Zienkiewicz O.C., Taylor R.L. Vol. 3. The finite - tiera.ru

x 2
1.0
0.8
0.6
0.4
0.4
0.2
'CBS'
0.2
'Ghia'
'CBS'
0
–0.4 –0.2 0 0.2 0.4 0.6 0.8 1.0
0
–0.4 –0.2 0 0.2 0.4 0.6 0.8 1.0
u 1
u 1
(a) Stokes flow, viscosity 1
(b) Re = 400
x 2
1.0
0.8
0.6
Use of the CBS algorithm for incompressible or nearly incompressible ¯ows 99
smaller number of iterations is required to reach steady state and gives an accurate
solution even at the higher Reynolds numbers. Here a solution for a Reynolds
number of 10 000 is given in Fig. 4.9.
4.3.3 Fully explicit mode and arti®cial compressibility
x 2
x 2
0.4
0.4
0.2
'Ghia'
'CBS'
0.2
'Ghia'
'CBS'
0
–0.4 –0.2 0 0.2 0.4 0.6 0.8 1.0
0
–0.6 –0.4 –0.2 0 0.2 0.4 0.6 0.8 1.0
u 1
u 1
(c) Re = 1000
(d) Re = 5000
Fig. 4.4 Lid-driven cavity. u 1: velocity distribution along vertical centre-line for different Reynolds numbers
(semi-implicit form).
It is of course impossible to model fully incompressible problems explicitly as the
length of the stable time step is simply zero. However, the reader will observe that
for steady-state solutions the ®rst term of the continuity equation, i.e.
1
c2 @p
…4:20†
@t
does not enter the steady-state calculations and we could thus use any reasonably
large value of c 2 instead of in®nity. This arti®ce has been used with some success
and the solution for a cavity is reported in reference 9 so we do not repeat the results
here.
1.0
0.8
0.6
1.0
0.8
0.6