This document provides instructions for computational fluid dynamics assignment 7 involving solving the 2D lid driven cavity problem. Students are asked to: 1) Use the staggered grid and SIMPLE algorithm to solve for the velocity field in a 1m x 1m cavity with air properties, a 0.05m grid, and 1m/s lid velocity. 2) Plot the x-velocity profile at the vertical centerline and y-velocity profile at the horizontal centerline, and compare to benchmark results provided.

1. Computational Fluid Dynamics
Assignment no. 7
Submission date – 20-4-2012
1. Solve the two-dimensional “Lid Driven Cavity” problem with the following
information: The cavity dimensions are 1 m × 1 m and the fluid in the cavity has a
constant density = 1 kg/m3 and a dynamic viscosity = 0.01Pa.s.(Re = 100) Use a
uniform grid of size x = y = 0.05 m. The horizontal lid at the top of the cavity
moves steadily with a velocity of 1 m/s in the +x-direction.
(a) Using the staggered grid and SIMPLE algorithm, solve for the velocity field in the
cavity. Use First Order Upwind (UDS) for solving the momentum equations.
Implement appropriate boundary conditions. For all iterative solutions use the
point-by-point Gauss- Seidal scheme. Use the overall convergence criterion of
10-7 for the mass source.
(b) Plot the x-velocity profile at vertical centerline (x = 0.5 m) and y-velocity profile at
horizontal centerline (y = 0.5 m) and compare with bench mark results.
X-Velocity profile Y-Velocity profile
Y X-Velocity X Y-velocity
1 1 1 0
0.9766 0.84123 0.9688 -0.05906
0.9688 0.78871 0.9609 -0.07391
0.9609 0.73722 0.9531 -0.08864
0.95 0.68717 0.9453 -0.10313
0.8516 0.23151 0.9063 -0.16914
0.7344 0.00332 0.8594 -0.22445
0.6172 -0.13641 0.8047 -0.24533
0.5 -0.2058 0.5 -0.05454
0.4531 -0.2109 0.2344 0.17527
0.2813 -0.156662 0.2266 0.17507
0.1719 -0.1015 0.1563 0.16077
0.1016 -0.06434 0.0938 0.12317
0.0703 -0.04775 0.0781 0.1089
0.0625 -0.04192 0.0703 0.10009
0.0547 -0.03717 0.0625 0.09233
0 0 0 0