216
7. Solution of the Navier-Stokes Equations
t
- Nonuniform
, \ --------- Uniform
8
-
Extrapolated
,
-
,
,
,
-
, ,
,
5
-
I
'\
-
'\
100
10000
No. of CV
Fig. 7.18. Heat flux through isothermal walls, Q, (left) and the errors in the
calculated heat flux and strength of the eddy (right) in a buoyancy-driven cavity
flow at the Rayleigh number Ra = lo5 and Prandtl number Pr = 0.1, as a function
of grid fineness (calculation using CDS and both uniform and non-uniform grids)
10
We also checked the effect of the under-relaxation factor for the velocity
on the solution in this case. As expected, it is much smaller than in the case
of lid-driven cavity, since the pressure variation is much smoother here. On
the coarsest grid (8 x 8 CV), the difference between solutions using a, = 0.9
and a, = 0.5 is about 0.23%, while on the grid with 128 x 128 CV it is below
0.0008%.
The efficiency of calculating steady incompressible flows using implicit
methods based on SIMPLE algorithm and colocated grids can be substantially improved using multigrid method for outer iterations. This will be
demonstrated for the two test cases studied here in Chap. 11.
Q. Nonuniform
----qm.., Nonuniform
- - - - - - - - - Q, Uniform
,/
------ $,... Uniform , , " /
- : - Ideal Slope
,,I
//
I
4
I
.01
,001
7. Solution of the Navier-Stokes Equations
t
- Nonuniform
, \ --------- Uniform
8
-
Extrapolated
,
-
,
,
,
-
, ,
,
5
-
I
'\
-
'\
100
10000
No. of CV
Fig. 7.18. Heat flux through isothermal walls, Q, (left) and the errors in the
calculated heat flux and strength of the eddy (right) in a buoyancy-driven cavity
flow at the Rayleigh number Ra = lo5 and Prandtl number Pr = 0.1, as a function
of grid fineness (calculation using CDS and both uniform and non-uniform grids)
10
We also checked the effect of the under-relaxation factor for the velocity
on the solution in this case. As expected, it is much smaller than in the case
of lid-driven cavity, since the pressure variation is much smoother here. On
the coarsest grid (8 x 8 CV), the difference between solutions using a, = 0.9
and a, = 0.5 is about 0.23%, while on the grid with 128 x 128 CV it is below
0.0008%.
The efficiency of calculating steady incompressible flows using implicit
methods based on SIMPLE algorithm and colocated grids can be substantially improved using multigrid method for outer iterations. This will be
demonstrated for the two test cases studied here in Chap. 11.
Q. Nonuniform
----qm.., Nonuniform
- - - - - - - - - Q, Uniform
,/
------ $,... Uniform , , " /
- : - Ideal Slope
,,I
//
I
4
I
.01
,001