Sharp interface limit and Thin interface limit in phase field model

[J. M. Kim]

Hi everyone.

 

When i use simulate some examples for phase field model (grain growth model), in order to save simulation time i change the grid space to 5times higher than original grid space.

 

The result is quiet unchanged, but i wander why.

 

If the phase fied equaions are not coupled with other parameters like concentration or temperature, some references mention that the results are independent of interface width.

 

Why the reuslts are independent of the interface width?

 

Is this connetected with Sharp interface limit and Thin interface limit, and what is the exact definition of two limits?

Best regars,

Kim

[Roma Gurung]

Hi Kim,

For example if quantitative phase field approach is utilized for phase field model in accordance to the article http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.025502, the terms interface width (l_i), size of the grid space (dx) and average radius of curvature (r) of the grain are related. The article mentions that , for l_i < 5r, simulations are more accurate for greater values of the ratio l_i/dx.

Yours Sincerely,

Anil Kunwar

[J. M. Kim]

Thank you for your response and reference.

That will be a great help.

Best regards,

Kim

[Aagesen, Larry K]

One thing to clarify is the difference between interface width and grid spacing. In phase-field models, the interface width is a function of model parameters that enter the governing equations, and is not dependent on the grid spacing or other details of the discretization. For example in the most basic Cahn-Hilliard model, the interface width is a function of the gradient energy coefficient kappa and the height of the free energy barrier between equilibrium phases. When you change the grid spacing and keep the system dimensions the same, you change the number of elements in the interfacial region, but not the width of the interface in the coordinate system you have chosen. So if you were to keep the system dimensions the same, simulate an interface between two phases with increasingly finer resolution, and plot the results on top of one another, you would see the same interface shape (width) represented with an increasing number of data points in the interfacial region, but the interface width in your coordinate system would not change.

Now as far how the change in grid spacing might affect the physics of your simulation, if you keep the governing equations of the model the same, as long as the number of element in the interface is high enough, you should get the same physical results. For the basic Cahn-Hilliard model I referred to earlier, a good rule of thumb would be that you would want at least 4-5 elements in the interface (defined as 0.1 < c < 0.9 if the equilibrium values of c are 0 and 1) if you are using linear Lagrange elements. You may be able to get away with fewer elements than that, and if you are looking only at qualitative differences after a few time steps, you may not notice any changes. But if you want to lower resolution below the 4-5 elements through the interface that I mentioned you probably should plot the system energy as a function of time to verify decreasing resolution is not affecting the system's evolution.

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[Roma Gurung]

hi Larry,

thank you for the clear explanation.

yours sincerely,

anil kunwar

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[J. M. Kim]

Really appriciate your detail explanation, It does a real big help to me.

 Best regards,

Kim

[Daniel Schwen]

Larry, we should probably start collecting answers like this one on a FAQ page on the PF wiki pages.
Daniel

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[Aagesen, Larry K]

Have a look at the new phase-field specific FAQ:

http://mooseframework.org/wiki/PhysicsModules/PhaseField/PhaseFieldFaq/

We will continue to add to it as questions come up.

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[Roma Gurung]

MOOSE team has encouraged us in learning emerging concepts of phase field modeling in computational materials science. 

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