Page 271 - Process Modelling and Simulation With Finite Element Methods

258 Process Modelling and Simulation with Finite Element Methods

from the nearest two “sink’ segments. The farthest sink, in the third quadrant,
gets about half the flux of the other two sinks.
The time dependent solution for the charges 91, q2 and q3 asymptotes to
plateau values near to those computed in the forward problem (see before (7.5))
as shown in Figure 7.3. The arbitrary split between the graphs is due to the
solution in three stages, arbitrarily split among (1) t E [0, 0.11; (2) t E [0.1, 11;
and (3) t E [l, 41. As the system approaches the time asymptote, i.e. in interval
(3), it is not particularly stiff and computes rapidly. The first interval is
extremely stiff andonly minor fluctuations in the potential lines with fast
animation, and no change to the colour coding.

Max I
Time=O.Ol Contour phi Time=O.l Contour ohi Max 1
o 9524 0 9524
0 9048 0 9048
0 8571 0 8571
0 8095 0 8095
0 7619 07619
07143 07143
0 6667 0 6667
0619 0 619
0 5714 05714
0 5238 0 523
0 4762 04762
0 4286 0 4285
0 381 3333
0 0 381
0 3?33
0 2857 0 2657
0 2181 0 2381
0 1906 0 1905
0 1429 0 l4X
0
0 0952 0476 0 0 0952 Od76
15 1 05 0 05 1 15 N” 234ea 15 1 05 0 05 1 15 M“ 0
Tirne=0.35 Contour: phi Mex I Tirne=O.B Contour: phi Idax 1
I a09524
0 9124
0 9048
08571
0 81395
07619
0 7143
0 5567
0 619
05714
0 6238
04762
0 4286
0 381
0 3333
0 2857
0 2381
0
01905 1429
o 0952
U- 0 0475
1s 1 05 0 05 1 15 *no 15 1 05 0 05 1 15 U” 0
Time=O.E Contour: phi MllX 3 Tirne=l Contour. phi Mar 1
0 9524 0 9524
0
0 901B 8571 0 3246
o no95 0891
0 6095
0
07619 0 7519 7143
0 7143
0 6667
0619 0 6667
0619
05711 05714
0 5238 0 6238
0 4m 0 4762
0 dzt6 0 4286
0 381 0 381
0 3333 0 3333
0 2657 0 2857
0 2381 0 2381
0 1Sa5 0 1905
014Z 0 1429
0 0476 0 0476
0 Oh2
0 0952
16 1 05 0 05 1 li MnD 1 05 05
15 0 1 15 M“ 0
Figure 7.2 Progression of potential contours from an initially electrically neutral domain with a
pseudo-time scale imposed. The voltage from the “firing” electrode with outward unit normal
(0.707,0.707) diffuses out through the duct, being warped by the inclusions, eventually reaching an
asymptotic profile that changes imperceptibly with further time evolution. Computations from time
14 show requires small step sizes.