For any transient problem, what is the right way to decide a timestep?

I ran a particular case with time steps of .01,.001,.0001,.00001.

As I plot the change in velocity at a point, with respect to time. All the plots for various timesteps don't overlap. Isn't it true that to have my solution timestep independent, my plots with various timesteps should overlap? Should I keep going to a smaller timestep? But I don't have forever to solve my problem.

I searched through all of the forum, but couldn't get a correct answer to my problem.

Thank You

Search the help file for "courant number"

Obtaining mesh/timestep independent results depends on many factors including both spatial and temporal resolution. Using ultrafine timesteps on a coarse mesh isnt going to gain you much.

Thanks Joe!

I know what you mean. I been through the courant number related posts, before I posted the question

And I understand from the post that if convergence isn't a problem within a timestep ( i reach to residuals of about E-6) , courant number is not important, since CFX is an implicit solver. And explicit solvers would require Courant numbers less than 1.Is this understanding flawed?

But anyway, a timestep of E-3 gives me a courant number equal to 5, and E-4 gets me something below 1.

I also realise that my solutions are almost the same with different timesteps. They are just out of phase. I have a paper that claims a transient result like that is good enough to show timestep independence, because the difference in phase is because the vortices are resolved differently in each case.Is this correct?