Convergence criterion
 

Dear all,

Problem: I have an unsteady implicit solution with a convergence criterion, say 1e-3. This solution is different from a solution obtained with say 1e-4. I keep the timestep constant and solve VOF at every timestep (not iteration).

Question: I assume that the error associated with solving VOF at the end of each timestep might increase with increasing number of iterations at each timestep. Since lowering the convergence criterion results in more iterations at each timestep, how do I know that the supposedly more accurate result of the transport equations is not inhibited by the fact that the surface is not decribed correctly at each iteration?

Thank you!

M

Re: Convergence criterion
 

With a constant time step, answers changing when your criteria goes from 10-3 to 10-4 says the solution isn't completely converged, as you've noted.

You need to decide by experiment how much is good enough. Run the problem through to completion several times, each time using a different convergence criteria. If you're interested in the transient solution, plot the surface shape with time for each problem, make a judgement on the results - do you want to accept the transient for 10-3 or do you really need to grind it down to 10-6? Only you know why you're doing the calculation and how much is enough.

You'll likely want to look at some other variables as well - maybe outlet flow rate vs time for several different convergence values?

Re: Convergence criterion
 

Hey Jim_Park,

Thank you for your answer. You are right of course. I might have been fuzzy in my formulation, but my point was of a more theoretical nature (say where experiments comes after calculations). Is there a "genereal guidline" when implementing VOF at the end of each timestep instead of at the end of each iteration? I imagine that this is dependant on how much the flowfield changes over a timestep. Or is it??

Best regs

M

Re: Convergence criterion
 

My most accurate answer: I don't know.

The Los Alamos folks who developed VOF (Tony Hirt, Bill Nichols and Bob Hotchkiss are the authors on LA-8355) use a similar technique for the momentum equations. That is, the momentum equations are advanced explicitly, then the continuity equation and pressure gradient parts of the momentum equations are solved simultaneously (iteratively) to finally advance the velocities and the pressure. And finally VOF is used to advance the surface or fluid interface explicitly.

The idea is to keep everything explicit that you possibly can (remember that the mainframe computers of the time were S L O W and had very little memory). Solve what you must implicitly to keep the solution stable.

I think it was natural to treat the VOF surface movement in the same way. Keeping VOF explicit does impose a limit on the allowable time step. But the LANL heritage is firmly embedded in transient simulation, so the time step was usually limited to yield an accurate transient anyway. One of the cardinal rules for time-stepping for those guys was/is to limit the time step so the fluid (interface or bulk) moved less than one computational cell per time step.

There's a history of the CFD development at Los Alamos on the group T-3 web page. It's worth reading.

Hope this is all worth something for you.

Re: Convergence criterion
 

Here's the link for that history:

www.lanl.gov/orgs/t/t3/history.shtml

Re: Convergence criterion
 

Thanks again Jim_Park,

I will absolutely read that referrence.

Regards

M