def __init__(self,
trenchDepth=None,
trenchSpacing=None,
boundaryLayerDepth=None,
cellSize=None,
aspectRatio=None,
angle=0.,
communicator=parallelComm):
"""
`trenchDepth` - Depth of the trench.
`trenchSpacing` - The distance between the trenches.
`boundaryLayerDepth` - The depth of the hydrodynamic boundary
layer.
`cellSize` - The cell Size.
`aspectRatio` - trenchDepth / trenchWidth
`angle` - The angle for the taper of the trench.
The trench mesh takes the parameters generally used to define
a trench region and recasts then for the general
`GapFillMesh`.
"""
heightBelowTrench = cellSize * 10.
heightAboveTrench = trenchDepth / 1.
fineRegionHeight = heightBelowTrench + trenchDepth + heightAboveTrench
transitionHeight = fineRegionHeight * 3.
domainWidth = trenchSpacing / 2.
domainHeight = heightBelowTrench + trenchDepth + boundaryLayerDepth
super(TrenchMesh, self).__init__(cellSize=cellSize,
desiredDomainWidth=domainWidth,
desiredDomainHeight=domainHeight,
desiredFineRegionHeight=fineRegionHeight,
transitionRegionHeight=transitionHeight,
communicator=parallelComm)
trenchWidth = trenchDepth / aspectRatio
x, y = self.cellCenters
Y = (y - (heightBelowTrench + trenchDepth / 2))
taper = numerix.tan(angle) * Y
self.electrolyteMask = numerix.where(y > trenchDepth + heightBelowTrench,
1,
numerix.where(y < heightBelowTrench,
0,
numerix.where(x > trenchWidth / 2 + taper,
0,
1)))
def __init__(self,
trenchDepth=None,
trenchSpacing=None,
boundaryLayerDepth=None,
cellSize=None,
aspectRatio=None,
angle=0.,
communicator=parallelComm):
"""
`trenchDepth` - Depth of the trench.
`trenchSpacing` - The distance between the trenches.
`boundaryLayerDepth` - The depth of the hydrodynamic boundary
layer.
`cellSize` - The cell Size.
`aspectRatio` - trenchDepth / trenchWidth
`angle` - The angle for the taper of the trench.
The trench mesh takes the parameters generally used to define
a trench region and recasts then for the general
`GapFillMesh`.
"""
heightBelowTrench = cellSize * 10.
heightAboveTrench = trenchDepth / 1.
fineRegionHeight = heightBelowTrench + trenchDepth + heightAboveTrench
transitionHeight = fineRegionHeight * 3.
domainWidth = trenchSpacing / 2.
domainHeight = heightBelowTrench + trenchDepth + boundaryLayerDepth
super(TrenchMesh, self).__init__(cellSize=cellSize,
desiredDomainWidth=domainWidth,
desiredDomainHeight=domainHeight,
desiredFineRegionHeight=fineRegionHeight,
transitionRegionHeight=transitionHeight,
communicator=parallelComm)
trenchWidth = trenchDepth / aspectRatio
x, y = self.cellCenters
Y = (y - (heightBelowTrench + trenchDepth / 2))
taper = numerix.tan(angle) * Y
self.electrolyteMask = numerix.where(y > trenchDepth + heightBelowTrench,
1,
numerix.where(y < heightBelowTrench,
0,
numerix.where(x > trenchWidth / 2 + taper,
0,
1)))
def getElectrolyteMask(self):
x, y = self.getCellCenters()
Y = (y - (self.heightBelowTrench + self.trenchDepth / 2))
## taper
taper = numerix.tan(self.angle) * Y
## bow
if abs(self.bowWidth) > 1e-12 and (-self.trenchDepth / 2 < Y < self.trenchDepth / 2):
param1 = self.trenchDepth**2 / 8 / self.bowWidth
param2 = self.bowWidth / 2
bow = -numerix.sqrt((param1 + param2)**2 - Y**2) + param1 - param2
else:
bow = 0
## over hang
Y = y - (self.heightBelowTrench + self.trenchDepth - self.overBumpRadius)
overBump = 0
if self.overBumpRadius > 1e-12:
overBump += numerix.where(Y > -self.overBumpRadius,
self.overBumpWidth / 2 * (1 + numerix.cos(Y * numerix.pi / self.overBumpRadius)),
0)
tmp = self.overBumpRadius**2 - Y**2
tmp = (tmp > 0) * tmp
overBump += numerix.where((Y > -self.overBumpRadius) & (Y > 0),
numerix.where(Y > self.overBumpRadius,
-self.overBumpRadius,
-(self.overBumpRadius - numerix.sqrt(tmp))),
0)
return numerix.where(y > self.trenchDepth + self.heightBelowTrench,
1,
numerix.where(y < self.heightBelowTrench,
0,
numerix.where(x > self.trenchWidth / 2 + taper - bow - overBump,
0,
1)))
value=initialTemperature,
hasOld=1
)
bench.stop('variables')
bench.start()
from fipy.tools import numerix
mVar = phase - 0.5 - kappa1 / numerix.pi * \
numerix.arctan(kappa2 * temperature)
phaseY = phase.getFaceGrad().dot((0, 1))
phaseX = phase.getFaceGrad().dot((1, 0))
psi = theta + numerix.arctan2(phaseY, phaseX)
Phi = numerix.tan(N * psi / 2)
PhiSq = Phi**2
beta = (1. - PhiSq) / (1. + PhiSq)
betaPsi = -N * 2 * Phi / (1 + PhiSq)
A = alpha**2 * c * (1.+ c * beta) * betaPsi
D = alpha**2 * (1.+ c * beta)**2
dxi = phase.getFaceGrad()._take((1, 0), axis = 1) * (-1, 1)
anisotropySource = (A * dxi).getDivergence()
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.explicitDiffusionTerm import ExplicitDiffusionTerm
from fipy.terms.implicitSourceTerm import ImplicitSourceTerm
phaseEq = TransientTerm(tau) == ExplicitDiffusionTerm(D) + \
ImplicitSourceTerm(mVar * ((mVar < 0) - phase)) + \
((mVar > 0.) * mVar * phase + anisotropySource)
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
def tan(self):
return self._UnaryOperatorVariable(lambda a: numerix.tan(a))
mesh=mesh,
value=initialTemperature,
hasOld=1)
bench.stop('variables')
bench.start()
from fipy.tools import numerix
mVar = phase - 0.5 - kappa1 / numerix.pi * \
numerix.arctan(kappa2 * temperature)
phaseY = phase.getFaceGrad().dot((0, 1))
phaseX = phase.getFaceGrad().dot((1, 0))
psi = theta + numerix.arctan2(phaseY, phaseX)
Phi = numerix.tan(N * psi / 2)
PhiSq = Phi**2
beta = (1. - PhiSq) / (1. + PhiSq)
betaPsi = -N * 2 * Phi / (1 + PhiSq)
A = alpha**2 * c * (1. + c * beta) * betaPsi
D = alpha**2 * (1. + c * beta)**2
dxi = phase.getFaceGrad()._take((1, 0), axis=1) * (-1, 1)
anisotropySource = (A * dxi).getDivergence()
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.explicitDiffusionTerm import ExplicitDiffusionTerm
from fipy.terms.implicitSourceTerm import ImplicitSourceTerm
phaseEq = TransientTerm(tau) == ExplicitDiffusionTerm(D) + \
ImplicitSourceTerm(mVar * ((mVar < 0) - phase)) + \
((mVar > 0.) * mVar * phase + anisotropySource)
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
