time step

Exchange about the physics background, diffuse interface theory, etc..
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zhubq
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Joined: Mon Jun 22, 2009 7:33 pm

time step

Post by zhubq » Wed Jul 08, 2009 10:08 am

In MiCRESS, when automatic time step is set, the time step will be optimized. what is the criterion? Is it only fourier stable condition for both phase fields and concentration? I think there is also a constraint that the displacement of interface should be smaller than its thinkness, right?

Bernd
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Joined: Mon Jun 23, 2008 9:29 pm

Re: time step

Post by Bernd » Wed Jul 08, 2009 2:57 pm

Dear zhubq,

There are two independent criteria for automatic time stepping: a pure "phase-field criterion" and a segregation criterion. Both are stability criteria, i.e. the simulation usually gets numerically instable if a bigger time step is used.

According to the phase-field criterion, the time step must not exceed a critical value, depending on the spacial resolution delta_x, the surface energy sigma and the interface mobility µ:
PF-Criterion.gif
corrected by Bernd
PF-Criterion.gif (835 Bytes) Viewed 2714 times
n is a dimensionality factor and can be 1/2, 1/4 or 1/6 for 1D, 2D and 3D.

The segregation criterion is only important in case of concentration coupling and depends on the redistribution thermodynamics:
Segregation-Criterion.gif
Segregation-Criterion.gif (3.1 KiB) Viewed 2769 times
For both criteria, a prefactor can be defined as optional parameter in order to allow manipulation, a value of 1.0 exactly corresponds to the above shown criteria:

# Time-step?
# Options: (real) automatic [0<factor_1<=1] [0<=factor_2<=1] [max.] [min.]
# (Fix time steps: just input the value)
automatic 0.9 0.9 1.E-2 1.E-6

The resulting time-step as well as the time-step values of the individual criteria can be observed in the .TabT output. Because a "worst case scenario" is used for the segregation criterion, in some cases a prefactor >1 may be still acceptable and could even substantially increase performance.

Bernd

zhubq
Posts: 84
Joined: Mon Jun 22, 2009 7:33 pm

Re: time step

Post by zhubq » Wed Jul 08, 2009 10:19 pm

Thank you very much!
the first criterion is simply straighforward as the time step is uniform for each grid point. what about the second? Is the time step needed to calculate for each point and use the smallest one?
and the time step seems changing with time when no concentration coupling.
Last edited by zhubq on Wed Jul 08, 2009 10:46 pm, edited 1 time in total.

Bernd
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Re: time step

Post by Bernd » Wed Jul 08, 2009 10:44 pm

Exactly!

And this is the reason why we give to the user the possibility to specify a minimal (and maximal) time-step: If one single interface cell gets "crazy" due to a numerical problem, and TQ is calculating unreasonable thermodynamic parameters, this single cell could extremely lower the global time-step. This can practically freeze the simulation if no minimal time-step is used.

If a minimal time step is used, then the interface mobility µ of those (exceptional) cells which would need a smaller time-step than the minimal one is reduced accordingly. One should check the .mueS output to make sure that this happens only for few cells.


Bernd

zhubq
Posts: 84
Joined: Mon Jun 22, 2009 7:33 pm

Re: time step

Post by zhubq » Thu Jul 09, 2009 7:19 pm

Hi, Is the first formula true? I found a similar one like:
delta_t<n*(delta_x)^2/(sigma*mu)
yours is
delta_t<n*(delta_x)/(sigma*mu)

Bernd
Posts: 1074
Joined: Mon Jun 23, 2008 9:29 pm

Re: time step

Post by Bernd » Thu Jul 09, 2009 7:59 pm

Sorry, you are right :oops:

I correct it in the post above...

Bernd

mtoloui
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Joined: Mon Jan 26, 2009 8:31 pm

Re: time step

Post by mtoloui » Wed Dec 02, 2009 2:46 am

For a problem where the phase field is not coupled with diffusion, like grain growth, can we adjust the time step manually?
What is the meaning of he factors; factor_1 and factor_2 for an uncoupled problem?
For instance in grain growth problem, I want to use time steps three times smaller than the automatic ones, what should I do?

Bernd
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Joined: Mon Jun 23, 2008 9:29 pm

Re: time step

Post by Bernd » Wed Dec 02, 2009 1:09 pm

Hi mtoloui,

You can always adjust the time step manually, if you check yourself for numerical stability.
In the case of uncoupled simulations, factor_2 is meaningless, but for reasons of the input format, you have to specify it.
If you want to perform an uncoupled simulation with 1/3 of the time step of the automatic phase-field criterion, you just can use factor_1=0.333.

Bernd

deepumaj1
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Re: time step

Post by deepumaj1 » Tue Jul 21, 2015 1:19 pm

Hi Bernd, can I have the reference(Journal) from where these stability criteria are taken.

Bernd
Posts: 1074
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Re: time step

Post by Bernd » Tue Jul 21, 2015 3:35 pm

Hi deepumaj1,

these criteria are proprietary developments. We recently published an extended version of the segregation criterion for multi-ternary extrapolation (which is available in MICRESS Version 6.2):

https://www.sciencedirect.com/science/a ... 01652?np=y

The older one for multi-binary redistribution is given in this thread.
The phase-field criterion has not been published anywhere...

Bernd

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