Ah okay, now I think I get it. If I understand correctly, the sentence
from the FAQs "explicitly supply the desired FaceVariable" could be
expressed in layman's terms with something like "explicitly supply the
desired type of interpolation to determine the value of the variable at
the face".
And please don't misinterpret my statement, I am grateful for a very
complete and well-written manual!
Thank you for the tip about the last terms of my equations. Now I feel
just about ready to dive into the core of the matter. I will experiment
with the different interpolations available.
Regards,
Etienne Rivard
Am Sa, 2.02.2008, 00:06, schrieb Jonathan Guyer:
>
>
> On Feb 1, 2008, at 9:57 AM, Etienne Rivard wrote:
>
>
>> First of all, thank you for your previous answers, it was very
>> helpful and quite hit the mark.
>
> We're glad we could help.
>
>
>> Now, I'm still struggling with the concept of Face/CellVariable.
>> What confuses me is the use of CellVariables in diffusion or
>> convection terms.
>>
>> For example in the module examples.diffusion.mesh1D on page 67,
>> phi, which is a CellVariable, is used in the coefficient of the
>> ImplicitDiffusionTerm. Is this one of those cases where "FiPy will
>> automatically substitute var.getArithmeticFaceValue()" as mentionned in
>> the FAQs?
>
> Exactly.
>
>
>> If so, how would it be possible to be more rigorous and "explicitly
>> supply the desired FaceVariable rather than letting FiPy assume one"? In
>> other words, how is it possible to explicitly supply a FaceVariable when
>> this variable is already declared as a CellVariable?
>
> phi.getArithmeticFaceValue() returns $\phi_f = (\phi_1 - \phi_2) \frac
> {d_{f2}}{d_{12}} + \phi_2$
> phi.getHarmonicFaceValue() returns $\phi_f = \frac{\phi_1 \phi_2} {(\phi_2
> - \phi_1) \frac{d_{f2}}{d_{12}} + \phi_1}$
>
>
> where $phi_1$ and $phi_2$ are the CellVariable values on either side of
> the face in question, $d_{12}$ is the distance between those cell centers,
> and $d_{f2}$ is the distance from the face to the center of cell 2. I
> thought that I'd done a geometric version, too, but it doesn't look like
> it. It wouldn't be hard. I've never needed it, whereas I use
> getHarmonicFaceValue() all the time (very important with concentration
> variables that step from very small values to very large values).
>
> If you need some other interpolation, you will need to subclass form
> fipy.variables.cellToFaceVariable.CellToFaceVariable. For example, in my
> own code, I've defined a CellToFaceVariable that implements
> Scharfetter-Gummel discretization (used in semiconductor charge
> transport) to interpolate from a CellVariable containing Fermi levels
> (chemical potentials) to produce a FaceVariable containing carrier
> concentrations. This will eventually be included with FiPy, but if somebody
> needs it in the meantime, just ask.
>
>> It is important to me because I encounter this situation in the
>> system of equations I would like to solve:
>>
>> \[
>> \frac{\partial}{\partial t}(c y_F) + \nabla \cdot (c \vec{v} y_F) =
>> \nabla \cdot (c \bar{D} \nabla y_F)
>> \]
>>
>>
>> \[
>> \frac{\partial}{\partial t}(c y_F \theta) + \nabla \cdot (c \vec{v}
>> y_F \theta) = \nabla \cdot (c \tilde{D} \nabla y_F \theta)
>> \]
>>
>>
>> \[
>> \frac{\partial}{\partial t}(c y_F \Psi) + \nabla \cdot (c \vec{v}
>> y_F \Psi) = \nabla \cdot (c \hat{D} \nabla y_F \Psi)
>> \]
>>
>>
>> The variables I'm solving for are yF, theta and Psi.
>>
>
> For these equations, the issue only seems to arise for the third term
> (RHS) of each equation. In those cases, you'll need to factor them
> for FiPy:
>
> 1) the first term is fine in FiPy, as is, and is just a DiffusionTerm
>
>
> whereas
>
> 2) $\nabla \cdot (c \tilde{D} \nabla y_F \theta)$ becomes $\nabla
> \cdot (c \tilde{D} \theta \nabla y_F) + \nabla \cdot (c \tilde{D} y_F
> \nabla \theta)$
> 3) $\nabla \cdot (c \hat{D} \nabla y_F \Psi)$ becomes $\nabla \cdot
> (c \hat{D} \Psi \nabla y_F) + \nabla \cdot (c \hat{D} y_F \nabla \Psi)$
>
>
> become a ConvectionTerm, with velocity proportional to $\nabla y_F$, so
> use yF.getFaceGrad() and a DiffusionTerm, with diffusivity proportional to
> $y_F$. Here you'll
> need to use the specific interpolation you want, but if you don't specify,
> then FiPy will use getArithmeticFaceValue().
>
>
