General CFD convergence Question
 

Can anyone explain to me why after solution is converged and if I kept running solution iteration it starts to diverge ,?

Without details is not possible to give you an answer ...Are you talking about convergence to a steady state in a time-marching scheme or convergence of a iterative method for an algebric system?

I suppose you are referring to convergence of the residual. What happens when you continue to iterate? Does the residual increase to a local maximum then decrease again? To another local minimum? What is happening to the solution (say visually) when it reaches the first local minimum? Is the (pseudo) convergence uniform or oscillating? With each step you predict, then step to the predicted minimum in a multiparameter space. Is the prediction overstepping the local minimum resulting in oscillation? Does divergence followed by apparent convergence take you to another local minimum? Could the initial "convergence" take you to a "state" that is unstable, that then "bifurcates"? I have wondered about these things myself.

Since no one else has responded to Munaf's question, I will make one more observation before this thread dies. In solving for natural convection flow in a cavity at Ra=1.5x10^5, I have experienced a situation like Munaf describes. In my problem, stream lines/fluid particles move toward the symmetry plane along a helical trajectory, then spiral outward, return to the end plane, spiral inward, and repeat. A spiral trajectory in the symmetry plane is shown in the lower left figure attached for Ra=1x10^4. At Ra=1.5x10^5, it seems that two centers develop, as shown in the lower right figure, which was found by stopping when the residual reached a first local minimum. The dual centers have been shown in several publications. At first glance this seems like flow found with the 2D thermal cavity, but there is a problem. The trajectories interleave as they spiral outward. But we know that neighboring particles or stream lines remain neighbors, except around stagnation points, so something strange is happening here. In fact, this configuration is unstable, and if iteration is continued, the residual increases to a local maximum, then decreases again. What is happening is that the symmetry is broken, and the residual increases while the (unsymmetric) flow is reorganizing. One might think of the flow around a circular cylinder, where flow is symmetric until the cylinder starts shedding vortices. Your situation may be different, but you might look for an explanation like this before you discard your results.

Sorry, file is too big. I will re-post this when I figure out how to make it smaller.

Until we do not get an answer about the details is very difficult to suppose what can be the problem...
If the converged solution is used to restart with exactly the same iteration parameters but the solution starts to depart from the previous convergence, I can suppose that a) the fields for the restarting have no longer the same finite arithmetics (that is a different precision) or b) there is the action of the round-off error.
But that can also depends on the criterion adopted to define the convergence. You could get that the residuals are actually decreasing and thereafter starts to increase when you try to solve a steady state system of equations but the physics is slowly unsteady due to bifurcation. That is, for example, the case of the 2d lid-driven cavity at Re=10^4 as well as the heated-driven cavity at high Ra number.