Under-Relaxation Parameters and their Optimum Values

What is the role of under-relaxation parameters and what are the optimum values of these parameters?

The default under-relaxation parameters for all variables are set to values that are near optimal for the largest possible number of cases. While these values are suitable for many problems, for some particularly nonlinear problems (e.g., some turbulent flows or high-Rayleigh-number natural-convection problems) it is prudent to reduce the under-relaxation factors initially.

For most problems it is recommended to begin a calculation with the default under-relaxation factors. If the residuals continue to increase after the first 4 or 5 iterations, the under-relaxation factors should be reduced.

Occasionally, you may make changes in the under-relaxation factors and resume your calculation, only to find that the residuals begin to increase. This increase most often results from increasing the under-relaxation factors too much. A cautious approach is to save the data file before making any changes to the under-relaxation factors, and to give the solution algorithm a few iterations to adjust to the new parameters. Typically, an increase in the under-relaxation factors brings about a slight increase in the residuals, but these increases should disappear as the solution progresses. If the residuals jump by a few orders of magnitude, you should consider halting the calculation and returning to the last good data file saved.