I'm solving the steady Navier-Stokes equations by artificial compressibility method. Since the flow around the cylinder is unsteady, I can't get a steady solution. Anyone has experience with this? Any method to damp out the unsteadiness?

why to damp the unsteadiness. I am interested on the rational behind a steady state solution

If you follow the recent massage " General CFD question " in this thread you will see that i am having almost an oposite question which is what is the relevence of a steady state solution.

I solved the same problem using Finite Volume and SIMPLE method and obtained A steady state solutionfor Re=3900.

I am certainly no expert but I was under the impression that a problem with an oscillating transient solution should provide an underconstrained system and a steady state solution should diverge.

How is it that a steady state solution can exist at all ? Like I said, I don't know much and am simply curious about the answer.

How you validate the computational results with test data?

There is many experimental data and LES quality solutions (Mittal, Buerer, Moin, etc,..) for the flow past cylinder at RE=140,000 and 3900. I used them