Handling Discontinuous/Jump Interface in Diffusion Problem

General discussions about how to formulate a script for FlexPDE.

Handling Discontinuous/Jump Interface in Diffusion Problem

Postby daveshel2003 on Wed Jun 17, 2020 7:53 am

Hi everyone,
I had a question pertaining to a diffusion B.C at the interface between two materials and hoping someone could help. In simplistic terms, I have two materials A and B that share an interface. A permeant (water) is diffuses through A and across the interface into B. Because these two materials have very different chemical potentials, the concentration at the boundary will not be continuous. For this particular set of materials, the concentration on the A side is roughly 1/2 of that on the B side at the interface. So I was curious if I could somehow add this constraint via the JUMP ccommand? This diffusion problem looks similar to the contact resistance examples, but there isn't really a "resistance" per se, so wasn't sure how to use the JUMP function in this case.

One option that came to mind was to completely decouple the concentration variable at the interface using the CONTACT(c)=0*JUMP(c ) where c is the concentration. But I would then need to somehow add a constraint that ties the two interfacial concentrations together (and I wasn't sure if that was feasible). Is there a way to do this?

My other fallback position is to just reformulate the entire problem in terms of gradients in the chemical potential, rather than gradients in concentration. I think this would take care of the continuity issue at the boundary issue, but I'd rather keep the problem in terms of concentration if that is possible....

thanks!
David
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Re: Handling Discontinuous/Jump Interface in Diffusion Problem

Postby moderator on Fri Jun 19, 2020 4:37 pm

You can use CONTACT/JUMP anytime you want a discontinuity in your variable at the interface. You will just have to decide on an appropriate factor to use in the JUMP statement. I think FlexPDE will be unhappy with a hard 0, so maybe something very small.
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Re: Handling Discontinuous/Jump Interface in Diffusion Problem

Postby moderator on Tue Jun 23, 2020 6:38 pm

Contact boundary condition is simply Flux=Coefficient*jump(variable).
If you can formulate a coefficient (not necessarily constant) from your chemical potentials that makes this equation correct, then you can use a simple Contact boundary condition.
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Re: Handling Discontinuous/Jump Interface in Diffusion Problem

Postby daveshel2003 on Wed Jul 08, 2020 8:59 pm

Thanks, I'll give the flux=Coeff*Jump(Variable) approach a try.

The CONTACT(c)=0*JUMP(c ) was mentioned in the manual under "Decoupling" section. I thought it just served as a flag to decouple the variables in each section, but after a second reading, I think it does this by forcing the flux to zero. So agree it is probably not the right approach....
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