## Numerical accuracy of double obstacle model

ripening phenomena, dislocations, grainboundary topology
zhubq
Posts: 84
Joined: Mon Jun 22, 2009 7:33 pm

### Numerical accuracy of double obstacle model

Hi there,

Long time no post. I recently implemented a very simple 1D recrystallization between two grains.
I found, the model has a 90% accuracy, e.g. the simulated interface velocity v.s. mobility x driving_force if I use a coarse grid; whereas if I decreased the grid spacing, the interface does not move unless I increased the number of grid points within the interface, e.g. from 5 to 7.
I think this is intrinsic problem the double-obstacle equation, right? Given a grid spacing, an interfacial energy, the driving force cannot be too small or too large.
If the driving force is too small, it will be like 0 (due to limited accuracy of floating number?); if it is too large, the interface will be distorted or unstable.

Ben

Bernd
Posts: 1250
Joined: Mon Jun 23, 2008 9:29 pm

### Re: Numerical accuracy of double obstacle model

Hi Ben,

Nice to hear from you!

In a certain sense, it is true that the double-obstacle potential has a stronger tendency to show discretization errors in the finite-differences scheme, because the interface profile has a much stronger decay at the borders of the interface. That is the reason why Janin implemented a correction scheme ("fd_correction") which helps a lot to achieve correct kinetics even for a small interface thickness. If you did not, you should definitively use "fd_correction".
But still, there is a rest of discretization errors which can cause the interface to stop if the driving force is too small. That means, even with df_correction, a small deformation of the interface profile is needed to move the front. This can be the case when a high interface energy is used (which works against deformation of the interface profile) and the absolute interface thickness is relatively small. We observed this sometimes in 1D-calculations where the interface energy was chosen too high.
Thus, I would expect that the problem should vanish either with using fd_correction (if you did not before) or with lowering the interface energy (or extra stabilisation if used). I a 1D simulation this should be no problem, in 2/3D this problem it is very unlikely that the problem occurs...
Please tell me whether my suggestion works. If not, I would like to see the input file and think about other possible explanations.

By the way: The problem of too large driving forces does not exist or is less severe for double-obstacle compared to double-well.

Bernd

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

### Re: Numerical accuracy of double obstacle model

Hi Bernd,

How are you?
Your suggestion is very useful. The fd_correction can overcome the problem completely.

Ben

Bernd
Posts: 1250
Joined: Mon Jun 23, 2008 9:29 pm

### Re: Numerical accuracy of double obstacle model

Dear Ben,

that is great!

Please note that with "fd_correction" the interface thickness appears 1 cell broader than without. This is due to a modified definition of the interface width. To get comparable results, you should decrease by 1 when switching on fd_correction.
Essentially, the new definition of the interface thickness is more correct, therefore we do not want to decrease internally...

Bernd