MICRESS Forum

Is there any detailed description of averaging method by which MICRESS calculates the average driving force? e.g. what is the meaning and functionality of the averaging factor which comes after the keyword "avg"?

Dear mtoloui,

unfortunately there is no detailed description existing about that. The parameters for the DeltaG options are for fine-tuning of the phase interaction. You should not pay too much attention to these parameters unless you really need to fine-adjust the kinetics if you work with low resolution or if you encounter numerical problems.

The first parameter "avg" stands for the intensity of averaging or a relative length over which averaging is done. This allows you to continuously move from no averaging to "complete" averaging of the chemical driving force along the interface normal. Averaging of the driving force avoids a spreading of the interface, which can occur if the resolution is too low and there is a strong gradient of the driving force over the interface. On the other side, averaging increases artificial solute trapping. The allowed values range from 0 to 1 (no averaging to complete averaging), a typical value that works in most cases is 0.5.

The second parameter "max" allows to specify an upper limit for the driving force in J/cm3. This mainly increases numerical stability. One should choose a value which is above what is to be expected to be on the save side (e.g. 1000). This parameter can be very interesting if e.g. extrem thermal conditions at the initial stage of a simulation for a short period at the beginning lead to numerical problems which would not allow you to get savely to a later more interesting stage. Be cautions not to "hang" in the limit if this is not intended!

The third parameter, "smooth" consists in a random rotation of the averaging direction around the interface normal (in degrees). I believe that this reduces the numerical grid anisotropy, but there is still no clear conclusion ...


Bernd

Dear Bernd,
As a matter of fact, I want to know how you calculate the average. Which formula do you use to calculate the average driving force? Is it just a mean of dG over the nodes at the interface or is it a weighted average or something else?

Dear mtoloui,

Excuse me that I did not answer your question completely!

The chemical driving force dG for each interface grid point is averaged along the direction of the normal through the interface. The weight of each cell in the averaging process consists of 3 factors:

1.) the length of the path along the normal through the given cell (i.e., cells which are just touched slightly by the normal direction have less weight). This is important to avoid possibly strong fluctuations of the driving force if the normal direction is changing slightly. A 'locking' of the averaging path to the main grid directions can be avoided by an extra noise on the normal direction using the 'smooth' keyword (see last post).

2.) the gradient term (i.e., effectively by the term SQRT(phi1*phi2) for the double obstacle potential) in the cell along the gradient path.

3.) according to the avg input which is transformed to an averaging length l:

l = avg / ( 1 - avg ) *eta

where eta is the interface thickness. The distance for averaging is restricted to the distance l from the interface grid point for which the averaged driving force is calculated. Inside the averaging region the corresponding weighting factor is proportionally decreasing from 1 in the center to 0 at the edge, outside it is 0.

For the extreme cases of avg=0 and avg=1 one gets thus no averaging at all or complete averaging over all the lenght of the interface including the weighting according to 1) and 2).

The cut-off of the driving force (max keyword) is done before averaging. A smoothing of the cut-off is done using a tanh function.