Page 112 - The Combined Finite-Discrete Element Method

SORTING CONTACT DETECTION ALGORITHM 95

10
9

8 •2
•1
•7
7 •4
•3 •6
6 •8
•5
5
4
d
3
y 2 d

1
x min
1 2 3 4 5 6 7 8 9 10
y min
x
Figure 3.21 Space divided into identical cells large enough to contain the largest discrete element
comprising the system. Centres of discrete elements are marked with dots; the thicker line marks
the bounding box of physical space.

Integer array X 4 5 4 5 4 5 3 6

Integer array Y 7 8 6 7 5 6 7 6

Integer array D
1 2 3 4 5 6 7 6
Figure 3.22 mapping of discrete elements onto cells for discrete element system shown in
Figure 3.21.

array D contains the ‘name’ of the discrete element, and arrays X and Y contain the
corresponding cell.
Step 2: Sorting of arrays representing mapping: after discrete elements have been mapped
onto cells, arrays X, Y and D are obtained. Array X contains the integerised current
x coordinates of all the discrete elements; array Y contains the integerised current y
coordinates of all the discrete elements; and array D contains the discrete element numbers.
It is worth noting that array D contains sequence 1, 2, 3,...,N, where N is the total
number of discrete elements comprising the combined finite-discrete element system.
Arrays X and Y contain a more or less random series of integer numbers, as shown in
Figure 3.22.