from fipy.meshes.grid2D import Grid2D
from fipy.solvers.linearPCGSolver import LinearPCGSolver
from fipy.variables.cellVariable import CellVariable
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
nx = 2
valueLeft = 0.
fluxRight = 1.
timeStepDuration = 1.
L = 1.
dx = L / nx
mesh = Grid2D(dx=dx, nx=nx)
var = CellVariable(name="solution variable", mesh=mesh, value=valueLeft)
x = mesh.getFaceCenters()[:, 0]
middleFaces = numerix.logical_or(x < L / 4., x >= 3. * L / 4.)
diffCoeff = numerix.where(middleFaces, 1., 0.1)
boundaryConditions = (FixedValue(mesh.getFacesLeft(), valueLeft),
FixedFlux(mesh.getFacesRight(), fluxRight))
if __name__ == '__main__':
ImplicitDiffusionTerm(coeff=diffCoeff).solve(
var, boundaryConditions=boundaryConditions)
import fipy.viewers
from parameters import parameters
from fipy.meshes.grid2D import Grid2D
from fipy.variables.cellVariable import CellVariable
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.implicitSourceTerm import ImplicitSourceTerm
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
params = parameters['case 2']
nx = 50
ny = 50
dx = 1.
L = nx * dx
mesh = Grid2D(nx=nx, ny=ny, dx=dx, dy=1.)
shift = 1.
KMVar = CellVariable(mesh=mesh, value=params['KM'] * shift, hasOld=1)
KCVar = CellVariable(mesh=mesh, value=params['KC'] * shift, hasOld=1)
TMVar = CellVariable(mesh=mesh, value=params['TM'] * shift, hasOld=1)
TCVar = CellVariable(mesh=mesh, value=params['TC'] * shift, hasOld=1)
P3Var = CellVariable(mesh=mesh, value=params['P3'] * shift, hasOld=1)
P2Var = CellVariable(mesh=mesh, value=params['P2'] * shift, hasOld=1)
RVar = CellVariable(mesh=mesh, value=params['R'], hasOld=1)
PN = P3Var + P2Var
KMscCoeff = params['chiK'] * (RVar + 1) * (1 - KCVar -
KMVar.getCellVolumeAverage())
$ python setup.py efficiency_test
"""
__docformat__ = 'restructuredtext'
if __name__ == "__main__":
from fipy.tools.parser import parse
from benchmarker import Benchmarker
bench = Benchmarker()
numberOfElements = parse('--numberOfElements',
action='store',
type='int',
default=100)
bench.start()
from fipy.tools import numerix
nx = int(numerix.sqrt(numberOfElements))
ny = nx
dx = 1.
dy = 1.
from fipy.meshes.grid2D import Grid2D
mesh = Grid2D(nx=nx, ny=nx, dx=dx, dy=dy)
bench.stop('mesh')
print bench.report(numberOfElements=numberOfElements)
L = 1.
dx = 0.1
velocity = 1.
cfl = 0.1
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.getCellCenters()[..., 0], mesh.getCellCenters()[..., 1]
distanceVariable.setValue(-1,
where=((x0 < x) & (x < x1)) & ((x0 < y) & (y < x1)))
surfactantVariable = SurfactantVariable(distanceVar=distanceVariable, value=1.)
surfactantEquation = SurfactantEquation(distanceVar=distanceVariable)
advectionEquation = buildHigherOrderAdvectionEquation(advectionCoeff=velocity)
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
#!/usr/bin/env python L = 1.0 N = 40 dL = L / N viscosity = 1. pressureRelaxation = 0.2 velocityRelaxation = 0.5 sweeps=10 from fipy.meshes.grid2D import Grid2D mesh = Grid2D(nx=N, ny=N, dx=dL, dy=dL) from fipy.variables.cellVariable import CellVariable psi = CellVariable(mesh=mesh, name='stream function') Xhat=(1,0) Yhat=(0,1) 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)
import fipy.tools.numerix as numerix
if numberOfElements != -1:
pos = trenchSpacing * cellsBelowTrench / 4 / numberOfElements
sqr = trenchSpacing * (trenchDepth + boundaryLayerDepth) \
/ (2 * numberOfElements)
cellSize = pos + numerix.sqrt(pos**2 + sqr)
else:
cellSize = 0.1e-7
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)
bench.stop('mesh')
bench.start()
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import \
DistanceVariable
distanceVar = DistanceVariable(name='distance variable',
mesh=mesh,
value=-1,
narrowBandWidth=narrowBandWidth,
hasOld=1)
nx = int(numerix.sqrt(numberOfElements))
ny = int(numerix.sqrt(numberOfElements))
steps = numberOfSteps
dx = 2.
dy = 2.
L = dx * nx
asq = 1.0
epsilon = 1
diffusionCoeff = 1
from fipy.meshes.grid2D import Grid2D
mesh = Grid2D(dx, dy, nx, ny)
from fipy.variables.cellVariable import CellVariable
from fipy.tools.numerix import random
var = CellVariable(name="phase field", mesh=mesh, value=random.random(nx * ny))
faceVar = var.getArithmeticFaceValue()
doubleWellDerivative = asq * (1 - 6 * faceVar * (1 - faceVar))
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
from fipy.terms.transientTerm import TransientTerm
diffTerm2 = ImplicitDiffusionTerm(coeff=(diffusionCoeff *
doubleWellDerivative, ))
diffTerm4 = ImplicitDiffusionTerm(coeff=(diffusionCoeff, -epsilon**2))
eqch = TransientTerm() - diffTerm2 - diffTerm4
action='store',
type='int',
default=400)
bench.start()
import fipy.tools.numerix as numerix
steps = 10
nx = int(numerix.sqrt(numberOfElements))
ny = nx
Lx = 2.5 * nx / 100.
dx = Lx / nx
from fipy.meshes.grid2D import Grid2D
mesh = Grid2D(dx, dx, nx, nx)
bench.stop('mesh')
timeStepDuration = 0.02
phaseTransientCoeff = 0.1
thetaSmallValue = 1e-6
beta = 1e5
mu = 1e3
thetaTransientCoeff = 0.01
gamma = 1e3
epsilon = 0.008
s = 0.01
alpha = 0.015
temperature = 10.
import fipy
import numpy as np
import matplotlib.pyplot as plt
# fipy example from https://math.nist.gov/mcsd/Seminars/2005/2005-03-01-wheeler-presentation.pdf
nx = 10
dx = 1
steps = 100
# create a mesh:
L = nx * dx
from fipy.meshes.grid2D import Grid2D
mesh = Grid2D(nx=nx, dx=dx)
# create a field variable, set the initial conditions:
from fipy.variables.cellVariable import CellVariable
var = CellVariable(mesh=mesh, value=0)
def centerCells(cell):
return abs(cell.getCenter()[0] - L / 2.0) < L / 10
var.setValue(value=1.0, cells=mesh.getCells(filter=centerCells))
# create the equation:
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
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",
mesh=mesh2,
value=valueBottomTop)
boundaryConditions2 = (FixedValue(mesh2.getFacesLeft(), valueLeftRight),
FixedValue(mesh2.getFacesRight(), valueLeftRight),
FixedValue(mesh2.getFacesTop(), valueBottomTop),
FixedValue(mesh2.getFacesBottom(), valueBottomTop))
eqn = ImplicitDiffusionTerm()
if __name__ == '__main__':
eqn.solve(var2, boundaryConditions=boundaryConditions2)
from fipy.viewers import make
