Dear Bernd:
I am simulating the solidification of some multi-component Al alloys. I have some questions about some numerical parameters in the dri file
(1) phase minimum: Currently, I use 5E-4.
(2) interface thickness: I use 5 cells.
The solidified phases include solution phase fcc_a1(Al), some intermetallics with no homogeneity, diamond(Si) phase. I have tried some smaller values of "phase minimum"( to 1E-8 gradually) or changed interface thickness to 4 cells. but it seems there is no significant difference. But I am still not sure whether they are really important because there are intermetallics with no homogeneity. Is the phase minimum or interface thickness an important numerical parameter in your previous simulation on multi-component Al alloys? How did you choose them ?
If I set "time step" in the dri file, another input should be set in the last part of dri file.
(3) # Maximum number of calls to the concentration solver per iteration?
Currently, I use 100. I am not sure about this input, could you give me some suggestions?
Thank you very much.
Best wishes.
swh
about some numerical parameters
Re: about some numerical parameters
Dear swh,
(1) The phase minimum should be small enough in order not to cause too much trapping of solute (as the step from phMin to 0 is not involving redistribution anymore). From this point of view, a value of 1E-4 is typically small enough. In cases when the factor between the composition of an element between two phases is very high (or small), an at least as small value is needed for phMin. Otherwise, the formation of a new interface cell with fraction phMin and high composition of this element would not be possible without forcing the composition of the other phase to be negative.
Apart from that, too small values of phMin increase the tendency of extreme composition values in the vanishing phase and and may favour fluctuations (see here).
There has been already a thread about the phase minimum (see here).
(2) A high interface thickness is important for a correct evaluation of curvature, like e.g. in grain growth. On the other side, increasing the interface thickness (in cells) is very bad for performance, because a higher resolution is needed when a certain size (e.g. a lamella of an intermetallic phase) has to be resolved. Therefore, in your case, I would go for the smallest interface thickness which still works properly - interface energies are anyway not known exactly, and exact ripening kinetics are not first priority. This strategy allows you to simulate a substantially bigger domain, or to better resolve the intermetallics!
The smallest reasonable value for the interface thickness is 3.5 cells or 2.5 cells with fd_correction. In the latter case, the interface thickness is defined differently, but the effective thickness will be the same! fd_correction is available since version 6 and should assure the correct interface profile.
(3) First of all I want to point out that automatic time stepping should be used as a default. It reduces the number of numerical parameters and strongly optimizes performance. Manual time stepping should be used only for test purposes or in exceptional cases.
In case of using manual time stepping, MICRESS asks for a number of (potential) diffusion time steps per phase-field time step. If the number is too small to fulfill a stable diffusion calculation, MICRESS will complain. If the number is higher than necessary, it will be more easy for MICRESS to synchronize diffusion and phase-field time stepping, and performance should increase slightly. (Note that the diffusion time steps will not decrease but rather increase slightly!). I recommend a value which is about 2-10 times higher than the required value (i.e. the value where MICRESS starts complaining).
Bernd
(1) The phase minimum should be small enough in order not to cause too much trapping of solute (as the step from phMin to 0 is not involving redistribution anymore). From this point of view, a value of 1E-4 is typically small enough. In cases when the factor between the composition of an element between two phases is very high (or small), an at least as small value is needed for phMin. Otherwise, the formation of a new interface cell with fraction phMin and high composition of this element would not be possible without forcing the composition of the other phase to be negative.
Apart from that, too small values of phMin increase the tendency of extreme composition values in the vanishing phase and and may favour fluctuations (see here).
There has been already a thread about the phase minimum (see here).
(2) A high interface thickness is important for a correct evaluation of curvature, like e.g. in grain growth. On the other side, increasing the interface thickness (in cells) is very bad for performance, because a higher resolution is needed when a certain size (e.g. a lamella of an intermetallic phase) has to be resolved. Therefore, in your case, I would go for the smallest interface thickness which still works properly - interface energies are anyway not known exactly, and exact ripening kinetics are not first priority. This strategy allows you to simulate a substantially bigger domain, or to better resolve the intermetallics!
The smallest reasonable value for the interface thickness is 3.5 cells or 2.5 cells with fd_correction. In the latter case, the interface thickness is defined differently, but the effective thickness will be the same! fd_correction is available since version 6 and should assure the correct interface profile.
(3) First of all I want to point out that automatic time stepping should be used as a default. It reduces the number of numerical parameters and strongly optimizes performance. Manual time stepping should be used only for test purposes or in exceptional cases.
In case of using manual time stepping, MICRESS asks for a number of (potential) diffusion time steps per phase-field time step. If the number is too small to fulfill a stable diffusion calculation, MICRESS will complain. If the number is higher than necessary, it will be more easy for MICRESS to synchronize diffusion and phase-field time stepping, and performance should increase slightly. (Note that the diffusion time steps will not decrease but rather increase slightly!). I recommend a value which is about 2-10 times higher than the required value (i.e. the value where MICRESS starts complaining).
Bernd
Re: about some numerical parameters
Hi Bernd,
I am do simulation involving Mn diffusion. Since I use a high mobility, the time step for phase-field solver is smaller than diffusion time step.
will it cause a numerical problem? Does the diffusion time step have to be set the same as phase-field solver in such a case?
Thank you.
Ben
I am do simulation involving Mn diffusion. Since I use a high mobility, the time step for phase-field solver is smaller than diffusion time step.
will it cause a numerical problem? Does the diffusion time step have to be set the same as phase-field solver in such a case?
Thank you.
Ben
Re: about some numerical parameters
Hi Ben,
generally speaking, there should be no problem with numerics due to that. But - if Mn is the fastest diffusing element - it could indicate that the numerical parameters (resolution, interface mobility) have not been chosen properly. E.g., if the transformation is assumed as diffusion limited, the mobility may be just higher than necessary, causing an unnecessary performance loss.
If there are good reasons why you want to use a such high interface mobility, you might think about using the "Cushion" option, which is available with terse input mode in the diffusion data input:
e.g.
...
1 2 multi
1 2 Cushion 0.1
...
end_diffusion_data
will reduce the diffusion time step for component 1 in phase 2 by a factor of 10 and possibly increase accuracy under such conditions.
Bernd
generally speaking, there should be no problem with numerics due to that. But - if Mn is the fastest diffusing element - it could indicate that the numerical parameters (resolution, interface mobility) have not been chosen properly. E.g., if the transformation is assumed as diffusion limited, the mobility may be just higher than necessary, causing an unnecessary performance loss.
If there are good reasons why you want to use a such high interface mobility, you might think about using the "Cushion" option, which is available with terse input mode in the diffusion data input:
e.g.
...
1 2 multi
1 2 Cushion 0.1
...
end_diffusion_data
will reduce the diffusion time step for component 1 in phase 2 by a factor of 10 and possibly increase accuracy under such conditions.
Bernd
Re: about some numerical parameters
Hi Bernd,
I got the mobility from simulation considering carbon diffusion, then applied it to simulation considering manganese diffusion.
Maybe I can reduce the magnitude of mobility with some tests proving that diffusion control is reached, mobility has little effect on kinetics.
Do you think I should reduce it to a level with which the diffusion time step is smaller than phase-field time step?
By the way, I was told to choose the interface thickness smaller than diffusion distance. However similar to solidification, I have two phases with quite different diffusivity.
If I use the diffusivity in solid, the interface thickness will be 1-2nm which is impossible in my modelling scale. So I use the diffusivity in liquid. But I am not sure whether there is problem, e.g. artifact, numerical error.
Ben
I got the mobility from simulation considering carbon diffusion, then applied it to simulation considering manganese diffusion.
Maybe I can reduce the magnitude of mobility with some tests proving that diffusion control is reached, mobility has little effect on kinetics.
Do you think I should reduce it to a level with which the diffusion time step is smaller than phase-field time step?
By the way, I was told to choose the interface thickness smaller than diffusion distance. However similar to solidification, I have two phases with quite different diffusivity.
If I use the diffusivity in solid, the interface thickness will be 1-2nm which is impossible in my modelling scale. So I use the diffusivity in liquid. But I am not sure whether there is problem, e.g. artifact, numerical error.
Ben
Re: about some numerical parameters
Hi Ben,
if the spatial resolution is high enough, you can just check out how much you can reduce the interface mobility without changing results. The time steps are no valid criterion!
Otherwise, you have to calibrate the interface mobility accordingly if diffusion limited growth kinetics is to be obtained (see here). Anyway, you will gain a lot of performance!
Regarding your second question, if quantitative phase-field simulation requires the diffusion length to be much bigger than the interface thickness, this always refers to the phase with the higher diffusion coefficients (liquid)!
Bernd
if the spatial resolution is high enough, you can just check out how much you can reduce the interface mobility without changing results. The time steps are no valid criterion!
Otherwise, you have to calibrate the interface mobility accordingly if diffusion limited growth kinetics is to be obtained (see here). Anyway, you will gain a lot of performance!
Regarding your second question, if quantitative phase-field simulation requires the diffusion length to be much bigger than the interface thickness, this always refers to the phase with the higher diffusion coefficients (liquid)!
Bernd