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Seeking help for Solid State Li battery modeling

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I'm working on a project for my master thesis. I need to simulate a solid state li battery but unfortunatly our school doen't provide the liscence for the battery simulation. Therefore, I'm doing it with equetion based modeling. The problem that I face with is that I cannot cuople the DAE for current with the other two PDEs since the variables are unknown for the DAE.

I would be really grateful if you have any suggestion with my modeling as my thesis depends on it.

Also the sample of what I'm doing can be found in comsol website: https://www.comsol.com/model/all-solid-state-lithium-ion-battery-12451


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