In calculaiton using an unsteady approach, do oscillations (odd-even oscillations, look like losing stability) imply that an unsteady flow is going to happen? If yes, how to pull out the correct unsteady solution?

Thanks for your point of view or clues for references.

T

Oscillations do not necessarily imply the advent of an unsteady flow. You need to make sure that your loss of "stability" is not a numerical issue. If your algorithm is stable numerically then you can begin to address issues such as numerical damping that can kill a non-steady solution. But if you are picking up odd-even oscillations it sounds to me as if you have a decoupling phenomenon occurring, which is not realistic but a problem with your numerics. Until you fix it you aren't going to be able to get a correct solution.