Page 148 - Introduction to Computational Fluid Dynamics

P1: IWV
CB908/Date
0 521 85326 5
0521853265c05
5.3 METHOD OF SOLUTION
Node tagging is now accomplished using the following convention: May 20, 2005 12:28 127
1. NTAG (I, J) = 0 identifies all nodes interior to the domain. That is, nodes falling
on the boundaries a-m, m-n, n-l, and l-a are excluded.
2. NTAG (I, J) = 1 identifies all interior nodes in the inert areas.
3. NTAGW (I, J) = 11, 12, 13, 14, 15 identifies nodes adjacent to the WEST
boundary with 11 for inflow boundary, 12 for symmetry boundary, 13 for exit
boundary, 14 for wall boundary, and 15 for periodic boundary. NTAGW is zero
for all other nodes.
4. Similarly, NTAGE (I , J) = 21, 22, 23, 24, 25 identifies nodes adjacent to the
EAST boundary, NTAGS (I , J) = 31, 32, 33, 34, 35 identifies nodes adjacent to
the SOUTH boundary, and NTAGN (I, J) = 41, 42, 43, 44, 45 identifies nodes
adjacent to the NORTH boundary.
Using this convention (which is quite arbitrary), NTAGW will have a fi-
nite number for i = 2 and j = 2, 3,..., 7 (boundary a-b) and for i = 6 and
j = 8, 9,..., JN − 1 (boundary c-d). Similarly, NTAGN will be finite for j = 7
and i = 2, 3, 4, 5 (boundary b-c), for j = JN − 1 and i = 6, 7, 8, 9, and again for
j = 7 and i = 10, 11,..., IN− 1 (boundary f-g). NTAGS and NTAGE can be
similarly specified.
The choice of numbers 11, 12, 13, etc. in NTAGW is arbitrary but brings one
advantage. That is, for near-west boundary nodes, NTAGW/10 = 1 in FORTRAN
and, therefore, a WEST boundary is readily identified. Similarly, NTAGN/40 = 1
readily identifies a NORTH boundary. Once this identification is done, the actual
numbers (11, 12, etc.) identify the type of boundary condition and therefore Su i, j
and Sp i, j for the near-boundary nodes can be set up. This facilitates specification of
different boundary conditions at the same physical boundary. Thus, if boundary a-b
is a wall, a part of it may be insulated and the rest may receive heat flux. Similarly,
with respect to mass transfer, a part may be inert but the rest may experience a finite
mass transfer flux.
Finally, at the inert or blocked node where NTAG (I, J) = 1, one simply specifies
30
30
Su i, j = 10 desired , Sp i, j = 10 . (5.80)
Examination of Equation 5.65 will show that since AP i, j can never be very large,
these settings render i, j = desired at the inert nodes. In Figure 5.6, the inert
regions are outside the domain of interest. However, it is easy to appreciate that
one can even have inert regions that are enclosed by the overall domain of interest
(hence the term blocked region), as shown in Figure 5.7. The figure also shows
how a domain with irregular boundaries may be specified by node tagging. Here,
10
the irregular boundary is approximated by a staircase-like zigzag boundary. Such

10 The accuracy of the solution will of course depend on the number of steps into which the true
boundary is subdivided.