pressure')
pressureCorrection = CellVariable(mesh=mesh)
xVelocity = CellVariable(mesh=mesh, name='X velocity')
yVelocity = CellVariable(mesh=mesh, name='Y velocity')
velocity = FaceVariable(mesh=mesh, rank=1)
porosity = CellVariable(mesh=mesh, value=0.0)
velocity_mag = (xVelocity**2 + yVelocity**2)**0.5
porosity[(mesh.x >= 0.4) & (mesh.x <= 0.6)] = 0.5
def apply_int(field, rec=1):
for i in range(rec):
field = _FacesToCells(field.arithmeticFaceValue)
return field
epsilon = 1 - porosity
darcy = 150*viscosity/Dp**2*(1-epsilon)**2/epsilon**3
fh = 1.75/Dp*(1-epsilon)/epsilon**3*velocity_mag
# note: we really don't care about the number of interpolations here
# since we are solving the pressure equation in the non-interpolated version
darcy_int = apply_int(darcy, rec=8)
fh_int = apply_int(fh, rec=8)
velocity = FaceVariable(mesh=mesh, rank=1)
xVelocityEq = -PowerLawConvectionTerm(coeff=velocity/(epsilon.arithmeticFaceValue**2)) + \
DiffusionTermCorrection(coeff=viscosity/epsilon) - \
pressure.grad.dot([1., 0.]) -\
ImplicitSourceTerm(coeff=darcy_int) -\
ImplicitSourceTerm(coeff=fh_int) +\
ImplicitSourceTerm(coeff=xVelocity*(epsilon.grad.dot([1.,0.]))/epsilon)
yVelocityEq = -PowerLawConvectionTerm(coeff=velocity/(epsilon.arithmeticFaceValue**2)) + \
DiffusionTermCorrection(coeff=viscosity/epsilon) - \
pressure.grad.dot([0., 1.]) -\
ImplicitSourceTerm(coeff=darcy_int) -\
ImplicitSourceTerm(coeff=fh_int) +\
ImplicitSourceTerm(coeff=yVelocity*(epsilon.grad.dot([0.,1.]))/epsilon) # (u u) \cdot \nabla \epsilon
apx = CellVariable(mesh=mesh, value=1.)
apy = CellVariable(mesh=mesh, value=1.)
bpx = CellVariable(mesh=mesh, value=1.)
bpy = CellVariable(mesh=mesh, value=1.)
ap_field = CellVariable(mesh=mesh, rank=1)
ap_field[0] = bpx/apx * mesh.cellVolumes
ap_field[1] = bpy/apy * mesh.cellVolumes
pressureCorrectionEq = DiffusionTermCorrection(coeff=ap_field) - velocity.divergence
volume = CellVariable(mesh=mesh, value=mesh.cellVolumes, name='Volume')
contrvolume=volume.arithmeticFaceValue
xVelocity.constrain(0., mesh.facesBottom| mesh.facesTop)
yVelocity.constrain(0., mesh.facesBottom| mesh.facesTop)
xVelocity.constrain(U, mesh.facesLeft)
yVelocity.constrain(0., mesh.facesLeft)
#pressureCorrection.faceGrad[0].constrain(viscosity*xVelocity.faceGrad, mesh.facesRight)
#X, Y = mesh.faceCenters
#pressureCorrection.constrain(0., mesh.facesRight)
#bcsPC = (FixedGradient(faces=mesh.facesRight, value=viscosity * (xVelocity.faceGrad.divergence).arithmeticFaceValue),)
#pressureCorrection.constrain(viscosity*xVelocity.faceGrad[0], mesh.facesRight)
pressureCorrection.constrain(velocity[0]*velocity[0]/2, mesh.facesRight)
for sweep in range(sweeps):
## solve the Stokes equations to get starred values
xVelocityEq.cacheMatrix(); xVelocityEq.cacheRHSvector()
xres = xVelocityEq.sweep(var=xVelocity, underRelaxation=velocityRelaxation)
xmat = xVelocityEq.matrix
xrhs = xVelocityEq.RHSvector
yVelocityEq.cacheMatrix(); xVelocityEq.cacheRHSvector()
yres = yVelocityEq.sweep(var=yVelocity, underRelaxation=velocityRelaxation)
ymat = yVelocityEq.matrix
yrhs = yVelocityEq.RHSvector
# Compute new body forces
body_force_x_int = (darcy_int + fh_int) * xVelocity * mesh.cellVolumes
body_force_y_int = (darcy_int + fh_int) * yVelocity * mesh.cellVolumes
body_force_x = (darcy + fh)*xVelocity * mesh.cellVolumes
body_force_y = (darcy + fh)*yVelocity * mesh.cellVolumes
body_force_x_int_rc = (body_force_x.arithmeticFaceValue/mesh._faceAreas).divergence*mesh.cellVolumes
body_force_y_int_rc = (body_force_y.arithmeticFaceValue/mesh._faceAreas).divergence*mesh.cellVolumes
## update the ap coefficient from the matrix diagonal
apx[:] = -numerix.asarray(xmat.takeDiagonal()) - body_force_x_int.value
apy[:] = -numerix.asarray(ymat.takeDiagonal()) - body_force_y_int.value
bpx[:] = 1/(1 + body_force_x.value/apx)
bpy[:] = 1/(1 + body_force_y.value/apx)
ap_field[0] = bpx/apx * mesh.cellVolumes
ap_field[1] = bpy/apy * mesh.cellVolumes
## update the face velocities based on starred values with the
## Rhie-Chow correction.
## cell pressure gradient
presgrad = pressure.grad
## face pressure gradient
facepresgrad = _FaceGradVariable(pressure)
# Computing modified RC terms
coef_dx = mesh.cellVolumes / apx
coef_dy = mesh.cellVolumes / apy
# Todo: not sure if the volume force correction should be done with the interpolated volume forces ot the non-inteprolated ones
velocity[0] = xVelocity.arithmeticFaceValue \
- bpx.arithmeticFaceValue*(coef_dx.arithmeticFaceValue * facepresgrad[0] - (coef_dx * presgrad[0]).arithmeticFaceValue) \
+ bpx.arithmeticFaceValue*(coef_dx.arithmeticFaceValue * body_force_x.arithmeticFaceValue - (coef_dx * body_force_x_int_rc).arithmeticFaceValue)
velocity[1] = yVelocity.arithmeticFaceValue \
- bpy.arithmeticFaceValue*(coef_dy.arithmeticFaceValue * facepresgrad[1] - (coef_dy * presgrad[1]).arithmeticFaceValue) \
+ bpy.arithmeticFaceValue*(coef_dy.arithmeticFaceValue * body_force_y.arithmeticFaceValue - (coef_dy * body_force_y_int_rc).arithmeticFaceValue)
velocity[..., mesh.facesBottom.value | mesh.facesTop.value] = 0.
velocity[0, mesh.facesLeft.value] = U
velocity[1, mesh.facesLeft.value] = 0
velocity[0] = xVelocity.arithmeticFaceValue \
+ contrvolume / apx.arithmeticFaceValue * \
(presgrad[0].arithmeticFaceValue-facepresgrad[0])\
+ contrvolume / apx.arithmeticFaceValue * \
(body_force_x.arithmeticFaceValue-body_force_x_int.arithmeticFaceValue)
velocity[1] = yVelocity.arithmeticFaceValue \
+ contrvolume / apy.arithmeticFaceValue * \
(presgrad[1].arithmeticFaceValue-facepresgrad[1])\
+ contrvolume / apx.arithmeticFaceValue * \
(body_force_y.arithmeticFaceValue-body_force_y_int.arithmeticFaceValue)
velocity[..., mesh.facesBottom.value | mesh.facesTop.value] = 0.
velocity[0, mesh.facesLeft.value] = U
velocity[1, mesh.facesLeft.value] = 0
## solve the pressure correction equation
pressureCorrectionEq.cacheRHSvector()
## left bottom point must remain at pressure 0, so no correction
pres = pressureCorrectionEq.sweep(var=pressureCorrection)
rhs = pressureCorrectionEq.RHSvector
## update the pressure using the corrected value
pressure.setValue(pressure + pressureRelaxation * pressureCorrection )
## update the velocity using the corrected pressure
xVelocity.setValue(xVelocity - pressureCorrection.grad[0] / \
apx * bpx * mesh.cellVolumes)
yVelocity.setValue(yVelocity - pressureCorrection.grad[1] / \
apy * bpy * mesh.cellVolumes)
if sweep%10 == 0:
print('sweep:', sweep, ', x residual:', xres, \
', y residual', yres, \
', p residual:', pres, \
', continuity:', max(abs(rhs)))
18/4:
import matplotlib.pyplot as plt
xc, yc = mesh.x.value, mesh.y.value
plt.figure(figsize=[8,2])
plt.tricontourf(xc, yc, xVelocity.value, 30)
plt.colorbar()
plt.title('X-Velocity')
plt.figure(figsize=[8,2])
plt.tricontourf(xc, yc, yVelocity.value, 30)
plt.colorbar()
plt.title('V-Velocity')
plt.figure(figsize=[8,2])
plt.tricontourf(xc, yc, xVelocity.value/epsilon, 30)
plt.colorbar()
plt.title('Porous X-Velocity')
plt.figure(figsize=[8,2])
plt.tricontourf(xc, yc, yVelocity.value/epsilon, 30)
plt.colorbar()
plt.title('Porous Y-Velocity')
plt.figure(figsize=[8,2])
plt.tricontourf(xc, yc, pressure.value, 30)
plt.colorbar()
plt.title('Pressure')
18/5:
import matplotlib.pyplot as plt
query_x = np.linspace(0., max(mesh.cellCenters[0]), 30)
query_y = query_x * 0 + 0.1
query_points = np.vstack([query_x, query_y])
new_u = custom_interpolation(xVelocity, query_points)
plt.plot(query_x, new_u)
plt.xlabel('x $[m]$')
plt.xlabel('u $[m/s]$')
plt.grid()
18/6:
from fipy import *
from fipy.variables.faceGradVariable import _FaceGradVariable
import numpy as np
from scipy import interpolate
D = 0.2
N = 20
dL = D / N
viscosity = 0.1
U = 1.0
Dp = 1000000.
#0.8 for pressure and 0.5 for velocity are typical relaxation values for SIMPLE
pressureRelaxation = 0.8
velocityRelaxation = 0.5
sweeps = 70
mesh = Grid2D(Lx=D*4, Ly=D, dx=dL, dy=dL)
pressure = CellVariable(mesh=mesh, name='pressure')
pressureCorrection = CellVariable(mesh=mesh)
xVelocity = CellVariable(mesh=mesh, name='X velocity')
yVelocity = CellVariable(mesh=mesh, name='Y velocity')
velocity = FaceVariable(mesh=mesh, rank=1)
porosity = CellVariable(mesh=mesh, value=0.0)
velocity_mag = (xVelocity**2 + yVelocity**2)**0.5
porosity[(mesh.x >= 0.4) & (mesh.x <= 0.6)] = 0.5
def apply_int(field, rec=1):
for i in range(rec):
field = _FacesToCells(field.arithmeticFaceValue)
return field
epsilon = 1 - porosity
darcy = 150*viscosity/Dp**2*(1-epsilon)**2/epsilon**3
fh = 1.75/Dp*(1-epsilon)/epsilon**3*velocity_mag
# note: we really don't care about the number of interpolations here
# since we are solving the pressure equation in the non-interpolated version
darcy_int = apply_int(darcy, rec=8)
fh_int = apply_int(fh, rec=8)
velocity = FaceVariable(mesh=mesh, rank=1)
xVelocityEq = -PowerLawConvectionTerm(coeff=velocity/(epsilon.arithmeticFaceValue**2)) + \
DiffusionTermCorrection(coeff=viscosity/epsilon) - \
pressure.grad.dot([1., 0.]) -\
ImplicitSourceTerm(coeff=darcy_int) -\
ImplicitSourceTerm(coeff=fh_int) +\
ImplicitSourceTerm(coeff=xVelocity*(epsilon.grad.dot([1.,0.]))/epsilon)
yVelocityEq = -PowerLawConvectionTerm(coeff=velocity/(epsilon.arithmeticFaceValue**2)) + \
DiffusionTermCorrection(coeff=viscosity/epsilon) - \
pressure.grad.dot([0., 1.]) -\
ImplicitSourceTerm(coeff=darcy_int) -\
ImplicitSourceTerm(coeff=fh_int) +\
ImplicitSourceTerm(coeff=yVelocity*(epsilon.grad.dot([0.,1.]))/epsilon) # (u u) \cdot \nabla \epsilon
apx = CellVariable(mesh=mesh, value=1.)
apy = CellVariable(mesh=mesh, value=1.)
bpx = CellVariable(mesh=mesh, value=1.)
bpy = CellVariable(mesh=mesh, value=1.)
ap_field = CellVariable(mesh=mesh, rank=1)
ap_field[0] = bpx/apx * mesh.cellVolumes
ap_field[1] = bpy/apy * mesh.cellVolumes
pressureCorrectionEq = DiffusionTermCorrection(coeff=ap_field) - velocity.divergence
volume = CellVariable(mesh=mesh, value=mesh.cellVolumes, name='Volume')
contrvolume=volume.arithmeticFaceValue
xVelocity.constrain(0., mesh.facesBottom| mesh.facesTop)
yVelocity.constrain(0., mesh.facesBottom| mesh.facesTop)
xVelocity.constrain(U, mesh.facesLeft)
yVelocity.constrain(0., mesh.facesLeft)
#pressureCorrection.faceGrad[0].constrain(viscosity*xVelocity.faceGrad, mesh.facesRight)
#X, Y = mesh.faceCenters
#pressureCorrection.constrain(0., mesh.facesRight)
#bcsPC = (FixedGradient(faces=mesh.facesRight, value=viscosity * (xVelocity.faceGrad.divergence).arithmeticFaceValue),)
#pressureCorrection.constrain(viscosity*xVelocity.faceGrad[0], mesh.facesRight)
pressureCorrection.constrain(velocity[0]*velocity[0]/2, mesh.facesRight)
for sweep in range(sweeps):
## solve the Stokes equations to get starred values
xVelocityEq.cacheMatrix(); xVelocityEq.cacheRHSvector()
xres = xVelocityEq.sweep(var=xVelocity, underRelaxation=velocityRelaxation)
xmat = xVelocityEq.matrix
xrhs = xVelocityEq.RHSvector
yVelocityEq.cacheMatrix(); xVelocityEq.cacheRHSvector()
yres = yVelocityEq.sweep(var=yVelocity, underRelaxation=velocityRelaxation)
ymat = yVelocityEq.matrix
yrhs = yVelocityEq.RHSvector
# Compute new body forces
body_force_x_int = (darcy_int + fh_int) * xVelocity * mesh.cellVolumes
body_force_y_int = (darcy_int + fh_int) * yVelocity * mesh.cellVolumes
body_force_x = (darcy + fh)*xVelocity * mesh.cellVolumes
body_force_y = (darcy + fh)*yVelocity * mesh.cellVolumes
body_force_x_int_rc = (body_force_x.arithmeticFaceValue/mesh._faceAreas).divergence*mesh.cellVolumes
body_force_y_int_rc = (body_force_y.arithmeticFaceValue/mesh._faceAreas).divergence*mesh.cellVolumes
## update the ap coefficient from the matrix diagonal
apx[:] = -numerix.asarray(xmat.takeDiagonal()) - body_force_x_int.value
apy[:] = -numerix.asarray(ymat.takeDiagonal()) - body_force_y_int.value
bpx[:] = 1/(1 + body_force_x.value/apx)
bpy[:] = 1/(1 + body_force_y.value/apx)
ap_field[0] = bpx/apx * mesh.cellVolumes
ap_field[1] = bpy/apy * mesh.cellVolumes
## update the face velocities based on starred values with the
## Rhie-Chow correction.
## cell pressure gradient
presgrad = pressure.grad
## face pressure gradient
facepresgrad = _FaceGradVariable(pressure)
# Computing modified RC terms
coef_dx = mesh.cellVolumes / apx
coef_dy = mesh.cellVolumes / apy
# Todo: not sure if the volume force correction should be done with the interpolated volume forces ot the non-inteprolated ones
velocity[0] = xVelocity.arithmeticFaceValue \
- bpx.arithmeticFaceValue*(coef_dx.arithmeticFaceValue * facepresgrad[0] - (coef_dx * presgrad[0]).arithmeticFaceValue) \
+ bpx.arithmeticFaceValue*(coef_dx.arithmeticFaceValue * body_force_x.arithmeticFaceValue - (coef_dx * body_force_x_int_rc).arithmeticFaceValue)
velocity[1] = yVelocity.arithmeticFaceValue \
- bpy.arithmeticFaceValue*(coef_dy.arithmeticFaceValue * facepresgrad[1] - (coef_dy * presgrad[1]).arithmeticFaceValue) \
+ bpy.arithmeticFaceValue*(coef_dy.arithmeticFaceValue * body_force_y.arithmeticFaceValue - (coef_dy * body_force_y_int_rc).arithmeticFaceValue)
velocity[..., mesh.facesBottom.value | mesh.facesTop.value] = 0.
velocity[0, mesh.facesLeft.value] = U
velocity[1, mesh.facesLeft.value] = 0
velocity[0] = xVelocity.arithmeticFaceValue \
+ contrvolume / apx.arithmeticFaceValue * \
(presgrad[0].arithmeticFaceValue-facepresgrad[0])\
+ contrvolume / apx.arithmeticFaceValue * \
(body_force_x.arithmeticFaceValue-body_force_x_int.arithmeticFaceValue)
velocity[1] = yVelocity.arithmeticFaceValue \
+ contrvolume / apy.arithmeticFaceValue * \
(presgrad[1].arithmeticFaceValue-facepresgrad[1])\
+ contrvolume / apx.arithmeticFaceValue * \
(body_force_y.arithmeticFaceValue-body_force_y_int.arithmeticFaceValue)
velocity[..., mesh.facesBottom.value | mesh.facesTop.value] = 0.
velocity[0, mesh.facesLeft.value] = U
velocity[1, mesh.facesLeft.value] = 0
## solve the pressure correction equation
pressureCorrectionEq.cacheRHSvector()
## left bottom point must remain at pressure 0, so no correction
pres = pressureCorrectionEq.sweep(var=pressureCorrection)
rhs = pressureCorrectionEq.RHSvector
## update the pressure using the corrected value
pressure.setValue(pressure + pressureRelaxation * pressureCorrection )
## update the velocity using the corrected pressure
xVelocity.setValue(xVelocity - pressureCorrection.grad[0] / \
apx * bpx * mesh.cellVolumes)
yVelocity.setValue(yVelocity - pressureCorrection.grad[1] / \
apy * bpy * mesh.cellVolumes)
if sweep%10 == 0:
print('sweep:', sweep, ', x residual:', xres, \
', y residual', yres, \
', p residual:', pres, \
', continuity:', max(abs(rhs)))
18/7:
import matplotlib.pyplot as plt
xc, yc = mesh.x.value, mesh.y.value
plt.figure(figsize=[8,2])
plt.tricontourf(xc, yc, xVelocity.value, 30)
plt.colorbar()
plt.title('X-Velocity')
plt.figure(figsize=[8,2])
plt.tricontourf(xc, yc, yVelocity.value, 30)
plt.colorbar()
plt.title('V-Velocity')
plt.figure(figsize=[8,2])
plt.tricontourf(xc, yc, xVelocity.value/epsilon, 30)
plt.colorbar()
plt.title('Porous X-Velocity')
plt.figure(figsize=[8,2])
plt.tricontourf(xc, yc, yVelocity.value/epsilon, 30)
plt.colorbar()
plt.title('Porous Y-Velocity')
plt.figure(figsize=[8,2])
plt.tricontourf(xc, yc, pressure.value, 30)
plt.colorbar()
plt.title('Pressure')
18/8:
import matplotlib.pyplot as plt
query_x = np.linspace(0., max(mesh.cellCenters[0]), 30)
query_y = query_x * 0 + 0.1
query_points = np.vstack([query_x, query_y])
new_u = custom_interpolation(xVelocity, query_points)
plt.plot(query_x, new_u)
plt.xlabel('x $[m]$')
plt.xlabel('u $[m/s]$')
plt.grid()
18/9:
import matplotlib.pyplot as plt
query_x = np.linspace(0., max(mesh.cellCenters[0]), 30)
query_y = query_x * 0 + 0.1
query_points = np.vstack([query_x, query_y])
new_p = custom_interpolation(pressure, query_points)
plt.plot(query_x, new_u)
plt.xlabel('x $[m]$')
plt.xlabel('u $[m/s]$')
plt.grid()
18/10:
import matplotlib.pyplot as plt
query_x = np.linspace(0., max(mesh.cellCenters[0]), 30)
query_y = query_x * 0 + 0.1
query_points = np.vstack([query_x, query_y])
new_p = custom_interpolation(pressure, query_points)
plt.plot(query_x, new_p)
plt.xlabel('x $[m]$')
plt.xlabel('u $[m/s]$')
plt.grid()
19/1:
from fipy.tools import numerix
from fipy.tools import inline
from fipy.variables.cellVariable import CellVariable
from fipy import *
class _FacesToCells(CellVariable):
r"""surface integral of `self.faceVariable`, :math:`\phi_f`
.. math:: \int_S \phi_f\,dS \approx \frac{\sum_f \phi_f A_f}{V_P}
Returns
-------
integral : CellVariable
volume-weighted sum
"""
def __init__(self, faceVariable, mesh = None):
if not mesh:
mesh = faceVariable.mesh
CellVariable.__init__(self, mesh, hasOld = 0, elementshape=faceVariable.shape[:-1])
self.faceVariable = self._requires(faceVariable)
def _calcValue(self):
if inline.doInline and self.faceVariable.rank < 2:
return self._calcValueInline()
else:
return self._calcValueNoInline()
def _calcValueInline(self):
NCells = self.mesh.numberOfCells
ids = self.mesh.cellFaceIDs
val = self._array.copy()
inline._runInline("""
int i;
for(i = 0; i < numberOfCells; i++)
{
int j;
value[i] = 0.;
float counter = 0;
for(j = 0; j < numberOfCellFaces; j++)
{
// cellFaceIDs can be masked, which caused subtle and
// unreproducible problems on OS X (who knows why not elsewhere)
long id = ids[i + j * numberOfCells];
if (id >= 0) {
value[i] += orientations[i + j * numberOfCells] * faceVariable[id];
counter += 1.'
}
}
value[i] = value[i] / counter;
}
""",
numberOfCellFaces = self.mesh._maxFacesPerCell,
numberOfCells = NCells,
faceVariable = self.faceVariable.numericValue,
ids = numerix.array(ids),
value = val,
orientations = numerix.array(self.mesh._cellToFaceOrientations),
cellVolume = numerix.array(self.mesh.cellVolumes))
return self._makeValue(value = val)
def _calcValueNoInline(self):
ids = self.mesh.cellFaceIDs
contributions = numerix.take(self.faceVariable, ids, axis=-1)
# FIXME: numerix.MA.filled casts away dimensions
s = (numerix.newaxis,) * (len(contributions.shape) - 2) + (slice(0, None, None),) + (slice(0, None, None),)
faceContributions = contributions
return numerix.tensordot(numerix.ones(faceContributions.shape[-2], 'd'),
numerix.MA.filled(faceContributions, 0.), (0, -2)) / self.mesh.cellFaceIDs.shape[0]
def custom_interpolation(variable, query_points):
f_int = interpolate.CloughTocher2DInterpolator(list(zip(variable.mesh.cellCenters.value[0],
variable.mesh.cellCenters.value[1])),
variable.value)
return f_int(query_points[0], query_points[1])
19/2:
from fipy import *
from fipy.variables.faceGradVariable import _FaceGradVariable
import numpy as np
from scipy import interpolate
D = 0.2
N = 20
dL = D / N
viscosity = 0.1
U = 1.0
Dp = 1000000.
#0.8 for pressure and 0.5 for velocity are typical relaxation values for SIMPLE
pressureRelaxation = 0.8
velocityRelaxation = 0.5
sweeps = 70
mesh = Grid2D(Lx=D*4, Ly=D, dx=dL, dy=dL)
pressure = CellVariable(mesh=mesh, name='pressure')
pressureCorrection = CellVariable(mesh=mesh)
xVelocity = CellVariable(mesh=mesh, name='X velocity')
yVelocity = CellVariable(mesh=mesh, name='Y velocity')
velocity = FaceVariable(mesh=mesh, rank=1)
porosity = CellVariable(mesh=mesh, value=0.0)
velocity_mag = (xVelocity**2 + yVelocity**2)**0.5
porosity[(mesh.x >= 0.4) & (mesh.x <= 0.6)] = 0.5
def apply_int(field, rec=1):
for i in range(rec):
field = _FacesToCells(field.arithmeticFaceValue)
return field
epsilon = 1 - porosity
darcy = 150*viscosity/Dp**2*(1-epsilon)**2/epsilon**3
fh = 1.75/Dp*(1-epsilon)/epsilon**3*velocity_mag
# note: we really don't care about the number of interpolations here
# since we are solving the pressure equation in the non-interpolated version
darcy_int = apply_int(darcy, rec=8)
fh_int = apply_int(fh, rec=8)
velocity = FaceVariable(mesh=mesh, rank=1)
xVelocityEq = -PowerLawConvectionTerm(coeff=velocity/(epsilon.arithmeticFaceValue**2)) + \
DiffusionTermCorrection(coeff=viscosity/epsilon) - \
pressure.grad.dot([1., 0.]) -\
ImplicitSourceTerm(coeff=darcy_int) -\
ImplicitSourceTerm(coeff=fh_int) +\
ImplicitSourceTerm(coeff=xVelocity*(epsilon.grad.dot([1.,0.]))/epsilon)
yVelocityEq = -PowerLawConvectionTerm(coeff=velocity/(epsilon.arithmeticFaceValue**2)) + \
DiffusionTermCorrection(coeff=viscosity/epsilon) - \
pressure.grad.dot([0., 1.]) -\
ImplicitSourceTerm(coeff=darcy_int) -\
ImplicitSourceTerm(coeff=fh_int) +\
ImplicitSourceTerm(coeff=yVelocity*(epsilon.grad.dot([0.,1.]))/epsilon) # (u u) \cdot \nabla \epsilon
apx = CellVariable(mesh=mesh, value=1.)
apy = CellVariable(mesh=mesh, value=1.)
bpx = CellVariable(mesh=mesh, value=1.)
bpy = CellVariable(mesh=mesh, value=1.)
ap_field = CellVariable(mesh=mesh, rank=1)
ap_field[0] = bpx/apx * mesh.cellVolumes
ap_field[1] = bpy/apy * mesh.cellVolumes
pressureCorrectionEq = DiffusionTermCorrection(coeff=ap_field) - velocity.divergence
volume = CellVariable(mesh=mesh, value=mesh.cellVolumes, name='Volume')
contrvolume=volume.arithmeticFaceValue
xVelocity.constrain(0., mesh.facesBottom| mesh.facesTop)
yVelocity.constrain(0., mesh.facesBottom| mesh.facesTop)
xVelocity.constrain(U, mesh.facesLeft)
yVelocity.constrain(0., mesh.facesLeft)
#pressureCorrection.faceGrad[0].constrain(viscosity*xVelocity.faceGrad, mesh.facesRight)
#X, Y = mesh.faceCenters
#pressureCorrection.constrain(0., mesh.facesRight)
#bcsPC = (FixedGradient(faces=mesh.facesRight, value=viscosity * (xVelocity.faceGrad.divergence).arithmeticFaceValue),)
#pressureCorrection.constrain(viscosity*xVelocity.faceGrad[0], mesh.facesRight)
pressureCorrection.constrain(velocity[0]*velocity[0]/2, mesh.facesRight)