Concentration dependent Diffusion

Hey,

I am trying to solve Fick's second law and simulate Diffusion, but with a non linear diffusion coefficient. The law states:

C' = D * d^2/dx^2 C http://upload.wikimedia.org/math/8/0/5/8056801cc902b7bfd7b384cc4ebff268.png

• Where C is the concentration
• D is the diffusion coefficiant
• x is a space coordinate

First I would like a linear dependence D = (C_0-C)*D_0

• With C_0 = initial concentration at a source
• C = concentration at the position the simulation calculates
• D_0 = initial diffusion coefficient

And later a quadratic dependence of C in D.

I used the PDE toolbox so far and it gave nice and fitting results for the linear problem of a constant D, however I can't figure out how to solve the problem with a concentration dependence in the diffusion coefficient.

How I see it this would be a nonlinear parabolic partial differential equation.

I would very much appreciate every form of help! Thank you in advance!

Cheers Andreas

Answer 1

[Bjorn Gustavsson]

On the matlab file exchange there are several tools for nonlinear diffusion filtering. These tools are designed for image filtering/processing, but they obviously do solve the nonlinear diffusion equations.

HTH,

[Andreas Bliersbach]

As far as I understood those diffusion filterings, you mentioned, D depends not on C but on its gradient. D =a* grad(C)

That however is not what I want, I would need a dependency of C

like D = (a-C)*b

Since I am not a very experienced Matlab User I find it very hard to wiggle around in a code I haven't written myself, so I don't know if I could rewrite those diffusion filterings you've mentioned!

Thank you for your reply anyway :)