def divergence(self):
r"""the divergence of `self`, :math:`\vec{u}`,
.. math:: \nabla\cdot\vec{u} \approx \frac{\sum_f (\vec{u}\cdot\hat{n})_f A_f}{V_P}
Returns
-------
divergence : CellVariable
one rank lower than `self`
Examples
--------
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(nx=3, ny=2)
>>> from builtins import range
>>> var = CellVariable(mesh=mesh, value=list(range(3*2)))
>>> print(var.faceGrad.divergence)
[ 4. 3. 2. -2. -3. -4.]
"""
if not hasattr(self, '_divergence'):
from fipy.variables.addOverFacesVariable import _AddOverFacesVariable
s = (slice(0, None, None), ) + (numerix.newaxis, ) * (
len(self.shape) - 2) + (slice(0, None, None), )
self._divergence = _AddOverFacesVariable(
(self * self.mesh._orientedAreaProjections[s]).sum(0))
return self._divergence
def _calcAnisotropySource(self, coeff, mesh, var):
if not hasattr(self, 'anisotropySource'):
if len(coeff) > 1:
gradients = var.getGrad().getHarmonicFaceValue().dot(self._getRotationTensor(mesh))
from fipy.variables.addOverFacesVariable import _AddOverFacesVariable
self.anisotropySource = _AddOverFacesVariable(gradients[1:].dot(coeff[1:])) * mesh.getCellVolumes()
def __calcAnisotropySource(self, coeff, mesh, var):
if not hasattr(self, 'anisotropySource'):
if len(coeff) > 1:
unconstrainedVar = var + 0
gradients = unconstrainedVar.grad.harmonicFaceValue.dot(self.__getRotationTensor(mesh))
from fipy.variables.addOverFacesVariable import _AddOverFacesVariable
self.anisotropySource = _AddOverFacesVariable(gradients[1:].dot(coeff[1:])) * mesh.cellVolumes
def __calcAnisotropySource(self, coeff, mesh, var):
if not hasattr(self, 'anisotropySource'):
if len(coeff) > 1:
unconstrainedVar = var + 0
gradients = unconstrainedVar.grad.harmonicFaceValue.dot(
self.__getRotationTensor(mesh))
from fipy.variables.addOverFacesVariable import _AddOverFacesVariable
self.anisotropySource = _AddOverFacesVariable(
gradients[1:].dot(coeff[1:])) * mesh.cellVolumes
def getDivergence(self):
"""
>>> from fipy.meshes.grid2D import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(nx=3, ny=2)
>>> var = CellVariable(mesh=mesh, value=range(3*2))
>>> print var.getFaceGrad().getDivergence()
[ 4. 3. 2. -2. -3. -4.]
"""
if not hasattr(self, 'divergence'):
from fipy.variables.addOverFacesVariable import _AddOverFacesVariable
self.divergence = _AddOverFacesVariable(self.dot(self.getMesh()._getOrientedAreaProjections()))
return self.divergence
def divergence(self):
"""
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(nx=3, ny=2)
>>> var = CellVariable(mesh=mesh, value=range(3*2))
>>> print var.faceGrad.divergence
[ 4. 3. 2. -2. -3. -4.]
"""
if not hasattr(self, '_divergence'):
from fipy.variables.addOverFacesVariable import _AddOverFacesVariable
s = (slice(0,None,None),) + (numerix.newaxis,) * (len(self.shape) - 2) + (slice(0,None,None),)
self._divergence = _AddOverFacesVariable((self * self.mesh._orientedAreaProjections[s]).sum(0))
return self._divergence
def divergence(self):
"""
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(nx=3, ny=2)
>>> var = CellVariable(mesh=mesh, value=range(3*2))
>>> print var.faceGrad.divergence
[ 4. 3. 2. -2. -3. -4.]
"""
if not hasattr(self, '_divergence'):
from fipy.variables.addOverFacesVariable import _AddOverFacesVariable
s = (slice(0, None, None), ) + (numerix.newaxis, ) * (
len(self.shape) - 2) + (slice(0, None, None), )
self._divergence = _AddOverFacesVariable(
(self * self.mesh._orientedAreaProjections[s]).sum(0))
return self._divergence