Page 196 - Introduction to Computational Fluid Dynamics

P1: IWV
CB908/Date
0 521 85326 5
0521853265c06
6.3 UNSTRUCTURED MESHES
Table 6.1: Vertex and element files. May 25, 2005 11:10 175
Vertex file Element file
NV x 1 x 2 x 3 NE NV1 NV2 NV3
1 0.5 0.0 0.0 1 24 33 25
2 1.5 0.0 0.0 2 24 32 33
3 1.5 1.0 0.0 3 19 39 25
4 −1.5 1.0 0.0 4 39 24 25
5 −1.5 0.0 0.0 5 25 33 42
6 −0.5 0.0 0.0 6 42 33 17
. . . . . . . .
. . . . . . . .
. . . . . . . .
11 1.3229 1.0 0.0 12 18 42 4
. . . . . . . .
. . . . . . . .
. . . . . . . .
24 −1.2708 0.2978 0.0 26 29 35 34
. . . . . . . .
. . . . . . . .
. . . . . . . .
31 0.509 0.3404 0.0 33 34 35 15
. . . . . . . .
. . . . . . . .
. . . . . . . .
39 −1.3958 0.2127 0.0 56 7 8 27
40 1.357 0.2127 0.0 57 9 10 26
41 1.357 0.7659 0.0 58 19 25 18
42 −1.3958 0.7659 0.0 59 20 21 24

writing a separate computer program. It is clear from Figure 6.7 that different ver-
tices will have different numbers of neighbouring vertices. In this approach, to
adopt an IOCV method for discretisation, one needs to construct a control volume
surrounding node P. Figure 6.8(a) shows a typical vertex P along with its neigh-
bours. Different approaches are possible for the control-volume construction, but
the one adopted here is as follows:

1. Identify elements having a common vertex at P.
2. Locate centroids of each element. This can be done by using known coordinates
of vertices of each element.
3. Connect the successive centroids by straight lines (shown dotted in Figure 6.8).

The dotted lines will enclose P and thus form a control volume surrounding
P. Such a construction at all vertices will yield a non-overlapping set of control
volumes. Discretisation can now be carried out for a typical control volume.
One disadvantage of this approach concerns application of boundary conditions.
Thus, consider a vertex (or a node) at the junction of two boundaries as shown in
Figure 6.8(b). Now, if the boundary conditions at the two boundaries of the junction
are different, the boundary condition at the junction node cannot be uniquely de-
fined. It is possible to overcome this difficulty but only at the expense of additional
bookkeeping.