Concentration dependent Diffusion
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Hey,
I am trying to solve Fick's second law and simulate Diffusion, but with a non linear diffusion coefficient. The law states:
- 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
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Bjorn Gustavsson
2011-2-16
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,
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