Hi Daniel,
Thanks for the reply. What you proposed made sense to me, so I implemented
it. However, I'm a little confused about how to properly set the adsorption
if I don't know other underlying details of the model. Suppose that my
problem, with constants, is
dC/dt = gammaC nabla^{2} C,
dN/dt = gammaN nabla^{2} N + A dC/dr |_{r = R1}
along with C(r,x,t) |_{r = R1} = B N(x,t). How can I find gammaAdsorption?
On Thu, Oct 8, 2009 at 4:32 PM, Daniel Wheeler <[email protected]>wrote:
>
> Hi,
>
> Thanks for your interest in FiPy. Having thought about your problem a
> little bit, it occurred to me that N and C are indistinguishable. You
> can model them both with the one equation and one variable. The left
> most layer of cells can simply hold of N (or the layer of cells where
> r=R1). You can also make the diffusion coefficient different in this
> layer of cells. So you can write it like this,
> assuming 2L = 1.0 and R1 = 0, and R2 = 1
>
> nr = 10
> nx = 10
> dr = 0.1
> dx = 0.1
>
> ## shift the mesh down one cell so that R=0 is the true boundary
> m = Grid1D(nx=nx, ny=nr + 1, dx=dx, dy=dr) + [[0],[-dr]
>
> CN = CellVariable(mesh=m, value=initialCondition)
>
> D = FaceVariable(mesh=m)
> X, R = mesh.getFaceCenters()
> D[R < 0] = gammaN
> D[R == 0] = gammaAdsorption
> D[R > 0] = gammaC
>
> eqn = TransientTerm() = DiffusionTerm(D)
>
> while True:
> eqn.solve(CN, dt=0.1)
>
> I think this will work and you won't have to worry about boundary
> conditions in any strange ways. The one thing to be careful about is
> the boundary conditions on the X == L and X == -L boundaries. They
> will have to be only for R > 0 otherwise you will be applying boundary
> conditions to the ends of the 1D N domain.
>
> Hope this helps. I'm sure you'll have some questions about what I did
> above so feel free to ask.
>
> Cheers
>
> On Wed, Oct 7, 2009 at 8:43 AM, pibyfour <[email protected]> wrote:
> > 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.
> >
>
>
>
> --
> Daniel Wheeler
>
>
