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.tools import serialComm
mesh = Grid2D(dx=cellSize,
dy=cellSize,
nx=xCells,
ny=yCells,
communicator=serialComm)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
distanceVar = DistanceVariable(name='distance variable',
mesh=mesh,
value=-1.,
hasOld=1)
bottomHeight = cellsBelowTrench * cellSize
trenchHeight = bottomHeight + trenchDepth
trenchWidth = trenchDepth / aspectRatio
sideWidth = (trenchSpacing - trenchWidth) / 2
x, y = mesh.cellCenters
distanceVar.setValue(1.,
where=(y > trenchHeight) |
((y > bottomHeight) &
(x < xCells * cellSize - sideWidth)))
distanceVar.calcDistanceFunction(order=2)
catalystVar = SurfactantVariable(name="catalyst variable",
value=catalystCoverage,
distanceVar=distanceVar)
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.interfaceVar
exchangeCurrentDensity = currentDensity0 + tmp
expo = numerix.exp(expoConstant * overpotential)
currentDensity = expo * exchangeCurrentDensity * metalVar \
/ metalConcentration
depositionRateVariable = currentDensity * molarVolume \
/ (charge * faradaysConstant)
extensionVelocityVariable = CellVariable(name='extension velocity',
mesh=mesh,
value=depositionRateVariable)
surfactantEquation = AdsorbingSurfactantEquation(
surfactantVar=catalystVar,
distanceVar=distanceVar,
bulkVar=bulkCatalystVar,
rateConstant=rateConstant0 + rateConstant3 * overpotential**3)
advectionEquation = TransientTerm() + AdvectionTerm(
extensionVelocityVariable)
metalEquation = buildMetalIonDiffusionEquation(
ionVar=metalVar,
distanceVar=distanceVar,
depositionRate=depositionRateVariable,
diffusionCoeff=metalDiffusion,
metalIonMolarVolume=molarVolume,
)
metalVar.constrain(metalConcentration, mesh.facesTop)
from surfactantBulkDiffusionEquation import buildSurfactantBulkDiffusionEquation
bulkCatalystEquation = buildSurfactantBulkDiffusionEquation(
bulkVar=bulkCatalystVar,
distanceVar=distanceVar,
surfactantVar=catalystVar,
diffusionCoeff=catalystDiffusion,
rateConstant=rateConstant0 * siteDensity)
bulkCatalystVar.constrain(catalystConcentration, mesh.facesTop)
if displayViewers:
try:
from mayaviSurfactantViewer import MayaviSurfactantViewer
viewer = MayaviSurfactantViewer(distanceVar,
catalystVar.interfaceVar,
zoomFactor=1e6,
datamax=0.5,
datamin=0.0,
smooth=1,
title='catalyst coverage')
except:
viewer = MultiViewer(
viewers=(Viewer(distanceVar, datamin=-1e-9, datamax=1e-9),
Viewer(catalystVar.interfaceVar)))
else:
viewer = None
levelSetUpdateFrequency = int(0.8 * narrowBandWidth \
/ (cellSize * cflNumber * 2))
for step in range(numberOfSteps):
if step > 5 and step % 5 == 0 and viewer is not None:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction(order=2)
extensionVelocityVariable.setValue(depositionRateVariable())
distanceVar.updateOld()
distanceVar.extendVariable(extensionVelocityVariable, order=2)
dt = cflNumber * cellSize / extensionVelocityVariable.max()
advectionEquation.solve(distanceVar, dt=dt)
surfactantEquation.solve(catalystVar, dt=dt)
metalEquation.solve(metalVar, dt=dt)
bulkCatalystEquation.solve(bulkCatalystVar,
dt=dt,
solver=GeneralSolver(tolerance=1e-15,
iterations=2000))
try:
import os
filepath = os.path.splitext(__file__)[0] + '.gz'
print catalystVar.allclose(numerix.loadtxt(filepath), rtol=1e-4)
except:
return 0
distanceToTravel = L / 5.
boxSize = .2
nx = int(L / dx)
ny = int(L / dx)
steps = int(distanceToTravel / dx / cfl)
timeStepDuration = cfl * dx / velocity
mesh = Grid2D(dx=dx, dy=dx, nx=nx, ny=ny)
x0 = (L - boxSize) / 2
x1 = (L + boxSize) / 2
distanceVariable = DistanceVariable(mesh=mesh, value=1., hasOld=1)
x, y = mesh.cellCenters
distanceVariable.setValue(-1,
where=((x0 < x) & (x < x1)) & ((x0 < y) & (y < x1)))
surfactantVariable = SurfactantVariable(distanceVar=distanceVariable, value=1.)
from fipy.variables.surfactantConvectionVariable import SurfactantConvectionVariable
surfactantEquation = TransientTerm() - \
ExplicitUpwindConvectionTerm(SurfactantConvectionVariable(distanceVariable))
advectionEquation = TransientTerm() + AdvectionTerm(velocity)
if __name__ == '__main__':
distanceViewer = Viewer(vars=distanceVariable, datamin=-.001, datamax=.001)
from fipy import Grid2D, DistanceVariable, Viewer
from fipy.tools import numerix
dx = 0.5
dy = 2.
nx = 5
ny = 5
Lx = nx * dx
Ly = ny * dy
mesh = Grid2D(dx = dx, dy = dy, nx = nx, ny = ny)
var = DistanceVariable(
name = 'level set variable',
mesh = mesh,
value = -1.,
hasOld = 1
)
x, y = mesh.cellCenters
var.setValue(1, where=((Lx / 3. < x) & (x < 2. * Lx / 3.)) & ((Ly / 3. < y) & (y < 2. * Ly / 3)))
if __name__ == '__main__':
var.calcDistanceFunction(order=1)
viewer = Viewer(vars=var, maxval=-5., minval=5.)
viewer.plot()
input('finished')
siteDensity = 1.
cinf = 1.
nx = 100
totalTimeSteps = 100
dt = 0.001
## build the mesh
dx = L / (nx - 1.5)
mesh = Grid1D(nx=nx, dx=dx, communicator=serialComm)
## build the distance variable
value = mesh.cellCenters[0] - 1.499 * dx
##distanceVar = DistanceVariable(mesh = mesh, value = dx * (arange(nx) - 0.999))
distanceVar = DistanceVariable(mesh=mesh, value=value, hasOld=1)
## Build the bulk diffusion equation
bulkVar = CellVariable(mesh=mesh, value=cinf)
surfactantVar = SurfactantVariable(distanceVar=distanceVar)
from .surfactantBulkDiffusionEquation import buildSurfactantBulkDiffusionEquation
bulkEqn = buildSurfactantBulkDiffusionEquation(bulkVar,
distanceVar=distanceVar,
surfactantVar=surfactantVar,
diffusionCoeff=diffusion,
rateConstant=rateConstant *
siteDensity)
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.tools import serialComm
mesh = Grid2D(dx = cellSize,
dy = cellSize,
nx = xCells,
ny = yCells,
communicator=serialComm)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
distanceVar = DistanceVariable(
name = 'distance variable',
mesh = mesh,
value = -1.,
hasOld = 1)
bottomHeight = cellsBelowTrench * cellSize
trenchHeight = bottomHeight + trenchDepth
trenchWidth = trenchDepth / aspectRatio
sideWidth = (trenchSpacing - trenchWidth) / 2
x, y = mesh.cellCenters
distanceVar.setValue(1., where=(y > trenchHeight) | ((y > bottomHeight) & (x < xCells * cellSize - sideWidth)))
distanceVar.calcDistanceFunction(order=2)
catalystVar = SurfactantVariable(
name = "catalyst variable",
value = catalystCoverage,
distanceVar = distanceVar)
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.interfaceVar
exchangeCurrentDensity = currentDensity0 + tmp
expo = numerix.exp(expoConstant * overpotential)
currentDensity = expo * exchangeCurrentDensity * metalVar / metalConcentration
depositionRateVariable = currentDensity * molarVolume / (charge * faradaysConstant)
extensionVelocityVariable = CellVariable(
name = 'extension velocity',
mesh = mesh,
value = depositionRateVariable)
surfactantEquation = AdsorbingSurfactantEquation(
surfactantVar = catalystVar,
distanceVar = distanceVar,
bulkVar = bulkCatalystVar,
rateConstant = rateConstant0 + rateConstant3 * overpotential**3)
advectionEquation = TransientTerm() + AdvectionTerm(extensionVelocityVariable)
metalEquation = buildMetalIonDiffusionEquation(
ionVar = metalVar,
distanceVar = distanceVar,
depositionRate = depositionRateVariable,
diffusionCoeff = metalDiffusion,
metalIonMolarVolume = molarVolume,
)
metalVar.constrain(metalConcentration, mesh.facesTop)
from .surfactantBulkDiffusionEquation import buildSurfactantBulkDiffusionEquation
bulkCatalystEquation = buildSurfactantBulkDiffusionEquation(
bulkVar = bulkCatalystVar,
distanceVar = distanceVar,
surfactantVar = catalystVar,
diffusionCoeff = catalystDiffusion,
rateConstant = rateConstant0 * siteDensity
)
bulkCatalystVar.constrain(catalystConcentration, mesh.facesTop)
if displayViewers:
try:
from .mayaviSurfactantViewer import MayaviSurfactantViewer
viewer = MayaviSurfactantViewer(distanceVar, catalystVar.interfaceVar, zoomFactor = 1e6, datamax=0.5, datamin=0.0, smooth = 1, title = 'catalyst coverage')
except:
viewer = MultiViewer(viewers=(
Viewer(distanceVar, datamin=-1e-9, datamax=1e-9),
Viewer(catalystVar.interfaceVar)))
else:
viewer = None
levelSetUpdateFrequency = int(0.8 * narrowBandWidth \
/ (cellSize * cflNumber * 2))
for step in range(numberOfSteps):
if step>5 and step % 5 == 0 and viewer is not None:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction(order=2)
extensionVelocityVariable.setValue(depositionRateVariable())
distanceVar.updateOld()
distanceVar.extendVariable(extensionVelocityVariable, order=2)
dt = cflNumber * cellSize / extensionVelocityVariable.max()
advectionEquation.solve(distanceVar, dt = dt)
surfactantEquation.solve(catalystVar, dt = dt)
metalEquation.solve(metalVar, dt = dt)
bulkCatalystEquation.solve(bulkCatalystVar, dt = dt, solver=GeneralSolver(tolerance=1e-15, iterations=2000))
try:
import os
filepath = os.path.splitext(__file__)[0] + '.gz'
print(catalystVar.allclose(numerix.loadtxt(filepath), rtol = 1e-4))
except:
return 0
nx = 50
velocity = 1.
cfl = 0.1
velocity = 1.
distanceToTravel = L / 10.
initialRadius = L / 4.
dx = L / nx
timeStepDuration = cfl * dx / velocity
steps = int(distanceToTravel / dx / cfl)
mesh = Grid2D(dx = dx, dy = dx, nx = nx, ny = nx)
distanceVariable = DistanceVariable(
name = 'level set variable',
mesh = mesh,
value = 1.,
hasOld = 1
)
x, y = mesh.cellCenters
cellRadius = numerix.sqrt((x - L / 2.)**2 + (y - L / 2.)**2)
distanceVariable.setValue(cellRadius - initialRadius)
initialSurfactantValue = 1.
surfactantVariable = SurfactantVariable(
value = initialSurfactantValue,
distanceVar = distanceVariable
)
advectionEquation = TransientTerm() + AdvectionTerm(velocity)
__docformat__ = 'restructuredtext'
from fipy import Grid2D, DistanceVariable, Viewer
from fipy.tools import numerix, serialComm
dx = 1.
dy = 1.
nx = 5
ny = 5
Lx = nx * dx
Ly = ny * dy
mesh = Grid2D(dx=dx, dy=dy, nx=nx, ny=ny, communicator=serialComm)
var = DistanceVariable(name='level set variable',
mesh=mesh,
value=-1.,
hasOld=1)
x, y = mesh.cellCenters
var.setValue(1,
where=((x < dx) | (x > (Lx - dx))
| (y < dy) | (y > (Ly - dy))))
if __name__ == '__main__':
var.calcDistanceFunction(order=1)
viewer = Viewer(vars=var, datamin=-5., datamax=5.)
viewer.plot()
input('finished')
from fipy import Grid2D, DistanceVariable, Viewer
from fipy.tools import numerix, serialComm
dx = 1.
dy = 1.
nx = 5
ny = 5
Lx = nx * dx
Ly = ny * dy
mesh = Grid2D(dx = dx, dy = dy, nx = nx, ny = ny, communicator=serialComm)
var = DistanceVariable(
name = 'level set variable',
mesh = mesh,
value = -1.,
hasOld = 1
)
x, y = mesh.cellCenters
var.setValue(1, where=((x < dx) | (x > (Lx - dx))
| (y < dy) | (y > (Ly - dy))))
if __name__ == '__main__':
var.calcDistanceFunction(order=1)
viewer = Viewer(vars=var, datamin=-5., datamax=5.)
viewer.plot()
input('finished')
L = 1.
nx = 50
cfl = 0.1
initialRadius = L / 4.
k = 1
dx = L / nx
steps = 20
from fipy.tools import serialComm
mesh = Grid2D(dx=dx, dy=dx, nx=nx, ny=nx, communicator=serialComm)
x, y = mesh.cellCenters
distanceVariable = DistanceVariable(
name='level set variable',
mesh=mesh,
value=numerix.sqrt((x - L / 2.)**2 + (y - L / 2.)**2) - initialRadius,
hasOld=1)
initialSurfactantValue = 1.
surfactantVariable = SurfactantVariable(value=initialSurfactantValue,
distanceVar=distanceVariable)
velocity = CellVariable(
name='velocity',
mesh=mesh,
value=1.,
)
advectionEquation = TransientTerm() + AdvectionTerm(velocity)
from fipy import Grid2D, DistanceVariable, Viewer
from fipy.tools import numerix
dx = 0.5
dy = 2.
nx = 5
ny = 5
Lx = nx * dx
Ly = ny * dy
mesh = Grid2D(dx = dx, dy = dy, nx = nx, ny = ny)
var = DistanceVariable(
name = 'level set variable',
mesh = mesh,
value = -1.,
hasOld = 1
)
x, y = mesh.cellCenters
var.setValue(1, where=((Lx / 3. < x) & (x < 2. * Lx / 3.)) & ((Ly / 3. < y) & (y < 2. * Ly / 3)))
if __name__ == '__main__':
var.calcDistanceFunction(order=1)
viewer = Viewer(vars=var, maxval=-5., minval=5.)
viewer.plot()
input('finished')
nx = 50
velocity = 1.
cfl = 0.1
velocity = 1.
distanceToTravel = L / 10.
initialRadius = L / 4.
dx = L / nx
timeStepDuration = cfl * dx / velocity
steps = int(distanceToTravel / dx / cfl)
mesh = Grid2D(dx = dx, dy = dx, nx = nx, ny = nx)
distanceVariable = DistanceVariable(
name = 'level set variable',
mesh = mesh,
value = 1.,
hasOld = 1
)
x, y = mesh.cellCenters
cellRadius = numerix.sqrt((x - L / 2.)**2 + (y - L / 2.)**2)
distanceVariable.setValue(cellRadius - initialRadius)
initialSurfactantValue = 1.
surfactantVariable = SurfactantVariable(
value = initialSurfactantValue,
distanceVar = distanceVariable
)
advectionEquation = TransientTerm() + AdvectionTerm(velocity)