Hello all,
I came across FiPy a few days ago and I'm certainly glad that I did -- it
seems incredibly useful. I've now run through most of the simple examples
and I think I understand what I'm doing. However, I want to solve a problem
with some unusual boundary conditions and I'd like to make sure that I know
how to implement them correctly. (Unfortunately, the manual is a little
confusing with regard to boundary conditions.)
My problem is as follows. I have two concentrations C = C(r,x,t) and N =
N(x,t). These are essentially bulk, C(r,x,t), and surface, N(x,t),
concentrations in a particular geometry. Here, r is a radius with R1 <= r <=
R2 and x is on an interval with -L <= x <= L. With various constants set
equal to one, the equations that govern the concentrations are:
dC/dt = nabla^{2} C,
dN/dt = nabla^{2} N + dC/dr |_{r = R1},
subject to some usual (fixed value and fixed flux) boundary conditions AND
the condition that C(r,x,t) |_{r = R1} = N(x,t).
Right now, my understanding is that I should specify C(r,x,t) |_{r = R1} =
N(x,t) as an outlet boundary condition like Section 5.5 of the manual, and
then I should just add the r part of the gradient of C(r,x,t) to the
equation for N(x,t). Is this accurate?
Any help would be really appreciated! And many thanks for making this
software available.
