Parameter fitting for a multi-domain PDE

New to Julia
1

Hi all,

I am trying to solve a system of reaction diffusion reaction equation on two different scale - one at a macro scale and one at micro scale. The micro-scale model receives conc as Dirichlet BC from the macro-scale model and the macro-scale model receives flux loaa into micro-scale model as a flux BC from the micro-scale model. I am doing experiments for this model to test the experimental validation of the model. So, my question is what would be the best way to approach this problem?
I have not used Julia before so I am not sure if this two different scale coupled model can be solved using MOLtoolkit or do i need to discretize them myself? Any sort of advice to the packages that might be useful is highly appreciated. Thank you!

I have also added a schematic of what I wish to achieve.

image
image1103×523 36.5 KB

2

Hi, this looks structurally similar to “Newman” battery model.

SkeelBerzins.jl may be a possibility - its author (you might contact him; I was his master thesis advisor) had such an example in his thesis, but it seems it is not in the package.

VoronoiFVM.jl (I am the main author) possibly may be tricked into it.

3

Thank you for the reply. I just checked out the package and it is interesting.
So, the idea would be to write two different transient diffusion-reaction equations and constantly go between the two scales at every time step? Is this your suggestion?
If I do that then would it be fast enough for the parameter fitting routine to converge? Please correct me if I am wrong these are just my first impressions.