3-D Lid Driven Cavity

Problem Definition:

The problem considers the laminar flow in a cubical enclosure of dimension 1X1X1 in which the lid is driven by a constant velocity u = 1 as shown in the figure below. The length of the cavity is considered to be unity and density (ρ) =1. The value of dynamic viscosity (μ) is calculated from

However, the computation has been carried out in a 1X1X0.5 domain where at z = 0.5, a symmetrical plane has been considered.

Results

Numerical simulations have been performed for Re = 100 for the present test case. The streamlines at z = 0 and z = 0.5 are shown in Fig. 2.2. The u-velocity profile along the vertical centreline and the v-velocity profile along the horizontal centreline for the cubic cavity are shown in the Fig. 2.3. The comparison of present results shows a good match with the result of Ku et al. [1]

Figure 2.2: Streamlines at z=0 and z=0.5 (a) (b)

Figure 2.3: (a) u velocity along vertical centreline (b) v velocity vector along

horizontal centreline

References

[1] Ku H.C., Hirish R.C., and Taylor T. (1987) ‘A Pseudospectral Method for Solution of the Three-Dimensional Incompressible Navier-Stokes Equation’, Journal of Computational Physics, Vol. 70, pp. 439–462.