def _getDiagonalSign(self, transientGeomCoeff=None, diffusionGeomCoeff=None):
if transientGeomCoeff is not None and diffusionGeomCoeff is not None:
diagonalSign = numerix.where(numerix.array(numerix.all(transientGeomCoeff == 0, axis=-1)),
numerix.array(2 * numerix.all(diffusionGeomCoeff[0] <= 0, axis=-1) - 1),
numerix.array(2 * numerix.all(transientGeomCoeff >= 0, axis=-1) - 1))
elif transientGeomCoeff is not None:
diagonalSign = 2 * numerix.all(transientGeomCoeff >= 0, axis=-1) - 1
elif diffusionGeomCoeff is not None:
diagonalSign = 2 * numerix.all(diffusionGeomCoeff[0] <= 0, axis=-1) - 1
else:
diagonalSign = 1
return diagonalSign
def _getDiagonalSign(self,
transientGeomCoeff=None,
diffusionGeomCoeff=None):
if transientGeomCoeff is not None and diffusionGeomCoeff is not None:
diagonalSign = numerix.where(
numerix.array(numerix.all(transientGeomCoeff == 0, axis=-1)),
numerix.array(
2 * numerix.all(diffusionGeomCoeff[0] <= 0, axis=-1) - 1),
numerix.array(2 *
numerix.all(transientGeomCoeff >= 0, axis=-1) -
1))
elif transientGeomCoeff is not None:
diagonalSign = 2 * numerix.all(transientGeomCoeff >= 0,
axis=-1) - 1
elif diffusionGeomCoeff is not None:
diagonalSign = 2 * numerix.all(diffusionGeomCoeff[0] <= 0,
axis=-1) - 1
else:
diagonalSign = 1
return diagonalSign
def _getWeight(self, var, transientGeomCoeff=None, diffusionGeomCoeff=None):
r"""
Testing that the sign of the equation is taken into account
when evaluation upwind direction.
>>> from fipy import Grid1D, CellVariable
>>> from fipy import TransientTerm, ConvectionTerm, ImplicitSourceTerm
>>> m = Grid1D(nx=3, dx=0.5)
>>> v = CellVariable(mesh=m)
>>> v.constrain(1, m.facesLeft)
>>> v.constrain(0, m.facesRight)
>>> (-TransientTerm(coeff=1 / m.x) ==
... ConvectionTerm(coeff=[[1]])
... + ImplicitSourceTerm(coeff=m.x)).solve(v, dt=1.)
>>> v0 = v.copy()
>>> v[:] = 0
>>> (TransientTerm(coeff=1 / m.x) ==
... - ConvectionTerm(coeff=[[1]])
... - ImplicitSourceTerm(coeff=m.x)).solve(v, dt=1.)
>>> print(numerix.allclose(v, v0))
True
"""
if self.stencil is None:
geomCoeff = self._getGeomCoeff(var)
large = 1e+20
pecletLarge = large - (geomCoeff < 0) * (2 * large)
if numerix.all(self._getDiagonalSign(transientGeomCoeff, diffusionGeomCoeff) < 0):
pecletLarge = -pecletLarge
if diffusionGeomCoeff is None or diffusionGeomCoeff[0] is None:
peclet = pecletLarge
else:
diffCoeff = diffusionGeomCoeff[0].numericValue
diffCoeff = diffCoeff - (diffCoeff == 0) * geomCoeff / pecletLarge
peclet = -geomCoeff / diffCoeff
alpha = self._alpha(peclet)
self.stencil = {'implicit' : {'cell 1 diag' : alpha,
'cell 1 offdiag' : (1-alpha),
'cell 2 diag' : -(1-alpha),
'cell 2 offdiag' : -alpha}}
return self.stencil
