Download ANSYS POLYSTAT 12.1 User`s Guide

Polystat User's Guide
In the figure below, we have four zones :
I II
.
Ωt
III
IV
. .
. . ...... ............... .. . .
. .. . .......... ... .
II
Next, we distribute randomly in all the flow domain, the same number of points N : we
assume that such a distribution is the optimal one.
At time t, for each zone, for the two distributions, we will determine the number of points
included in it. Based on these numbers, we can evaluate a relative error of distribution for
each zone Z :
ε (Z ) =
nbr ( Z) − nbo( Z)
,
N
(32)
where nbr is the number of points of the real distribution included in zone_Z, at time t and
nbo is the number of points of the optimal distribution included in the same zone.
If ε is zero for a zone, the right number of points is found in that zone,
If ε is negative for a zone, there is a lack of points in that zone compared to optimum,
If ε is positive for a zone, there are too many points in that zone compared to optimum.
Eventually, we can define a global index based on all the zones :
εg = 1
2
nb.zones
ε( z )
(33)
z =1
The number of points and the zones partitioning can influence dramatically the indices
described above. When comparing two different mixers, it is recommended to keep constant
the ratio number of points/zone. In order to have relevant results, this ratio should be higher
than 100 !
November 2009
26