Diffusion Equation with Limited Source

[gschrank]

Good afternoon!

I've been working on a multiphysics model that combines transport phenomena with a user solver. In the model, I am, in part, modelling the diffusion of a reactant from a sources in a reaction vessel. The source is modeled using mass transfer boundary condition with the equilibrium (i.e. the "external") concentration being governed by the local temperature. The model is a transient model.

It is becoming apparent that it would be useful to try to model my sources as limited sources. That is, in the current formulation, no matter how quickly the mass transfer occurs at the source, it can always produce more. This is not the reality of the situation, and in actuality the source can be depleted because there is only so much initial material at the source.

I was thinking I could probably write a users' function to keep track of this. The function would have some initial amount of material on the boundary (the initial mass), and then would simply keep track of how much the material is reduced at each timestep based on the mass flux. However, before I go and write something, I wanted to check if this is already available in the Elmer framework.

[raback]

Hi

To my recollection there is no such model out currently. Actually we are working with a model for Li-Ion-battery where the source is computed at each node from a 1D transient diffusion equation. When the equation is exhausted the battery is empty. Unfortunately this model is not yet out under open source.

I could see something more simple here as well. You could use the ModelPDE and activate just the mass matrix (time derivative part). Not maybe ideal since the equation is really not position dependent so solving for a linear system is somewhat an overkill.

Would your model be simple 0D reservoir at each node? I guess a lot on the optimal strategy depends on how the flux depends on the source. For Li-Ion the Butler-Volmer equations are highly nonlinear causing some headache.

-Peter