Civil Engineering Reference
In-Depth Information
In the previous example, difficulties would have arisen had the ratio of
u
to
c
x
been
large, because the transformation involving exp
would not have been numerically
feasible (Smith
et al
., 1973). Under these circumstances (and even when
(u/c
x
)
0)
equation (2.132) can still be solved, but with the drawback that the element and system
matrices become unsymmetrical, although the latter are still banded.
Program 8.8 will be used to solve a purely convective problem, that is with
c
x
=
c
y
=
0.
The problem chosen is again one-dimensional as shown in Figure 8.25, so the equation
c
x
=
c
y
=
f
fixed at 1.0 for 0.2 secs,
thereafter fixed at 0.0
1
2
3
4
convective
velocity
v=1.0 m/s
5
6
100 elements @ 0.02
= 2 m
197
198
199
200
y
nxe nye np_types
1 100 1
prop(cx,cy)
0.0 0.0
etype(not needed)
x_coords, y_coords
0.00 0.02
0.00 -0.02 -0.04 -0.06 -0.08 -0.10 -0.12 -0.14 -0.16 -0.18
.
y_coords(11-90) data omitted here
.
-1.80 -1.82 -1.84 -1.86 -1.88 -1.90 -1.92 -1.94 -1.96 -1.98
-2.00
201
202
x
∂f
=
∂
y
0
0.02 m
dtim nstep theta npri nres ntime ux uy
0.04 25 0.5 1 3 25 0.0 1.0
fixed_freedoms,(node(i),i=1,fixed_freedoms)
2
1 2
Figure 8.25
Mesh and data for Program 8.8 example
