## time step

### time step

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?

### Re: time step

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

n is a dimensionality factor and can be 1/2, 1/4 or 1/6 for 1D, 2D and 3D.

The

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

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: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: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

### Re: time step

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.

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.

### Re: time step

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

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

### Re: time step

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)

delta_t<n*(delta_x)^2/(sigma*mu)

yours is

delta_t<n*(delta_x)/(sigma*mu)

### Re: time step

Sorry, you are right

I correct it in the post above...

Bernd

I correct it in the post above...

Bernd

### Re: time step

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?

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?

### Re: time step

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

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

### Re: time step

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

### Re: time step

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

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