On Nov 23, 2009, at 7:10 AM, S. Chris Colbert wrote:
I think I have I found the flaw in my methods. And it stems from my
failure to
do a proper dimensional analysis.
You weren't helped by those examples, which neither appear to ever
write down what actual equations they are solving and then say things
like "Heat is uniformly generated in the bock at a rate of 20 W/m^2",
when as you correctly identified, it has to be volumetric heat
generation. Sure, "everybody" knows the heat flux equation, but units
matter and equations matter.
Perhaps this example might make for a nice tutorial addition in the
Fipy
manual. I would be willing to write it up if you all are willing to
accept it.
This would be a welcome example. Keep in mind that FiPy's users come
from disparate fields, so spell out what equation you're solving and
what all the coefficients are; certainly don't assume that everybody
knows what "adiabatic" means. Also, it's more likely to get integrated
quickly if it's written in the doctest style that the examples in the
manual are done in.
Also, if I still have glaring holes in my logic or method, please
let me know!
Nothing glaring, but I'll address some of the other questions that you
brought up:
Now, since i'm only interested in steady, I figured I could just
jack up the
diffusivity coefficient to 1. and then I can use the step sizes you
see in the
code, but I dont know how valid this is?
Increasing the time step should be OK, subject to the standard
concerns about accuracy. For the steady-state solution, I think you're
OK, though, as long as the problem converges at all. Since you have
convection at the boundaries, I'm not sure you're free change the
diffusion coefficient without altering the steady-state temperature
profile.
Also, I tried modeling the problem using an ImplicitSource() term
ala the doc
examples but I could never get it to work. First, FaceVariable(...,
rank=1);
I assume you're talking about the FAQ "How do I apply an outlet or
inlet boundary condition?"? That is the right place to be looking.
the "..." is invalid python syntax, and I couldn't find in the
manual what that
is supposed to represent.
That's just a placeholder for the rest of the arguments to define the
FaceVariable, e.g., "mesh=mesh, value=[[0.], [1.]]". I'll see if
there's a clearer way to express that, without going into detail that
isn't relevant to that particular discussion.
When I let the ellipsis just equal my mesh, I seem
to be unable to set the left side of mesh to take values depending
on T (to
model the correct flux term). I always get numpy broadcasting
complaints when
trying to set value to a non-scalar value. Any ideas on this?
I would have to see what you tried. This works (modulo any adjustments
for density and heat capacity):
mask = mesh.getFacesBottom()
outCoeff = (mask * [[0], [-h]]).getDivergence()
convectionOut = ImplicitSourceTerm(coeff=outCoeff) - outCoeff *
Tinf
What does .getDivergence()
actually represent. i.e. what does it do, and why is it required? Is
this
related to the Divergence vector operator?
Yes, u.getDivergence() is the same as $\nabla\cdot\vec{u}$
