Is it sufficient to judge convergence only by examining residual levels while modeling fluid flow and heat transfer problems? If not, what are the different metrics used for judging convergence?
A truly converged solution is one that is no longer changing with successive iterations.
If the residuals for all problem variables fall below the convergence criteria but are still in decline, the solution is still changing, to a greater or lesser degree. A better indicator occurs when the residuals flatten in a traditional residual plot (of residual value vs. iteration).
Convergence can be judged not only by examining scaled residual levels, but also by monitoring the average velocity (or any other property) at different locations. The solution is considered to have converged when there is no further observable change in the velocity (or any other property) at each location.
I can suggest some references:
- NAFEMS guide on convergence
https://www.nafems.org/join/resources/cfdconvergence/
- a comparison of different criteria from LLNL
http://repository.icse.utah.edu/dspace/bitstream/123456789/9952/1/SolutionVerification.pdf
- the use of the Grid Convergence Index (CGI) derived from Richardson's extrapolation method
Article Perspective: A Method for Uniform Reporting of Grid Refinement Studies
https://pdfs.semanticscholar.org/9f8e/4c04161df659abcd5920f3b207d78dcefe7f.pdf
Generally, there are three parameters to examine a numerical solution, whether it is converged or not.
1. Balancing of mass and energy (each control volume should be balanced properly)
2. Most importantly: Monitor of any field property should be constant. (should not change with iterations)
3. Scaled residuals.(should fall bellow an appropriate given value)
All these three criteria should satisfy with relative to each other because all these are inter depended with each other. However, priority should be given in the order 2>1>3.
Only the person with good experience in numerical simulations in that particular problem field can better judge a solution whether it is converged or not.
Thank You.
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