[Ursmooth]

Hello, I am relatively new to CFD and I am calculating a flow over a cylinder Re=100,Transient case. I am trying to do a convergence study. You can see by my that my solution start to converge, then it becomes unsteady and the residual goes up, when the solution is "steady unsteady" the residual stays constant. How do you do a convergence study on a transient case? And how do you decrease your residual?

From my understanding a residual is the difference from your previous solution at a time step to the solution at the next time step. For a steady state you would just increase your iterations until your change in solution is met, but my cylinder is oscillating so this will never happen. So what is the criteria for convergence? Do you have to look at the residual before your solution becomes unsteady?

[FMDenaro]

No at all, your definition of residual is wrong. I give you an example from a lineaa system A.x=q.
At the kth and k+1 iterations you have

A.xk-q=rk
A.xk+1-q=rk+1

where r is the residual. What you instead defined is

(xk+1-xk)=A^-1.(rk+1-rk)

In terms of the convergence to the exact solution, you can see that you have differences