def _getDerivative(self, order):
newOrder = self.order - order
if newOrder not in self.derivative:
if newOrder > 1:
self.derivative[newOrder] = NthOrderBoundaryCondition(self.faces, self.value, newOrder)
elif newOrder == 1:
self.derivative[newOrder] = FixedFlux(self.faces, self.value)
elif newOrder == 0:
self.derivative[newOrder] = FixedValue(self.faces, self.value)
else:
self.derivative[newOrder] = None
return self.derivative[newOrder]
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
valueLeft = 0.
valueRight = 1.
import examples.diffusion.steadyState.mesh20x20
import os.path
mesh = GmshImporter2D(
os.path.join(examples.diffusion.steadyState.mesh20x20.__path__[0],
'modifiedMesh.msh'))
## "%s/%s" % (sys.__dict__['path'][0], "examples/diffusion/steadyState/mesh20x20/modifiedMesh.msh"))
var = CellVariable(name="solution variable", mesh=mesh, value=valueLeft)
exteriorFaces = mesh.getExteriorFaces()
xFace = exteriorFaces.getCenters()[..., 0]
boundaryConditions = (FixedValue(
exteriorFaces.where(xFace**2 < 0.000000000000001), valueLeft),
FixedValue(
exteriorFaces.where(
(xFace - 20)**2 < 0.000000000000001),
valueRight))
if __name__ == '__main__':
ImplicitDiffusionTerm().solve(var, boundaryConditions=boundaryConditions)
viewer = fipy.viewers.make(vars=var)
viewer.plot()
varArray = numerix.array(var)
x = mesh.getCellCenters()[:, 0]
analyticalArray = valueLeft + (valueRight - valueLeft) * x / 20
errorArray = varArray - analyticalArray
errorVar = CellVariable(name="absolute error",
mesh=mesh,
#Laplacian=0
nx = 50
dx = 1.
from fipy.meshes.grid1D import Grid1D
mesh = Grid1D(nx=nx, dx=dx)
from fipy.variables.cellVariable import CellVariable
phi = CellVariable(name="solution variable", mesh=mesh, value=0)
z = CellVariable(name="dummy", mesh=mesh, value=0)
valueLeft = 1
valueRight = 0
from fipy.boundaryConditions.fixedValue import FixedValue
BCs = (FixedValue(faces=mesh.getFacesRight(), value=valueRight),
FixedValue(faces=mesh.getFacesLeft(), value=valueLeft))
from fipy.terms.explicitDiffusionTerm import ExplicitDiffusionTerm
eqX = ExplicitDiffusionTerm(coeff=1)
from fipy import viewers
viewer = viewers.make(vars=(phi), limits={'datamin': 0., 'datamax': 1.})
viewer.plot()
eqX.solve(var=phi, boundaryConditions=BCs)
viewer.plot()
velocity = -1.
timeStepDuration = cfl * dx / abs(velocity)
steps = 1000
mesh = Grid1D(dx = dx, nx = nx)
startingArray = numerix.zeros(nx, 'd')
startingArray[50:90] = 1.
var = CellVariable(
name = "advection variable",
mesh = mesh,
value = startingArray)
boundaryConditions = (
FixedValue(mesh.getFacesLeft(), valueLeft),
FixedValue(mesh.getFacesRight(), valueRight)
)
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.explicitUpwindConvectionTerm import ExplicitUpwindConvectionTerm
eq = TransientTerm() - ExplicitUpwindConvectionTerm(coeff = (velocity,))
if __name__ == '__main__':
viewer = fipy.viewers.make(vars=(var,))
for step in range(steps):
eq.solve(var,
dt = timeStepDuration,
boundaryConditions = boundaryConditions,
u=psi.getGrad().dot(Yhat)
v=-psi.getGrad().dot(Xhat)
U=psi.getFaceGrad()
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
eq=ImplicitDiffusionTerm(0.00001) \
+ u * u.getGrad().dot(Xhat) \
+ v * u.getGrad().dot(Yhat) \
- 2 * u.getGrad().dot(Yhat).getGrad().dot(Yhat)
from fipy.boundaryConditions.nthOrderBoundaryCondition import NthOrderBoundaryCondition
from fipy.boundaryConditions.fixedValue import FixedValue
BC = (NthOrderBoundaryCondition(faces=mesh.getFacesBottom(), value=0,order=1),
FixedValue(faces=mesh.getFacesBottom(), value=0),
NthOrderBoundaryCondition(faces=mesh.getFacesLeft(), value=0,order=1),
NthOrderBoundaryCondition(faces=mesh.getFacesTop(), value=1,order=1),
NthOrderBoundaryCondition(faces=mesh.getFacesTop(), value=0,order=2))
from fipy.boundaryConditions.fixedFlux import FixedFlux
BC = (FixedFlux(faces=mesh.getFacesBottom(), value=0),
FixedValue(faces=mesh.getFacesBottom(), value=0),
FixedValue(faces=mesh.getFacesTop(), value=1),
FixedFlux(faces=mesh.getFacesTop(), value=1),
FixedFlux(faces=mesh.getFacesLeft(), value=0))
##viewer1 = Grid3DPyxViewer(var, zvalue = 1.0)
##viewer3 = Grid3DPyxViewer(var, zvalue = 3.0)
##viewer5 = Grid3DPyxViewer(var, zvalue = 5.0)
##viewer7 = Grid3DPyxViewer(var, zvalue = 7.0)
##viewer9 = Grid3DPyxViewer(var, zvalue = 9.0)
## from fipy import viewers
## viewer = viewers.make(vars = var)
## viewer.plot()
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
ImplicitDiffusionTerm().solve(var,
boundaryConditions=(
FixedValue(mesh.getFacesLeft(), valueSides),
FixedValue(mesh.getFacesRight(), valueSides),
FixedValue(mesh.getFacesTop(), valueSides),
FixedValue(mesh.getFacesBottom(),
valueSides),
FixedValue(mesh.getFacesFront(), valueFront),
FixedValue(mesh.getFacesBack(), valueBack),
))
## viewer.plot()
if __name__ == '__main__':
##viewer1.plot(resolution = 0.2, xlabel = "X values (Z value = 1)", minval = valueFront, maxval = valueBack)
##raw_input("press enter to continue")
##viewer3.plot(resolution = 0.2, xlabel = "X values (Z value = 3)", minval = valueFront, maxval = valueBack)
##raw_input("press enter to continue")
from fipy.models.levelSet.surfactant.surfactantBulkDiffusionEquation \
import buildSurfactantBulkDiffusionEquation
bulkCatalystEquation = buildSurfactantBulkDiffusionEquation(
bulkVar=bulkCatalystVar,
distanceVar=distanceVar,
surfactantVar=catalystVar,
diffusionCoeff=catalystDiffusion,
rateConstant=rateConstant0 * siteDensity)
bench.stop('terms')
bench.start()
from fipy.boundaryConditions.fixedValue import FixedValue
metalEquationBCs = (FixedValue(mesh.getFacesTop(),
bulkMetalConcentration), )
catalystBCs = (FixedValue(mesh.getFacesTop(), catalystConcentration), )
bench.stop('BCs')
levelSetUpdateFrequency = int(0.8 * narrowBandWidth \
/ (cellSize * cflNumber * 2))
step = 0
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction()
extensionVelocityVariable.setValue(depositionRateVariable())
diffTerm = ImplicitDiffusionTerm(coeff=viscosity)
from fipy.terms.exponentialConvectionTerm import ExponentialConvectionTerm
convTerm = ExponentialConvectionTerm(coeff=velocity, diffusionTerm=diffTerm)
eq1 = diffTerm - u * u.getGrad().dot(Xhat) - v * u.getGrad().dot(Yhat)
eq2 = velocity.getDivergence()
#eq2= u.getGrad() + v.getGrad()
eq2 = u.getFaceGrad().dot(Xhat) * Xhat + v.getFaceGrad().dot(Yhat) * Yhat
eq2 = u.getGrad().dot(Xhat) + v.getGrad().dot(Yhat)
eq2 = ImplicitDiffusionTerm(1) + u.getGrad().dot(Xhat) + v.getGrad().dot(Yhat)
from fipy.boundaryConditions.fixedValue import FixedValue
BCu = (FixedValue(faces=mesh.getFacesBottom(),
value=0), FixedValue(faces=mesh.getFacesLeft(), value=1))
BCv = (FixedValue(faces=mesh.getFacesBottom(),
value=0), FixedValue(faces=mesh.getFacesLeft(), value=0))
from fipy import viewers
viewer = viewers.make(vars=(u, v), limits={'datamin': 0., 'datamax': 1.})
def hit_continue(Prompt='Hit any key to continue'):
raw_input(Prompt)
steps = 10
for step in range(steps):
if ((leftSide(face) or inMiddle(face) or rightSide(face))
or not (face.getID() in bigMesh.getExteriorFaces())):
return 0
else:
return 1
var = CellVariable(name="concentration", mesh=bigMesh, value=valueLeft)
eqn = TransientTerm() == ExplicitDiffusionTerm()
exteriorFaces = bigMesh.getExteriorFaces()
xFace = exteriorFaces.getCenters()[..., 0]
boundaryConditions = (
FixedValue(exteriorFaces.where(xFace**2 < 0.000000000000001), valueLeft),
FixedValue(exteriorFaces.where((xFace - (dx * nx))**2 < 0.000000000000001),
(valueLeft + valueRight) * 0.5),
FixedValue(
exteriorFaces.where((xFace - (2 * dx * nx))**2 < 0.000000000000001),
valueRight))
answer = numerix.array([
0.00000000e+00, 8.78906250e-23, 1.54057617e-19, 1.19644866e-16,
5.39556276e-14, 1.55308505e-11, 2.94461712e-09, 3.63798469e-07,
2.74326174e-05, 1.01935828e-03, 9.76562500e-24, 1.92578125e-20,
1.70937109e-17, 8.99433979e-15, 3.10726059e-12, 7.36603377e-10,
1.21397338e-07, 1.37456643e-05, 1.02532568e-03, 4.57589878e-02,
2.63278194e-07, 5.70863224e-12, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 1.51165440e-13, 1.23805218e-07,
1.51873310e-03, 5.87457842e-01, 3.78270971e-06, 2.41898556e-10,
nx = 10
ny = 5
nz = 3
dx = 1.
dy = 1.
dz = 1.
valueBottomTop = 0.
valueLeftRight = 1.
mesh = Grid3D(dx=dx, dy=dy, dz=dz, nx=nx, ny=ny, nz=nz)
var = CellVariable(name="solution variable", mesh=mesh, value=valueBottomTop)
boundaryConditions = (FixedValue(mesh.getFacesLeft(), valueLeftRight),
FixedValue(mesh.getFacesRight(), valueLeftRight),
FixedValue(mesh.getFacesTop(), valueBottomTop),
FixedValue(mesh.getFacesBottom(), valueBottomTop))
#do the 2D problem for comparison
nx = 10
ny = 5
dx = 1.
dy = 1.
mesh2 = Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
var2 = CellVariable(name="solution variable 2D",
from fipy.meshes.grid2D import Grid2D
mesh = Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
from fipy.variables.cellVariable import CellVariable
phi = CellVariable(name = "solution variable",mesh = mesh,value = 0)
D = 1.
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
eq = ImplicitDiffusionTerm(coeff=D)
valueLeft = 1
valueRight = 0
from fipy.boundaryConditions.fixedValue import FixedValue
BCs = (FixedValue(faces=mesh.getFacesLeft(),value=0),
FixedValue(faces=mesh.getFacesRight(),value=1),
FixedValue(faces=mesh.getFacesTop(),value=0),
FixedValue(faces=mesh.getFacesBottom(),value=0))
from fipy import viewers
viewer = viewers.make(vars=phi,
limits={'datamin': 0., 'datamax': 1.})
viewer.plot()
timeStepDuration = 10 * 0.9 * dx**2 / (2 * D)
steps = 10
eq.solve(var=phi,boundaryConditions=BCs)
distanceVar = DistanceVariable(mesh=mesh, value=value, hasOld=1)
## Build the bulk diffusion equation
bulkVar = CellVariable(mesh=mesh, value=cinf)
surfactantVar = SurfactantVariable(distanceVar=distanceVar)
bulkEqn = buildSurfactantBulkDiffusionEquation(bulkVar,
distanceVar=distanceVar,
surfactantVar=surfactantVar,
diffusionCoeff=diffusion,
rateConstant=rateConstant *
siteDensity)
bcs = (FixedValue(mesh.getFacesRight(), cinf), )
## Build the surfactant equation
surfEqn = AdsorbingSurfactantEquation(surfactantVar=surfactantVar,
distanceVar=distanceVar,
bulkVar=bulkVar,
rateConstant=rateConstant)
## Build the analytical solutions,
x = mesh.getCellCenters()[1:, 0] - dx
def concentrationFunc(theta):
tmp = (1 + rateConstant * siteDensity * (1 - theta) * L / diffusion)
def _getDerivative(self, order):
if order == 1:
return FixedValue(self.faces, self.value)
else:
return BoundaryCondition._getDerivative(self, order)
def runSimpleTrenchSystem(faradaysConstant=9.6e4,
gasConstant=8.314,
transferCoefficient=0.5,
rateConstant0=1.76,
rateConstant3=-245e-6,
catalystDiffusion=1e-9,
siteDensity=9.8e-6,
molarVolume=7.1e-6,
charge=2,
metalDiffusion=5.6e-10,
temperature=298.,
overpotential=-0.3,
metalConcentration=250.,
catalystConcentration=5e-3,
catalystCoverage=0.,
currentDensity0=0.26,
currentDensity1=45.,
cellSize=0.1e-7,
trenchDepth=0.5e-6,
aspectRatio=2.,
trenchSpacing=0.6e-6,
boundaryLayerDepth=0.3e-6,
numberOfSteps=5,
displayViewers=True):
cflNumber = 0.2
numberOfCellsInNarrowBand = 10
cellsBelowTrench = 10
yCells = cellsBelowTrench \
+ int((trenchDepth + boundaryLayerDepth) / cellSize)
xCells = int(trenchSpacing / 2 / cellSize)
from fipy.meshes.grid2D import Grid2D
mesh = Grid2D(dx=cellSize, dy=cellSize, nx=xCells, ny=yCells)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import \
DistanceVariable
distanceVar = DistanceVariable(name='distance variable',
mesh=mesh,
value=-1,
narrowBandWidth=narrowBandWidth,
hasOld=1)
bottomHeight = cellsBelowTrench * cellSize
trenchHeight = bottomHeight + trenchDepth
trenchWidth = trenchDepth / aspectRatio
sideWidth = (trenchSpacing - trenchWidth) / 2
x, y = mesh.getCellCenters()[..., 0], mesh.getCellCenters()[..., 1]
distanceVar.setValue(1,
where=(y > trenchHeight) |
((y > bottomHeight) &
(x < xCells * cellSize - sideWidth)))
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
bulkCatalystVar = CellVariable(name='bulk catalyst variable',
mesh=mesh,
value=catalystConcentration)
metalVar = CellVariable(name='metal variable',
mesh=mesh,
value=metalConcentration)
expoConstant = -transferCoefficient * faradaysConstant \
/ (gasConstant * temperature)
tmp = currentDensity1 * catalystVar.getInterfaceVar()
exchangeCurrentDensity = currentDensity0 + tmp
import fipy.tools.numerix as numerix
expo = numerix.exp(expoConstant * overpotential)
currentDensity = expo * exchangeCurrentDensity * metalVar \
/ metalConcentration
depositionRateVariable = currentDensity * molarVolume \
/ (charge * faradaysConstant)
extensionVelocityVariable = CellVariable(name='extension velocity',
mesh=mesh,
value=depositionRateVariable)
from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \
import AdsorbingSurfactantEquation
surfactantEquation = AdsorbingSurfactantEquation(
surfactantVar=catalystVar,
distanceVar=distanceVar,
bulkVar=bulkCatalystVar,
rateConstant=rateConstant0 + rateConstant3 * overpotential**3)
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.getFacesTop(), metalConcentration)
from fipy.models.levelSet.surfactant.surfactantBulkDiffusionEquation \
import buildSurfactantBulkDiffusionEquation
bulkCatalystEquation = buildSurfactantBulkDiffusionEquation(
bulkVar=bulkCatalystVar,
distanceVar=distanceVar,
surfactantVar=catalystVar,
diffusionCoeff=catalystDiffusion,
rateConstant=rateConstant0 * siteDensity)
catalystBCs = FixedValue(mesh.getFacesTop(), catalystConcentration)
if displayViewers:
try:
from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer
viewers = (MayaviSurfactantViewer(distanceVar,
catalystVar.getInterfaceVar(),
zoomFactor=1e6,
limits={
'datamax': 0.5,
'datamin': 0.0
},
smooth=1,
title='catalyst coverage'), )
except:
from fipy.viewers import make
viewers = (make(distanceVar,
limits={
'datamin': -1e-9,
'datamax': 1e-9
}), make(catalystVar.getInterfaceVar()))
else:
viewers = ()
levelSetUpdateFrequency = int(0.8 * narrowBandWidth \
/ (cellSize * cflNumber * 2))
for step in range(numberOfSteps):
if step % 5 == 0:
for viewer in viewers:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction()
extensionVelocityVariable.setValue(depositionRateVariable())
distanceVar.updateOld()
catalystVar.updateOld()
metalVar.updateOld()
bulkCatalystVar.updateOld()
distanceVar.extendVariable(extensionVelocityVariable)
dt = cflNumber * cellSize / numerix.max(extensionVelocityVariable)
advectionEquation.solve(distanceVar, dt=dt)
surfactantEquation.solve(catalystVar, dt=dt)
metalEquation.solve(metalVar,
dt=dt,
boundaryConditions=metalEquationBCs)
bulkCatalystEquation.solve(bulkCatalystVar,
dt=dt,
boundaryConditions=catalystBCs)
try:
import os
import examples.levelSet.electroChem
filepath = os.path.join(examples.levelSet.electroChem.__path__[0],
'test.gz')
from fipy.tools import dump
from fipy.tools import numerix
print catalystVar.allclose(numerix.array(dump.read(filepath)),
rtol=1e-4)
except:
return 0
for i in range(1, 501):
meshList = meshList + [
SkewedGrid2D(dx=1.0, dy=1.0, nx=20, ny=20, rand=(0.001 * i))
]
for mesh in meshList:
var = CellVariable(name="solution variable",
mesh=mesh,
value=valueLeft)
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
ImplicitDiffusionTerm().solve(
var,
boundaryConditions=(FixedValue(mesh.getFacesLeft(), valueLeft),
FixedValue(mesh.getFacesRight(), valueRight)))
varArray = numerix.array(var)
x = mesh.getCellCenters()[:, 0]
analyticalArray = valueLeft + (valueRight - valueLeft) * x / 20
errorArray = varArray - analyticalArray
nonOrthoArray = mesh._getNonOrthogonality()
RMSError = (numerix.add.reduce(errorArray * errorArray) /
len(errorArray))**0.5
RMSNonOrtho = (numerix.add.reduce(nonOrthoArray * nonOrthoArray) /
len(nonOrthoArray))**0.5
RMSNonOrthoList += [RMSNonOrtho]
RMSErrorList += [RMSError]
from fipy.terms.transientTerm import TransientTerm
a = 1
timeStepDuration = 0.01
steps = 1000
eq = ImplicitDiffusionTerm(coeff=(
a, a)) + (u.getOld().getOld() - 2 * u.getOld() + u) / timeStepDuration**2
from fipy.boundaryConditions.fixedValue import FixedValue
from fipy.boundaryConditions.fixedFlux import FixedFlux
from fipy.boundaryConditions.nthOrderBoundaryCondition import NthOrderBoundaryCondition
BCs = (NthOrderBoundaryCondition(faces=mesh.getFacesRight(), value=0, order=2),
NthOrderBoundaryCondition(faces=mesh.getFacesRight(), value=1, order=3),
FixedValue(faces=mesh.getFacesLeft(),
value=0), FixedFlux(faces=mesh.getFacesLeft(), value=0))
from fipy import viewers
viewer = viewers.make(vars=(u))
def hit_continue(Prompt='Hit any key to continue'):
raw_input(Prompt)
for step in range(steps):
u.updateOld()
eq.solve(var=u, boundaryConditions=BCs, dt=timeStepDuration)
eq = ImplicitDiffusionTerm(coeff=(a, a)) + (
u.getOld().getOld() - 2 * u.getOld() + u) / timeStepDuration**2
viewer.plot()