def test_update_intensity(self, chan):
# check that setting surface intensity updates the intensity profile
chan.setup()
I = chan.intensities.numericValue
assert (I == 0).all()
chan.update_intensities(100)
assert numerix.allclose((100 * chan.attenuation_profile),
chan.intensities.numericValue)
def assertArrayWithinTolerance(self,
first,
second,
atol=1e-10,
rtol=1e-10,
msg=None):
"""Fail if the two objects are unequal by more than tol.
"""
if not numerix.allclose(first, second, rtol=rtol, atol=atol):
raise self.failureException(msg or '\n%s\nis not\n%s' %
(first, second))
def test_seed_normal(self, unit, loc, scale, coeff, error):
create = dict(value=3., unit=unit, hasOld=True)
name = 'MyVar'
seed = dict(profile='normal',
params=dict(loc=loc, scale=scale, coeff=coeff))
v = ModelVariable(name=name, create=create, seed=seed)
domain = SedimentDBLDomain()
v.domain = domain
if error:
with pytest.raises(error):
v.setup()
return
else:
v.setup()
from scipy.stats import norm
from fipy.tools import numerix
C = 1.0 / numerix.sqrt(2 * numerix.pi)
# loc and scale should be in units of the domain mesh
if hasattr(loc, 'unit'):
loc_ = loc.inUnitsOf(domain.depths.unit).value
else:
loc_ = loc
if hasattr(scale, 'unit'):
scale_ = scale.inUnitsOf(domain.depths.unit).value
else:
scale_ = scale
if unit:
coeff = PF(coeff, unit)
normrv = norm(loc=loc_, scale=C**2 * scale_)
val = coeff * normrv.pdf(domain.depths) * C * scale_
# from pprint import pprint
# pprint(zip(v.var, val))
print(type(val), type(v.var))
if unit:
# array comparison between variable & physicalfield is problematic
val = val.numericValue
assert numerix.allclose(v.var.numericValue, val)
def allclose(self, other, rtol=1.e-5, atol=1.e-8):
"""
>>> var = Variable((1, 1))
>>> print var.allclose((1, 1))
1
>>> print var.allclose((1,))
1
The following test is to check that the system does not run
out of memory.
>>> from fipy.tools import numerix
>>> var = Variable(numerix.ones(10000))
>>> print var.allclose(numerix.zeros(10000))
False
"""
operatorClass = Variable._OperatorVariableClass(self, baseClass=Variable)
return self._BinaryOperatorVariable(lambda a,b: numerix.allclose(a, b, atol=atol, rtol=rtol),
other,
operatorClass=operatorClass,
opShape=(),
canInline=False)
def _connectFaces(self, faces0, faces1):
"""
Merge faces on the same mesh. This is used to create periodic
meshes. The first list of faces, `faces1`, will be the faces
that are used to add to the matrix diagonals. The faces in
`faces2` will not be used. They aren't deleted but their
adjacent cells are made to point at `faces1`. The list
`faces2` are not altered, they still remain as members of
exterior faces.
>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> mesh = NonUniformGrid2D(nx = 2, ny = 2, dx = 1., dy = 1.)
>>> print((mesh.cellFaceIDs == [[0, 1, 2, 3],
... [7, 8, 10, 11],
... [2, 3, 4, 5],
... [6, 7, 9, 10]]).flatten().all()) # doctest: +PROCESSOR_0
True
>>> mesh._connectFaces(numerix.nonzero(mesh.facesLeft), numerix.nonzero(mesh.facesRight))
>>> print((mesh.cellFaceIDs == [[0, 1, 2, 3],
... [7, 6, 10, 9],
... [2, 3, 4, 5],
... [6, 7, 9, 10]]).flatten().all()) # doctest: +PROCESSOR_0
True
"""
## check for errors
## check that faces are members of exterior faces
from fipy.variables.faceVariable import FaceVariable
faces = FaceVariable(mesh=self, value=False)
faces[faces0] = True
faces[faces1] = True
assert (faces | self.exteriorFaces == self.exteriorFaces).all()
## following assert checks number of faces are equal, normals are opposite and areas are the same
assert numerix.allclose(numerix.take(self._areaProjections, faces0, axis=1),
numerix.take(-self._areaProjections, faces1, axis=1))
## extract the adjacent cells for both sets of faces
faceCellIDs0 = self.faceCellIDs[0]
faceCellIDs1 = self.faceCellIDs[1]
## set the new adjacent cells for `faces0`
MA.put(faceCellIDs1, faces0, MA.take(faceCellIDs0, faces0))
MA.put(faceCellIDs0, faces0, MA.take(faceCellIDs0, faces1))
self.faceCellIDs[0] = faceCellIDs0
self.faceCellIDs[1] = faceCellIDs1
## extract the face to cell distances for both sets of faces
faceToCellDistances0 = self._faceToCellDistances[0]
faceToCellDistances1 = self._faceToCellDistances[1]
## set the new faceToCellDistances for `faces0`
MA.put(faceToCellDistances1, faces0, MA.take(faceToCellDistances0, faces0))
MA.put(faceToCellDistances0, faces0, MA.take(faceToCellDistances0, faces1))
self._faceToCellDistances[0] = faceToCellDistances0
self._faceToCellDistances[1] = faceToCellDistances1
## calculate new cell distances and add them to faces0
numerix.put(self._cellDistances, faces0, MA.take(faceToCellDistances0 + faceToCellDistances1, faces0))
## change the direction of the face normals for faces0
for dim in range(self.dim):
faceNormals = self.faceNormals[dim].copy()
numerix.put(faceNormals, faces0, MA.take(faceNormals, faces1))
self.faceNormals[dim] = faceNormals
## Cells that are adjacent to faces1 are changed to point at faces0
## get the cells adjacent to faces1
faceCellIDs = MA.take(self.faceCellIDs[0], faces1)
## get all the adjacent faces for those particular cells
cellFaceIDs = numerix.take(self.cellFaceIDs, faceCellIDs, axis=1)
for i in range(cellFaceIDs.shape[0]):
## if the faces is a member of faces1 then change the face to point at
## faces0
cellFaceIDs[i] = MA.where(cellFaceIDs[i] == faces1,
faces0,
cellFaceIDs[i])
## add those faces back to the main self.cellFaceIDs
numerix.put(self.cellFaceIDs[i], faceCellIDs, cellFaceIDs[i])
## calculate new topology
self._setTopology()
## calculate new geometry
self._handleFaceConnection()
self.scale = self.scale['length']
def runLeveler(kLeveler=0.018,
bulkLevelerConcentration=0.02,
cellSize=0.1e-7,
rateConstant=0.00026,
initialAcceleratorCoverage=0.0,
levelerDiffusionCoefficient=5e-10,
numberOfSteps=400,
displayRate=10,
displayViewers=True):
kLevelerConsumption = 0.0005
aspectRatio = 1.5
faradaysConstant = 9.6485e4
gasConstant = 8.314
acceleratorDiffusionCoefficient = 4e-10
siteDensity = 6.35e-6
atomicVolume = 7.1e-6
charge = 2
metalDiffusionCoefficient = 4e-10
temperature = 298.
overpotential = -0.25
bulkMetalConcentration = 250.
bulkAcceleratorConcentration = 50.0e-3
initialLevelerCoverage = 0.
cflNumber = 0.2
numberOfCellsInNarrowBand = 20
cellsBelowTrench = 10
trenchDepth = 0.4e-6
trenchSpacing = 0.6e-6
boundaryLayerDepth = 98.7e-6
i0Suppressor = 0.3
i0Accelerator = 22.5
alphaSuppressor = 0.5
alphaAccelerator = 0.4
alphaAdsorption = 0.62
m = 4
b = 2.65
A = 0.3
Ba = -40
Bb = 60
Vd = 0.098
Bd = 0.0008
etaPrime = faradaysConstant * overpotential / gasConstant / temperature
from fipy import TrenchMesh
from fipy.tools import numerix
mesh = TrenchMesh(cellSize=cellSize,
trenchSpacing=trenchSpacing,
trenchDepth=trenchDepth,
boundaryLayerDepth=boundaryLayerDepth,
aspectRatio=aspectRatio,
angle=numerix.pi * 4. / 180.,
bowWidth=0.,
overBumpRadius=0.,
overBumpWidth=0.)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import DistanceVariable
distanceVar = DistanceVariable(name='distance variable',
mesh=mesh,
value=-1,
narrowBandWidth=narrowBandWidth)
distanceVar.setValue(1, where=mesh.getElectrolyteMask())
distanceVar.calcDistanceFunction(narrowBandWidth=1e10)
from fipy.models.levelSet.surfactant.surfactantVariable import SurfactantVariable
levelerVar = SurfactantVariable(name="leveler variable",
value=initialLevelerCoverage,
distanceVar=distanceVar)
acceleratorVar = SurfactantVariable(name="accelerator variable",
value=initialAcceleratorCoverage,
distanceVar=distanceVar)
from fipy.variables.cellVariable import CellVariable
bulkAcceleratorVar = CellVariable(name='bulk accelerator variable',
mesh=mesh,
value=bulkAcceleratorConcentration)
bulkLevelerVar = CellVariable(name='bulk leveler variable',
mesh=mesh,
value=bulkLevelerConcentration)
metalVar = CellVariable(name='metal variable',
mesh=mesh,
value=bulkMetalConcentration)
def depositionCoeff(alpha, i0):
expo = numerix.exp(-alpha * etaPrime)
return 2 * i0 * (expo - expo * numerix.exp(etaPrime))
coeffSuppressor = depositionCoeff(alphaSuppressor, i0Suppressor)
coeffAccelerator = depositionCoeff(alphaAccelerator, i0Accelerator)
exchangeCurrentDensity = acceleratorVar.getInterfaceVar() * (
coeffAccelerator - coeffSuppressor) + coeffSuppressor
currentDensity = metalVar / bulkMetalConcentration * exchangeCurrentDensity
depositionRateVariable = currentDensity * atomicVolume / charge / faradaysConstant
extensionVelocityVariable = CellVariable(name='extension velocity',
mesh=mesh,
value=depositionRateVariable)
from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \
import AdsorbingSurfactantEquation
kAccelerator = rateConstant * numerix.exp(-alphaAdsorption * etaPrime)
kAcceleratorConsumption = Bd + A / (numerix.exp(Ba *
(overpotential + Vd)) +
numerix.exp(Bb * (overpotential + Vd)))
q = m * overpotential + b
levelerSurfactantEquation = AdsorbingSurfactantEquation(
levelerVar,
distanceVar=distanceVar,
bulkVar=bulkLevelerVar,
rateConstant=kLeveler,
consumptionCoeff=kLevelerConsumption * depositionRateVariable)
accVar1 = acceleratorVar.getInterfaceVar()
accVar2 = (accVar1 > 0) * accVar1
accConsumptionCoeff = kAcceleratorConsumption * (accVar2**(q - 1))
acceleratorSurfactantEquation = AdsorbingSurfactantEquation(
acceleratorVar,
distanceVar=distanceVar,
bulkVar=bulkAcceleratorVar,
rateConstant=kAccelerator,
otherVar=levelerVar,
otherBulkVar=bulkLevelerVar,
otherRateConstant=kLeveler,
consumptionCoeff=accConsumptionCoeff)
from fipy.models.levelSet.advection.higherOrderAdvectionEquation \
import buildHigherOrderAdvectionEquation
advectionEquation = buildHigherOrderAdvectionEquation(
advectionCoeff=extensionVelocityVariable)
from fipy.boundaryConditions.fixedValue import FixedValue
from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \
import buildMetalIonDiffusionEquation
metalEquation = buildMetalIonDiffusionEquation(
ionVar=metalVar,
distanceVar=distanceVar,
depositionRate=depositionRateVariable,
diffusionCoeff=metalDiffusionCoefficient,
metalIonMolarVolume=atomicVolume)
metalEquationBCs = FixedValue(mesh.getTopFaces(), bulkMetalConcentration)
from fipy.models.levelSet.surfactant.surfactantBulkDiffusionEquation \
import buildSurfactantBulkDiffusionEquation
bulkAcceleratorEquation = buildSurfactantBulkDiffusionEquation(
bulkVar=bulkAcceleratorVar,
distanceVar=distanceVar,
surfactantVar=acceleratorVar,
otherSurfactantVar=levelerVar,
diffusionCoeff=acceleratorDiffusionCoefficient,
rateConstant=kAccelerator * siteDensity)
bulkAcceleratorEquationBCs = (FixedValue(mesh.getTopFaces(),
bulkAcceleratorConcentration), )
bulkLevelerEquation = buildSurfactantBulkDiffusionEquation(
bulkVar=bulkLevelerVar,
distanceVar=distanceVar,
surfactantVar=levelerVar,
diffusionCoeff=levelerDiffusionCoefficient,
rateConstant=kLeveler * siteDensity)
bulkLevelerEquationBCs = (FixedValue(mesh.getTopFaces(),
bulkLevelerConcentration), )
eqnTuple = ((advectionEquation, distanceVar,
()), (levelerSurfactantEquation, levelerVar,
()), (acceleratorSurfactantEquation, acceleratorVar,
()), (metalEquation, metalVar, metalEquationBCs),
(bulkAcceleratorEquation, bulkAcceleratorVar,
bulkAcceleratorEquationBCs),
(bulkLevelerEquation, bulkLevelerVar, bulkLevelerEquationBCs))
levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize /
cflNumber / 2)
totalTime = 0.0
if displayViewers:
from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer
viewers = (MayaviSurfactantViewer(distanceVar,
acceleratorVar.getInterfaceVar(),
zoomFactor=1e6,
limits={
'datamax': 0.5,
'datamin': 0.0
},
smooth=1,
title='accelerator coverage'),
MayaviSurfactantViewer(distanceVar,
levelerVar.getInterfaceVar(),
zoomFactor=1e6,
limits={
'datamax': 0.5,
'datamin': 0.0
},
smooth=1,
title='leveler coverage'))
for step in range(numberOfSteps):
if displayViewers:
if step % displayRate == 0:
for viewer in viewers:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction(deleteIslands=True)
extensionVelocityVariable.setValue(depositionRateVariable)
extOnInt = numerix.where(
distanceVar > 0,
numerix.where(distanceVar < 2 * cellSize,
extensionVelocityVariable, 0), 0)
dt = cflNumber * cellSize / numerix.max(extOnInt)
id = numerix.max(numerix.nonzero(distanceVar._getInterfaceFlag()))
distanceVar.extendVariable(extensionVelocityVariable,
deleteIslands=True)
extensionVelocityVariable[mesh.getFineMesh().getNumberOfCells():] = 0.
for eqn, var, BCs in eqnTuple:
var.updateOld()
for eqn, var, BCs in eqnTuple:
eqn.solve(var, boundaryConditions=BCs, dt=dt)
totalTime += dt
try:
testFile = 'testLeveler.gz'
import os
import examples.levelSet.electroChem
from fipy.tools import dump
data = dump.read(
os.path.join(examples.levelSet.electroChem.__path__[0], testFile))
N = mesh.getFineMesh().getNumberOfCells()
print numerix.allclose(data[:N], levelerVar[:N], rtol=1e-3)
except:
return 0
def runGold(faradaysConstant=9.6e4,
consumptionRateConstant=2.6e+6,
molarVolume=10.21e-6,
charge=1.0,
metalDiffusion=1.7e-9,
metalConcentration=20.0,
catalystCoverage=0.15,
currentDensity0=3e-2 * 16,
currentDensity1=6.5e-1 * 16,
cellSize=0.1e-7,
trenchDepth=0.2e-6,
aspectRatio=1.47,
trenchSpacing=0.5e-6,
boundaryLayerDepth=90.0e-6,
numberOfSteps=10,
taperAngle=6.0,
displayViewers=True):
cflNumber = 0.2
numberOfCellsInNarrowBand = 20
cellsBelowTrench = 10
from fipy.tools import numerix
from fipy import TrenchMesh
mesh = TrenchMesh(cellSize=cellSize,
trenchSpacing=trenchSpacing,
trenchDepth=trenchDepth,
boundaryLayerDepth=boundaryLayerDepth,
aspectRatio=aspectRatio,
angle=numerix.pi * taperAngle / 180.,
bowWidth=0.,
overBumpRadius=0.,
overBumpWidth=0.)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import DistanceVariable
distanceVar = DistanceVariable(name='distance variable',
mesh=mesh,
value=-1,
narrowBandWidth=narrowBandWidth)
distanceVar.setValue(1, where=mesh.getElectrolyteMask())
distanceVar.calcDistanceFunction(narrowBandWidth=1e10)
from fipy.models.levelSet.surfactant.surfactantVariable import SurfactantVariable
catalystVar = SurfactantVariable(name="catalyst variable",
value=catalystCoverage,
distanceVar=distanceVar)
from fipy.variables.cellVariable import CellVariable
metalVar = CellVariable(name='metal variable',
mesh=mesh,
value=metalConcentration)
exchangeCurrentDensity = currentDensity0 + currentDensity1 * catalystVar.getInterfaceVar(
)
currentDensity = metalVar / metalConcentration * exchangeCurrentDensity
depositionRateVariable = currentDensity * molarVolume / charge / faradaysConstant
extensionVelocityVariable = CellVariable(name='extension velocity',
mesh=mesh,
value=depositionRateVariable)
from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \
import AdsorbingSurfactantEquation
catalystSurfactantEquation = AdsorbingSurfactantEquation(
catalystVar,
distanceVar=distanceVar,
bulkVar=0,
rateConstant=0,
consumptionCoeff=consumptionRateConstant * extensionVelocityVariable)
from fipy.models.levelSet.advection.higherOrderAdvectionEquation \
import buildHigherOrderAdvectionEquation
advectionEquation = buildHigherOrderAdvectionEquation(
advectionCoeff=extensionVelocityVariable)
from fipy.boundaryConditions.fixedValue import FixedValue
from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \
import buildMetalIonDiffusionEquation
metalEquation = buildMetalIonDiffusionEquation(
ionVar=metalVar,
distanceVar=distanceVar,
depositionRate=depositionRateVariable,
diffusionCoeff=metalDiffusion,
metalIonMolarVolume=molarVolume)
metalEquationBCs = FixedValue(mesh.getTopFaces(), metalConcentration)
if displayViewers:
try:
from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer
viewers = (MayaviSurfactantViewer(distanceVar,
catalystVar.getInterfaceVar(),
zoomFactor=1e6,
limits={
'datamax': 1.0,
'datamin': 0.0
},
smooth=1,
title='catalyst coverage'), )
except:
class PlotVariable(CellVariable):
def __init__(self, var=None, name=''):
CellVariable.__init__(self,
mesh=mesh.getFineMesh(),
name=name)
self.var = self._requires(var)
def _calcValue(self):
return numerix.array(
self.var[:self.mesh.getNumberOfCells()])
from fipy.viewers import make
viewers = (make(PlotVariable(var=distanceVar),
limits={
'datamax': 1e-9,
'datamin': -1e-9
}),
make(PlotVariable(var=catalystVar.getInterfaceVar())))
else:
viewers = ()
levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize /
cflNumber / 2)
step = 0
while step < numberOfSteps:
if step % 10 == 0:
for viewer in viewers:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction(deleteIslands=True)
extensionVelocityVariable.setValue(
numerix.array(depositionRateVariable))
argmax = numerix.argmax(extensionVelocityVariable)
dt = cflNumber * cellSize / extensionVelocityVariable[argmax]
distanceVar.extendVariable(extensionVelocityVariable,
deleteIslands=True)
distanceVar.updateOld()
catalystVar.updateOld()
metalVar.updateOld()
advectionEquation.solve(distanceVar, dt=dt)
catalystSurfactantEquation.solve(catalystVar, dt=dt)
metalEquation.solve(metalVar,
boundaryConditions=metalEquationBCs,
dt=dt)
step += 1
try:
from fipy.tools import dump
import os
import examples.levelSet.electroChem
data = dump.read(
os.path.join(examples.levelSet.electroChem.__path__[0],
'goldData.gz'))
n = mesh.getFineMesh().getNumberOfCells()
print numerix.allclose(catalystVar[:n], data[:n], atol=1.0)
except:
return 0
def allclose(self, a, b, rtol=1.e-5, atol=1.e-8):
return numerix.allclose(a, b, rtol=rtol, atol=atol)
def runGold(faradaysConstant=9.6e4,
consumptionRateConstant=2.6e+6,
molarVolume=10.21e-6,
charge=1.0,
metalDiffusion=1.7e-9,
metalConcentration=20.0,
catalystCoverage=0.15,
currentDensity0=3e-2 * 16,
currentDensity1=6.5e-1 * 16,
cellSize=0.1e-7,
trenchDepth=0.2e-6,
aspectRatio=1.47,
trenchSpacing=0.5e-6,
boundaryLayerDepth=90.0e-6,
numberOfSteps=10,
taperAngle=6.0,
displayViewers=True):
cflNumber = 0.2
numberOfCellsInNarrowBand = 20
cellsBelowTrench = 10
from fipy.tools import numerix
from fipy import TrenchMesh
mesh = TrenchMesh(cellSize = cellSize,
trenchSpacing = trenchSpacing,
trenchDepth = trenchDepth,
boundaryLayerDepth = boundaryLayerDepth,
aspectRatio = aspectRatio,
angle = numerix.pi * taperAngle / 180.,
bowWidth = 0.,
overBumpRadius = 0.,
overBumpWidth = 0.)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import DistanceVariable
distanceVar = DistanceVariable(
name = 'distance variable',
mesh = mesh,
value = -1,
narrowBandWidth = narrowBandWidth)
distanceVar.setValue(1, where=mesh.getElectrolyteMask())
distanceVar.calcDistanceFunction(narrowBandWidth = 1e10)
from fipy.models.levelSet.surfactant.surfactantVariable import SurfactantVariable
catalystVar = SurfactantVariable(
name = "catalyst variable",
value = catalystCoverage,
distanceVar = distanceVar)
from fipy.variables.cellVariable import CellVariable
metalVar = CellVariable(
name = 'metal variable',
mesh = mesh,
value = metalConcentration)
exchangeCurrentDensity = currentDensity0 + currentDensity1 * catalystVar.getInterfaceVar()
currentDensity = metalVar / metalConcentration * exchangeCurrentDensity
depositionRateVariable = currentDensity * molarVolume / charge / faradaysConstant
extensionVelocityVariable = CellVariable(
name = 'extension velocity',
mesh = mesh,
value = depositionRateVariable)
from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \
import AdsorbingSurfactantEquation
catalystSurfactantEquation = AdsorbingSurfactantEquation(
catalystVar,
distanceVar = distanceVar,
bulkVar = 0,
rateConstant = 0,
consumptionCoeff = consumptionRateConstant * extensionVelocityVariable)
from fipy.models.levelSet.advection.higherOrderAdvectionEquation \
import buildHigherOrderAdvectionEquation
advectionEquation = buildHigherOrderAdvectionEquation(
advectionCoeff = extensionVelocityVariable)
from fipy.boundaryConditions.fixedValue import FixedValue
from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \
import buildMetalIonDiffusionEquation
metalEquation = buildMetalIonDiffusionEquation(
ionVar = metalVar,
distanceVar = distanceVar,
depositionRate = depositionRateVariable,
diffusionCoeff = metalDiffusion,
metalIonMolarVolume = molarVolume)
metalEquationBCs = FixedValue(mesh.getTopFaces(), metalConcentration)
if displayViewers:
try:
from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer
viewers = (
MayaviSurfactantViewer(distanceVar, catalystVar.getInterfaceVar(), zoomFactor = 1e6, limits = { 'datamax' : 1.0, 'datamin' : 0.0 }, smooth = 1, title = 'catalyst coverage'),)
except:
class PlotVariable(CellVariable):
def __init__(self, var = None, name = ''):
CellVariable.__init__(self, mesh = mesh.getFineMesh(), name = name)
self.var = self._requires(var)
def _calcValue(self):
return numerix.array(self.var[:self.mesh.getNumberOfCells()])
from fipy.viewers import make
viewers = (
make(PlotVariable(var = distanceVar), limits = {'datamax' : 1e-9, 'datamin' : -1e-9}),
make(PlotVariable(var = catalystVar.getInterfaceVar())))
else:
viewers = ()
levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize / cflNumber / 2)
step = 0
while step < numberOfSteps:
if step % 10 == 0:
for viewer in viewers:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction(deleteIslands = True)
extensionVelocityVariable.setValue(numerix.array(depositionRateVariable))
argmax = numerix.argmax(extensionVelocityVariable)
dt = cflNumber * cellSize / extensionVelocityVariable[argmax]
distanceVar.extendVariable(extensionVelocityVariable, deleteIslands = True)
distanceVar.updateOld()
catalystVar.updateOld()
metalVar.updateOld()
advectionEquation.solve(distanceVar, dt = dt)
catalystSurfactantEquation.solve(catalystVar, dt = dt)
metalEquation.solve(metalVar, boundaryConditions = metalEquationBCs, dt = dt)
step += 1
try:
from fipy.tools import dump
import os
import examples.levelSet.electroChem
data = dump.read(os.path.join(examples.levelSet.electroChem.__path__[0], 'goldData.gz'))
n = mesh.getFineMesh().getNumberOfCells()
print numerix.allclose(catalystVar[:n], data[:n], atol=1.0)
except:
return 0
def runLeveler(kLeveler=0.018, bulkLevelerConcentration=0.02, cellSize=0.1e-7, rateConstant=0.00026, initialAcceleratorCoverage=0.0, levelerDiffusionCoefficient=5e-10, numberOfSteps=400, displayRate=10, displayViewers=True):
kLevelerConsumption = 0.0005
aspectRatio = 1.5
faradaysConstant = 9.6485e4
gasConstant = 8.314
acceleratorDiffusionCoefficient = 4e-10
siteDensity = 6.35e-6
atomicVolume = 7.1e-6
charge = 2
metalDiffusionCoefficient = 4e-10
temperature = 298.
overpotential = -0.25
bulkMetalConcentration = 250.
bulkAcceleratorConcentration = 50.0e-3
initialLevelerCoverage = 0.
cflNumber = 0.2
numberOfCellsInNarrowBand = 20
cellsBelowTrench = 10
trenchDepth = 0.4e-6
trenchSpacing = 0.6e-6
boundaryLayerDepth = 98.7e-6
i0Suppressor = 0.3
i0Accelerator = 22.5
alphaSuppressor = 0.5
alphaAccelerator = 0.4
alphaAdsorption = 0.62
m = 4
b = 2.65
A = 0.3
Ba = -40
Bb = 60
Vd = 0.098
Bd = 0.0008
etaPrime = faradaysConstant * overpotential / gasConstant / temperature
from fipy import TrenchMesh
from fipy.tools import numerix
mesh = TrenchMesh(cellSize = cellSize,
trenchSpacing = trenchSpacing,
trenchDepth = trenchDepth,
boundaryLayerDepth = boundaryLayerDepth,
aspectRatio = aspectRatio,
angle = numerix.pi * 4. / 180.,
bowWidth = 0.,
overBumpRadius = 0.,
overBumpWidth = 0.)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import DistanceVariable
distanceVar = DistanceVariable(
name = 'distance variable',
mesh = mesh,
value = -1,
narrowBandWidth = narrowBandWidth)
distanceVar.setValue(1, where=mesh.getElectrolyteMask())
distanceVar.calcDistanceFunction(narrowBandWidth = 1e10)
from fipy.models.levelSet.surfactant.surfactantVariable import SurfactantVariable
levelerVar = SurfactantVariable(
name = "leveler variable",
value = initialLevelerCoverage,
distanceVar = distanceVar)
acceleratorVar = SurfactantVariable(
name = "accelerator variable",
value = initialAcceleratorCoverage,
distanceVar = distanceVar)
from fipy.variables.cellVariable import CellVariable
bulkAcceleratorVar = CellVariable(name = 'bulk accelerator variable',
mesh = mesh,
value = bulkAcceleratorConcentration)
bulkLevelerVar = CellVariable(
name = 'bulk leveler variable',
mesh = mesh,
value = bulkLevelerConcentration)
metalVar = CellVariable(
name = 'metal variable',
mesh = mesh,
value = bulkMetalConcentration)
def depositionCoeff(alpha, i0):
expo = numerix.exp(-alpha * etaPrime)
return 2 * i0 * (expo - expo * numerix.exp(etaPrime))
coeffSuppressor = depositionCoeff(alphaSuppressor, i0Suppressor)
coeffAccelerator = depositionCoeff(alphaAccelerator, i0Accelerator)
exchangeCurrentDensity = acceleratorVar.getInterfaceVar() * (coeffAccelerator - coeffSuppressor) + coeffSuppressor
currentDensity = metalVar / bulkMetalConcentration * exchangeCurrentDensity
depositionRateVariable = currentDensity * atomicVolume / charge / faradaysConstant
extensionVelocityVariable = CellVariable(
name = 'extension velocity',
mesh = mesh,
value = depositionRateVariable)
from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \
import AdsorbingSurfactantEquation
kAccelerator = rateConstant * numerix.exp(-alphaAdsorption * etaPrime)
kAcceleratorConsumption = Bd + A / (numerix.exp(Ba * (overpotential + Vd)) + numerix.exp(Bb * (overpotential + Vd)))
q = m * overpotential + b
levelerSurfactantEquation = AdsorbingSurfactantEquation(
levelerVar,
distanceVar = distanceVar,
bulkVar = bulkLevelerVar,
rateConstant = kLeveler,
consumptionCoeff = kLevelerConsumption * depositionRateVariable)
accVar1 = acceleratorVar.getInterfaceVar()
accVar2 = (accVar1 > 0) * accVar1
accConsumptionCoeff = kAcceleratorConsumption * (accVar2**(q - 1))
acceleratorSurfactantEquation = AdsorbingSurfactantEquation(
acceleratorVar,
distanceVar = distanceVar,
bulkVar = bulkAcceleratorVar,
rateConstant = kAccelerator,
otherVar = levelerVar,
otherBulkVar = bulkLevelerVar,
otherRateConstant = kLeveler,
consumptionCoeff = accConsumptionCoeff)
from fipy.models.levelSet.advection.higherOrderAdvectionEquation \
import buildHigherOrderAdvectionEquation
advectionEquation = buildHigherOrderAdvectionEquation(
advectionCoeff = extensionVelocityVariable)
from fipy.boundaryConditions.fixedValue import FixedValue
from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \
import buildMetalIonDiffusionEquation
metalEquation = buildMetalIonDiffusionEquation(
ionVar = metalVar,
distanceVar = distanceVar,
depositionRate = depositionRateVariable,
diffusionCoeff = metalDiffusionCoefficient,
metalIonMolarVolume = atomicVolume)
metalEquationBCs = FixedValue(mesh.getTopFaces(), bulkMetalConcentration)
from fipy.models.levelSet.surfactant.surfactantBulkDiffusionEquation \
import buildSurfactantBulkDiffusionEquation
bulkAcceleratorEquation = buildSurfactantBulkDiffusionEquation(
bulkVar = bulkAcceleratorVar,
distanceVar = distanceVar,
surfactantVar = acceleratorVar,
otherSurfactantVar = levelerVar,
diffusionCoeff = acceleratorDiffusionCoefficient,
rateConstant = kAccelerator * siteDensity)
bulkAcceleratorEquationBCs = (FixedValue(
mesh.getTopFaces(),
bulkAcceleratorConcentration),)
bulkLevelerEquation = buildSurfactantBulkDiffusionEquation(
bulkVar = bulkLevelerVar,
distanceVar = distanceVar,
surfactantVar = levelerVar,
diffusionCoeff = levelerDiffusionCoefficient,
rateConstant = kLeveler * siteDensity)
bulkLevelerEquationBCs = (FixedValue(
mesh.getTopFaces(),
bulkLevelerConcentration),)
eqnTuple = ( (advectionEquation, distanceVar, ()),
(levelerSurfactantEquation, levelerVar, ()),
(acceleratorSurfactantEquation, acceleratorVar, ()),
(metalEquation, metalVar, metalEquationBCs),
(bulkAcceleratorEquation, bulkAcceleratorVar, bulkAcceleratorEquationBCs),
(bulkLevelerEquation, bulkLevelerVar, bulkLevelerEquationBCs))
levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize / cflNumber / 2)
totalTime = 0.0
if displayViewers:
from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer
viewers = (
MayaviSurfactantViewer(distanceVar, acceleratorVar.getInterfaceVar(), zoomFactor = 1e6, limits = { 'datamax' : 0.5, 'datamin' : 0.0 }, smooth = 1, title = 'accelerator coverage'),
MayaviSurfactantViewer(distanceVar, levelerVar.getInterfaceVar(), zoomFactor = 1e6, limits = { 'datamax' : 0.5, 'datamin' : 0.0 }, smooth = 1, title = 'leveler coverage'))
for step in range(numberOfSteps):
if displayViewers:
if step % displayRate == 0:
for viewer in viewers:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction(deleteIslands = True)
extensionVelocityVariable.setValue(depositionRateVariable)
extOnInt = numerix.where(distanceVar > 0,
numerix.where(distanceVar < 2 * cellSize,
extensionVelocityVariable,
0),
0)
dt = cflNumber * cellSize / numerix.max(extOnInt)
id = numerix.max(numerix.nonzero(distanceVar._getInterfaceFlag()))
distanceVar.extendVariable(extensionVelocityVariable, deleteIslands = True)
extensionVelocityVariable[mesh.getFineMesh().getNumberOfCells():] = 0.
for eqn, var, BCs in eqnTuple:
var.updateOld()
for eqn, var, BCs in eqnTuple:
eqn.solve(var, boundaryConditions = BCs, dt = dt)
totalTime += dt
try:
testFile = 'testLeveler.gz'
import os
import examples.levelSet.electroChem
from fipy.tools import dump
data = dump.read(os.path.join(examples.levelSet.electroChem.__path__[0], testFile))
N = mesh.getFineMesh().getNumberOfCells()
print numerix.allclose(data[:N], levelerVar[:N], rtol = 1e-3)
except:
return 0
def assertArrayWithinTolerance(self, first, second, atol = 1e-10, rtol = 1e-10, msg=None): """Fail if the two objects are unequal by more than tol. """ if not numerix.allclose(first, second, rtol = rtol, atol = atol): raise self.failureException, (msg or '\n%s\nis not\n%s' % (first, second))
def relative_error(a, b):
if np.allclose(b.numericValue, 0):
return PhysicalField(0.0, '')
else:
return PhysicalField((a - b) / a, '')
def _connectFaces(self, faces0, faces1):
"""
Merge faces on the same mesh. This is used to create periodic
meshes. The first list of faces, `faces1`, will be the faces
that are used to add to the matrix diagonals. The faces in
`faces2` will not be used. They aren't deleted but their
adjacent cells are made to point at `faces1`. The list
`faces2` are not altered, they still remain as members of
exterior faces.
>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> mesh = NonUniformGrid2D(nx = 2, ny = 2, dx = 1., dy = 1.)
>>> print((mesh.cellFaceIDs == [[0, 1, 2, 3],
... [7, 8, 10, 11],
... [2, 3, 4, 5],
... [6, 7, 9, 10]]).flatten().all()) # doctest: +PROCESSOR_0
True
>>> mesh._connectFaces(numerix.nonzero(mesh.facesLeft), numerix.nonzero(mesh.facesRight))
>>> print((mesh.cellFaceIDs == [[0, 1, 2, 3],
... [7, 6, 10, 9],
... [2, 3, 4, 5],
... [6, 7, 9, 10]]).flatten().all()) # doctest: +PROCESSOR_0
True
"""
## check for errors
## check that faces are members of exterior faces
from fipy.variables.faceVariable import FaceVariable
faces = FaceVariable(mesh=self, value=False)
faces[faces0] = True
faces[faces1] = True
assert (faces | self.exteriorFaces == self.exteriorFaces).all()
## following assert checks number of faces are equal, normals are opposite and areas are the same
assert numerix.allclose(numerix.take(self._areaProjections, faces0, axis=1),
numerix.take(-self._areaProjections, faces1, axis=1))
## extract the adjacent cells for both sets of faces
faceCellIDs0 = self.faceCellIDs[0]
faceCellIDs1 = self.faceCellIDs[1]
## set the new adjacent cells for `faces0`
MA.put(faceCellIDs1, faces0, MA.take(faceCellIDs0, faces0))
MA.put(faceCellIDs0, faces0, MA.take(faceCellIDs0, faces1))
self.faceCellIDs[0] = faceCellIDs0
self.faceCellIDs[1] = faceCellIDs1
## extract the face to cell distances for both sets of faces
faceToCellDistances0 = self._faceToCellDistances[0]
faceToCellDistances1 = self._faceToCellDistances[1]
## set the new faceToCellDistances for `faces0`
MA.put(faceToCellDistances1, faces0, MA.take(faceToCellDistances0, faces0))
MA.put(faceToCellDistances0, faces0, MA.take(faceToCellDistances0, faces1))
self._faceToCellDistances[0] = faceToCellDistances0
self._faceToCellDistances[1] = faceToCellDistances1
## calculate new cell distances and add them to faces0
numerix.put(self._cellDistances, faces0, MA.take(faceToCellDistances0 + faceToCellDistances1, faces0))
## change the direction of the face normals for faces0
for dim in range(self.dim):
faceNormals = self.faceNormals[dim].copy()
numerix.put(faceNormals, faces0, MA.take(faceNormals, faces1))
self.faceNormals[dim] = faceNormals
## Cells that are adjacent to faces1 are changed to point at faces0
## get the cells adjacent to faces1
faceCellIDs = MA.take(self.faceCellIDs[0], faces1)
## get all the adjacent faces for those particular cells
cellFaceIDs = numerix.take(self.cellFaceIDs, faceCellIDs, axis=1)
for i in range(cellFaceIDs.shape[0]):
## if the faces is a member of faces1 then change the face to point at
## faces0
cellFaceIDs[i] = MA.where(cellFaceIDs[i] == faces1,
faces0,
cellFaceIDs[i])
## add those faces back to the main self.cellFaceIDs
numerix.put(self.cellFaceIDs[i], faceCellIDs, cellFaceIDs[i])
## calculate new topology
self._setTopology()
## calculate new geometry
self._handleFaceConnection()
self.scale = self.scale['length']
def allclose(self, a, b, rtol=1.e-5, atol=1.e-8):
return self.mpi4py_comm.allreduce(numerix.allclose(a,
b,
rtol=rtol,
atol=atol),
op=MPI.LAND)
def allclose(self, a, b, rtol=1.e-5, atol=1.e-8):
return self.mpi4py_comm.allreduce(numerix.allclose(a, b, rtol=rtol, atol=atol), op=self.MPI.LAND)
def allclose(self, a, b, rtol=1.e-5, atol=1.e-8):
return numerix.allclose(a, b, rtol=rtol, atol=atol)
def allcloseParallel(a, b):
return MPI.COMM_WORLD.allreduce(numerix.allclose(a, b, rtol=rtol, atol=atol), op=MPI.LAND)
