Question Regarding Convergence and Time Step Selection
 

Hi,

I've been reading practical tutorials and seen that a reasonable target value for RMS residual for steady state simulations is 0.0001.

However, I'm not quite sure for transient problems what is an appropriatte target value. I understand transient simulations are solved by computing a steady state solution for many discrete points in time. Each steady state solution is iterated through a number of inner loops called “coefficient loops”. What is a reasonable RMS target for each time step? I've read that 3-5 loops should allow you to reach convergence.

I've noticed CFX by default monitors the RMS for each timestep. If the RMS value for that timestep is above the target, does that mean the solution is not converged? Should I wait until all monitored RMS quantities are below the target for all time steps from there on to be confident about my solution?

What other quantities are good practice to monitor in order to trust the obtained solution?

Thanks!

I usually use a target value of 1e-4 for the MAX Residual.

And yes, if the residual is higher than your set convergence limit, then the solution for that timestep has not converged within the maximum number of coefficient loop iterations.

No. It is problem dependent. Some need tighter convergence some looser. That's why you have to do a sensitivity check for your type of simulation. 1e-4 is a useful starting point but it nothing more than your first guess.

Wrong. Transient simulations are quite different to steady state as the underlying equations now have additional transient terms. Because the underlying equations are different the numerical approach is different. But yes, I can see how it looks like a series of steady state simulations - but it is not. The residual values to converge a steady state simulation are not equivalent to the residuals reported in the same simulation run as a transient - the residual is calculated different and so the numbers are not comparable.

1e-4 is a good starting point, but again nothing more than a starting point. You need to do a sensitivity analysis to determine whether tighter or looser is OK.

Yes, this is a good way of determining the timestep size for a transient simulation. Note that this will also mean that as you tighten the convergence critereon you will get smaller timesteps - the two effects are coupled numerically.

Once you have determined what convergence you require by a sensitivity analysis then yes, if you have not achieved it your simulation is not converged. If you have guessed the convergence critereon then who knows whether it is converged or not.

That depends on the problem and what you want to do with it. If you are looking at aerofoils then you are probably most interested in lift and drag. If you are looking at a valve design then maybe pressure loss. If you are looking at a HVAC flow then maybe the temperature at various points in the room. You should monitor whatever is important to your analysis and check it looks like it has converged.

Hi,

Thank you very much for your replies.

Glen,

I'm not exactly sure how to perform that sensitivity analysis. What you mean is that I should see how my answer varies as I use different target values for RMS? As long as the answer doesn't change significantly as I increase the target RMS, I could use that higher value (or lower, eventually), right?

Yes, that is correct. You vary the input and see how the output changes. You can then set the input to the level which gives a level of convergence acceptable for the accuracy you are looking for.