convergence Vs under relaxation-2phase flow-2dpipe
 

hello all.
I need an explanation for the following.
I tried a small 2 phase problem with a small 2d pipe.
8000 hexa elements-very good quality.
air-water mixture inlet. turbulent flow
1.Used water at inlet and iterated till convergence was achieved at 10^-7 residual criteria.
2.used 1 as initial condition and introduced air at inlet. The iteration ran for ages and the residuals never reached 10^-3.
3.I drastically reduced the relaxation factors to the order 10^-3.
4.The solution stabilized and achieved convergence at 10^-6(all residuals).
Could this be a false convergence result? I am aware one should reduce residuals slowly from 0.8,0.7 and so on; however i reduced it to 10^-3 just to see what happens. I am unable to explain why it achieved convergence in just a few hundred iterations.

Is your 2d pipe axisymmetric? Axissymmetric 2d simulations sometimes have a problem with stability and need a little help from slightly smaller urf's than a non-axissymmetric case.

You can always make your residuals arbitrarily small (down to machine precision) by reducing your urf's to ridiculously small residuals.

But residuals don't tell you anything about convergence and accuracy. For that you need to be checking solution values. To see if your simulation is converged try changing the urf's back to the original values. You will find that your solution behaves as before and does not stay at the lower levels.

What's really important for two-phase flows is an accurate calculation of the interface. With only water you can achieve 10^-7 in residuals because there's no interface. When you introduce air, there's now an interface that numerically oscillations (because of numerical instabilities or whatever) and that makes it very hard to achieve small residuals. You also need a sharp and well-resolved interface to improve your accuracy.

Thanks for the response. And yes the solution is stable with the small residuals however if I choose default urf's the residual go around 10^-3 and oscillate . In other words would this solution be safe to use or should I start over through a different approach ?

I have some experience with external single phase flows but I'm currently not sure how to validate my results . I would not be able to identify a good resolution of the interface from the bad one .

I would never trust the result of anyone that used anything but the default urf's. I'm willing to accept factors of 1/2, or 1/4 but not factors of 1/1000.

Residuals do not give information about convergence unless they oscillate around a fixed value which just means that your solution is grid saturated and you need a better grid, i.e. a finer grid to resolve more features of the problem or higher quality grid to reduce numerical oscillations.

You should be observing these solution values and come up with the judgment yourself if it is ok or not. Look at basic values like velocities, temperature, etc. But look in terms of the solution, not these stupid residuals.

“The first principle is that you must not fool yourself and you are the easiest person to fool.” ― Richard Feynman