2D Lid Driven Cavity problem

• Problem discription. The 2D Lid driven cavity problem describes the flow in a rectangular container which is driven by the uniform motion of one lid. It is a thoroughly studied problem and serves as a good example to check the accuracy of new algorithms.
  • P.N. Shankar and M.D. Deshpande, Fluid Mechanics in the driven cavity, Annu. Rev. Fluid Mech., 32:93-136 (2000).
  • U. Ghia, K.N. Ghia and C.T. Shin, High-Re Solution for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comp. Physics, 48:387-411 (1982).
  Here we test the pseudostress-velocity formulation using the driven cavity problem. Details can be found in my research papers.
  

• Results from the Stokes equation.
  • Flow driven by one lid. We compute the Stokes driven cavity flow on the rectangular area (0,1)*(0,d) driven by the upper lid. We are interested in the behaviour of two corner eddy as d changes. It is known that the two primary corner eddies start to touch at the mid-plane when d=1.6295. Some streamline portrait for different values of d are list in the following.

    d=1.00	d=1.62	d=1.64	d=2.00	d=3.00

    

  • Flow driven by two lids. Again the domain is (0,1)*(0,d). The upper lid and the lower lid are moving on different directions. The following are streamline portraits. Some critical values of d where the flow transforms are d=2.498, d=2.798, d=2.910, see F.Gurcan, Streamline Topologies in Stokes flow within Lid-Driven Cavities. Theo. Comp. Fluid. Dynamic. 17:19-30 (2003).

  d=1.00	d=1.50	d=2.70	d=2.85	d=3.00

  

• Results from Navier-Stokes equations. Here we give the result for Re=1000, mesh=128*128. The velocity profile on centerlines are compared with Ghia, Ghia, Shin 82' and Botella, Peyret 98.
• Animation of start-up flow. (7M)

  Streamline	Vorticity	Velocity profile