Dear Sir, I have a basic doubt, Does the unsteady result at any particular time level (say suppose t=10) using any method ( like Fractional step method, vorticity stream function method, finite volume method) are same.

I can understand the steady state result must be same for any method. But what about unsteady result ?

Advices are welcome

In a sense, this like asking if the results are the same on a 10 x 10 mesh and a 20 x 20 mesh for the same problem. Or asking if the results are the same for an advective flow when the differencing is upwind-weighted vs. centered differences. You should expect errors between different spatial difference techniques for the steady-state results as well.

The approximation errors for each transient method are unique - so the solutions are unique (and different) at any value of t. What you hope for is that the differences at any value of t are small.

So the answer is "no", the results should not be the same at any t. But, if each transient method is correctly coded and properly applied, the differences should be "small."

Hope this helps.