Surface Area Convergence Data

About

The surface area calculations have come under scrutiny when examining the burn rate, and the lack of convergance therein. The point of this page, and the data presented within is to first determine whether the surface area calculations do converge over a set of reasonable resolutions. If not, it will hopefully provide insight into a solution.
The current setup is to test several different geometries including: cylinders, holes, cubic shapes, triangular shapes. Results can be seen below.

04/08/09 - Finished wedge runs from 45-85 degrees in 5 degree incriments. Brings up fact that I need to output surface area at each cell, thus I'll be implementing that code on Friday (or so). Most of the 0.725 runs are complete and 0.675 runs are about halfway there. Should have the data visually availale online by late Friday as well.
04/06/09 - Considering unpacked geometry as the major focus for correction at this point, 0.65 is no longer a candidate for a new threshold value for burning cells. While it creates quicker convergence of logarithmic trends in packed geometry, the overall error is larger. Furthermore, it appears that it creates instability in the number of burning cells, as can be seen in several cases below, including: both cases with 16 unpacked cylinders, and both cases with unpacked holes. Currently, values of 0.675 and 0.725 are being tested to see if results are better. Prediction: 0.675 will have a smaller slope than 0.7 for error trend, also that total error might be focused at a zero, closer to 1mm spacial resolution. As of now, the problem must lie within computation of density gradient. Thus, I'm pursuing more wedges of different angles, so that I can come up with some correction coefficient.
04/03/09 - Values of threshold value have been set to 0.65 and 0.75 and results have been added to this page. Mixed results occured, however, it still appears 0.7 is the best value. Most results, however indicated a value slightly lower (but nowhere near as low as 0.65) might be the best. However, as the graphs go up on this page, it becomes apparent that the threshold value is not the root of the problem. Where 0.65 increases rate of convergence for packed cylinders and holes (which is desirable), the value isn't appropriate for non packed cases. Furthermore, 0.75 appears to be better for some non packed cases, however, doesn't quite hold up for packed. Next step, to look at the wedge case, and really understand why the surface area calculations give error.
03/29/09 - Currently, the hypothesis being tested is that the threshhold value max mass/min mass for determining burning cell state is wrong. Different values are being tested to determine whether they provide better data. Overall, this idea arose from the exponential trend seen in the number of burning cells for circular geometries. The number of burning cells for double resolution should be a factor of 2 to 4 times that of the original value, most likely closer to 2. Extra cells would increase the amount of surface area, even to the point of overestimating the area, as can be seen in the unpacked cylinders.

Cases



16 Holes Not Packed



Wedge

Misc.

All file linked to by this page can be found in this directory.
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Contact: josuf dot the dot uf at gmail

Updated: 04/09/09
Created: 02/23/09