FD correction

Exchange about the physics background, diffuse interface theory, etc..
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khajezade
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FD correction

Post by khajezade » Tue May 15, 2018 3:08 am

Hi there;

I was wondering how do you extend your FD-correction formulism to multicomponent systems with non-conserved phase parameter? Any paper that I can refer to?

Thanks,

Ali

deepumaj1
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Re: FD correction

Post by deepumaj1 » Tue May 15, 2018 4:31 am

Hi Ali,
I would like to recommend you to look at the following papers in this context, if you haven't gone through them already.
J. Eiken, B. Böttger, and I. Steinbach, Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application, Phys. Rev. E 73, 066122 (https://journals.aps.org/pre/abstract/1 ... .73.066122)

J. Eiken, The Finite Phase-Field Method - A Numerical Diffuse Interface Approach for Microstructure
Simulation with Minimized Discretization Error, MRS Proceedings 2012 1369 : mrss11-1369-xx05-05
DOI: 10.1557/opl.2012.510. (https://www.cambridge.org/core/journals ... 559C1EC8C0)

ps: You made multiple entries for this post. Please delete one of them. Thanks.

Best Regards,
Deepu

khajezade
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Re: FD correction

Post by khajezade » Tue May 15, 2018 7:54 pm

Hi Deepu,

Thanks for the reply.
Yes, I have already studied these papers. I think the first paper is the general guideline of how you have got the phase field equation and also extrapolation scheme to use external thermodynamical databases. However, I couldn't find anything regarding FD-correction (Please correct me if I am wrong). The second paper is actually the one that raised my question about finite difference correction. All the formalism is about systems with two phases. Basically, you assume a sinusoidal form for one phase at the interface, then rewrite the general phase field equation with that. It is really simple as phi_2=1-phi_1. What if you have more non-conserved order parameters? How do you rewrite equation 31 in the first paper with an analytical profile? I can understand that I can write the profile of each order parameter as a sine function but I do not know the contribution of each profile.


Best Regards,

Ali

janin
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Re: FD correction

Post by janin » Wed May 16, 2018 12:31 pm

Hi Ali,
you are right, the FD-correction approach was theoretically derived for two-phase systems only. The problem with multiple phases is that we don't have the analytical formulation of the phase-field profile within the junction areas. I spend a lot of time on this problem, but so far without success. The interface profile is already very complex for simple triple junctions, but even more for unequal interfacial energies in 2D and much more complex in 3D and for higher order junctions.
Therefore, in Micress, we use the complete theoretical FD-correction only for two-phase interface cells, while the FD-correction terms for the junctions were pragmatically adjusted by comparing the Micress results with analytical benchmarks solutions (e.g. running the benchmark B012 in the Examples/benchmark folder for varying dihedral angles).
Regards,
Janin

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