Curvature output (.Krum)

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G_azizi
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Curvature output (.Krum)

Post by G_azizi » Fri Feb 04, 2022 6:13 pm

Hello,
Would you please tell me how micress calculate interface curvature and comes out with .krum file?
it would be appreciated if sent me the related reference(s). is MICRESS using following paper:
On the numerical evaluation of local curvature for diffuse interface models of microstructure evolution

Thanks,

janin
Posts: 39
Joined: Thu Oct 23, 2008 3:06 pm

Re: Curvature output (.Krum)

Post by janin » Mon Feb 07, 2022 4:35 pm

Hi,
In fact, two different ways of curvature evaluation are inplemented within Micress.

A general advantage of the phase-field method is that the kinetic phase-field equation ( derived from the free energy functional) implicitely accounts for capillarity forces and profile readjustment. The numerical evaluation of the curvature as part of the interfacial force is very accurate in Micress, especially as a dedicated finite-difference correction is used. It has, however, to be noted that the interfacial force term additionally accounts for another aspect: the readjustment of the diffuse phase-field profile. As both aspects are mixed within a single interfacial term, it cannot be used for independent curvature evaluation, as e.g. desired for output).

For this reason, the interfacial curvature which written to the output file *.krum stems from another evaluation, where the curvature is directly calculated by the divergence of the interfacial normal vector:
 \kappa =   \nabla \cdot \vec{n}_{\alpha\beta}  =   \nabla \cdot \quad
 \(\frac{ \nabla{\phi}_\alpha -  \nabla{\phi}_\beta}
        { |\nabla{\phi}_\alpha - \nabla{\phi}_\beta |} \)  .
It should be noted that the numerical dicretization of this direct evaluation can be much less accurate than the implicit evaluation used within the phase-field equation. It especially becomes critical if the diffuse interface profile is resolved by a low number of interface cells only, and no values from second-neighbor cells are available.

As far as I see, the paper you cited cannot be applied to Micress. The authors seem to compare the direct evaluation of the curvature (eq.1 and eq.2 in the paper) to the evaluation of the whole interface term (eq.6), but at first glance, I couldn't find any mentioning of the implicit profile readjustment, which represents the critical difference between the two terms. The implicit stabilization of the diffuse profile is a fundamental feature of the phase-field method and a major difference to level-set models. Moreover, they seem not to use any finite-difference correction, so the results should naturally become very inaccurate for low numbers of interface cells.

Best regards,
Janin

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