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Non linear diffusion equation #41
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@IvanOstr thanks! Yes, I believe the method can handle the addition of such a source term (and actually, any arbitrary source term as long as it doesn't depend on The software currently doesn't support it though. I can't promise I'll add such a feature in the short term (even though it seems nice to have it), but I'll gladly take a pull request (here and/or at https://github.com/gerlero/Fronts.jl) that adds it. |
Had more time to think about this one. I'm no longer that optimistic about the feasibility of supporting a source term—or at least, an arbitrary one—, as I'm not sure how that would interact with the method's assumption that the concentration is always equal to the initial value at I'm guessing you have thought about this far longer than I have (for our usage I've never had to consider a source term), so please correct me if you think I might be wrong here. |
Thank you very much for the responses :) |
@IvanOstr I've tried adding a source term to the equation. Unfortunately, it turns out that the Boltzmann transformation into an ODE needs a zero source term in order to be able to cancel out the |
Hello guys,
Good job on the package, it seems very handy and easy to use!
Although it is not an issure per se, I would like to ask you whether this software or method can be used for non linear diffusion equations other types also.
More specifically - I have a diffusion equation of plasma with "-kn^2" added to it. I want to solve it in r or r-z using cylindrical coordinates. What type of solution would you recommend?
My equation is:
![image](https://private-user-images.githubusercontent.com/39938309/268485485-a87c648b-0dcf-49f3-a652-81f1fe0b762a.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.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._1Ws-w1NBwRmW3IgLLsrJvvdjFAsS6o8YCmFv1QULlo)
Thanks and good day,
Ivan
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