def _getOldAdjacentValues(self, oldArray, id1, id2, dt):
oldArray1, oldArray2 = ExplicitUpwindConvectionTerm._getOldAdjacentValues(self, oldArray, id1, id2, dt)
mesh = oldArray.mesh
interiorIDs = numerix.nonzero(mesh.interiorFaces)[0]
interiorFaceAreas = numerix.take(mesh._faceAreas, interiorIDs)
interiorFaceNormals = numerix.take(mesh._orientedFaceNormals, interiorIDs, axis=-1)
# Courant-Friedrichs-Levy number
interiorCFL = abs(numerix.take(self._getGeomCoeff(oldArray), interiorIDs)) * dt
gradUpwind = (oldArray2 - oldArray1) / numerix.take(mesh._cellDistances, interiorIDs)
vol1 = numerix.take(mesh.cellVolumes, id1)
oldArray1 += 0.5 * self._getGradient(numerix.dot(numerix.take(oldArray.grad, id1, axis=-1), interiorFaceNormals), gradUpwind) \
* (vol1 - interiorCFL) / interiorFaceAreas
vol2 = numerix.take(mesh.cellVolumes, id2)
oldArray2 += 0.5 * self._getGradient(numerix.dot(numerix.take(oldArray.grad, id2, axis=-1), -interiorFaceNormals), -gradUpwind) \
* (vol2 - interiorCFL) / interiorFaceAreas
return oldArray1, oldArray2
def _getOldAdjacentValues(self, oldArray, id1, id2, dt):
oldArray1, oldArray2 = ExplicitUpwindConvectionTerm._getOldAdjacentValues(self, oldArray, id1, id2, dt)
mesh = oldArray.getMesh()
interiorIDs = numerix.nonzero(mesh.getInteriorFaces())[0]
interiorFaceAreas = numerix.take(mesh._getFaceAreas(), interiorIDs)
interiorFaceNormals = numerix.take(mesh._getOrientedFaceNormals(), interiorIDs, axis=-1)
# Courant-Friedrichs-Levy number
interiorCFL = abs(numerix.take(self._getGeomCoeff(mesh), interiorIDs)) * dt
gradUpwind = (oldArray2 - oldArray1) / numerix.take(mesh._getCellDistances(), interiorIDs)
vol1 = numerix.take(mesh.getCellVolumes(), id1)
self.CFL = interiorCFL / vol1
oldArray1 += 0.5 * self._getGradient(numerix.dot(numerix.take(oldArray.getGrad(), id1, axis=-1), interiorFaceNormals), gradUpwind) \
* (vol1 - interiorCFL) / interiorFaceAreas
vol2 = numerix.take(mesh.getCellVolumes(), id2)
self.CFL = numerix.maximum(interiorCFL / vol2, self.CFL)
oldArray2 += 0.5 * self._getGradient(numerix.dot(numerix.take(oldArray.getGrad(), id2, axis=-1), -interiorFaceNormals), -gradUpwind) \
* (vol2 - interiorCFL) / interiorFaceAreas
return oldArray1, oldArray2
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,
solver = LinearCGSSolver(tolerance = 1.e-15, steps = 2000))
viewer.plot()
viewer.plot()
raw_input('finished')
def __init__(self,
surfactantVar=None,
distanceVar=None,
bulkVar=None,
rateConstant=None,
otherVar=None,
otherBulkVar=None,
otherRateConstant=None,
consumptionCoeff=None):
"""
Create a `AdsorbingSurfactantEquation` object.
:Parameters:
- `surfactantVar`: The `SurfactantVariable` to be solved for.
- `distanceVar`: The `DistanceVariable` that marks the interface.
- `bulkVar`: The value of the `surfactantVar` in the bulk.
- `rateConstant`: The adsorption rate of the `surfactantVar`.
- `otherVar`: Another `SurfactantVariable` with more surface affinity.
- `otherBulkVar`: The value of the `otherVar` in the bulk.
- `otherRateConstant`: The adsorption rate of the `otherVar`.
- `consumptionCoeff`: The rate that the `surfactantVar` is consumed during deposition.
"""
self.eq = TransientTerm(coeff=1) - ExplicitUpwindConvectionTerm(
SurfactantConvectionVariable(distanceVar))
self.dt = Variable(0.)
mesh = distanceVar.mesh
adsorptionCoeff = self.dt * bulkVar * rateConstant
spCoeff = adsorptionCoeff * distanceVar._cellInterfaceFlag
scCoeff = adsorptionCoeff * distanceVar.cellInterfaceAreas / mesh.cellVolumes
self.eq += ImplicitSourceTerm(spCoeff) - scCoeff
if otherVar is not None:
otherSpCoeff = self.dt * otherBulkVar * otherRateConstant * distanceVar._cellInterfaceFlag
otherScCoeff = -otherVar.interfaceVar * scCoeff
self.eq += ImplicitSourceTerm(otherSpCoeff) - otherScCoeff
vars = (surfactantVar, otherVar)
else:
vars = (surfactantVar, )
total = 0
for var in vars:
total += var.interfaceVar
maxVar = (total > 1) * distanceVar._cellInterfaceFlag
val = distanceVar.cellInterfaceAreas / mesh.cellVolumes
for var in vars[1:]:
val -= distanceVar._cellInterfaceFlag * var
spMaxCoeff = 1e20 * maxVar
scMaxCoeff = spMaxCoeff * val * (val > 0)
self.eq += ImplicitSourceTerm(spMaxCoeff) - scMaxCoeff - 1e-40
if consumptionCoeff is not None:
self.eq += ImplicitSourceTerm(consumptionCoeff)
