Page 229 - Introduction to Computational Fluid Dynamics

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b 0 521 85326 5 2D CONVECTION – COMPLEX DOMAINS
b e
f
c
c
a d
a
d

TETRAHEDRAL ELEMENT PENTAHEDRAL ELEMENT
Figure 6.30. Some 3D polyhedral cells.

These techniques for sparse matrices become productive when the number of
elements is large.
4. It may surprise the reader to note that the unstructured grid procedure is the most
general. Since the procedure can handle any polygonal cells (in two dimensions),
the Cartesian and curvilinear grids are already included. In the latter cases,
however, the advantages of an (I, J) structure must be sacrificed.
5. The procedure for unstructured grids developed in this chapter can be straight-
forwardly extended to 3D polyhedral cells (see Figure 6.30). The only difference
in three dimensions is that all evaluations with i = 1, 2 must now be carried
out over i = 1, 2, and 3. By way of illustration, consider the line structure at
the triangular cell face of a tetrahedral cell shown in Figure 6.31(a). Two lines

c 5

t
ξ 2
t c 6 E 2
n c 2
E 2
c c 4
c r
ξ 3
r
n
P 2
s
E 1 c 3
P 2 s
P
e c 1
E ξ 1
P 1
a) LINE STRUCTURE NEAR A CELL FACE b) CELL FACE CONTROL VOLUME
Figure 6.31. Construction at the polygonal cell face.