Navier-Stokes Lid Driven Cavity: Does this figure make sense?
 

I'm having trouble solving the Navier-Stokes equations for the lid driven cavity problem. I am using a staggered-grid finite difference discretization scheme with dirichlet boundary conditions and leaky B.C.s on top. (u=1, v=0 for the top)

For nu = 1/500, 40x40 grid, 40 time points from t=0,1, I get this figure for my stream-function visualization. Does this seem a bit off to anyone else? What might I be doing wrong here? (I suppose there could be many things...)

Thanks for the help.

I suppose you are very far from the steady state...check the time-derivatives if you are running an unsteady solver or the residuals if you are running a steady-state solver.

Could you be more specific about how to check the time-derivatives? I just ran it to time t = 100 with 1000 time points and got the same result.

I'm using a runge-kutta method to solve the time-dependent N-S equations.

Thanks for the suggestion!

you must evaluate the dv/dt in your domain and ensure that they are below a small threshold.