What Convergence Criteria Should be Used?

This is not an easy answer to give, as it depends upon the User’s requirements, and upon the software package being used. For example, for a simple demonstration calculation, a not-well converged solution might be adequate to illustrate some principles, and for use as a starting guess for a more refined calculation. In other situations where the quantity of interest is in a small localised area of the flow, and the flow rates there are much smaller than inlet flow rates, eg heat transfer inside a small separated region, then a very high level of convergence might be required.

A detailed discussion on the definition of suitable Convergence Criteria is beyond the scope of this note. More information may be found in [2 ]. A simple recommendation is that the user should think about what they wish to achieve, and use a number of different criteria to assess whether or not a solution is converged. These criteria include: the residuals given by the software package being used; global imbalances in mass, momentum, energy etc; whether key global quantities, such as forces on a body,  have reached an equilibrium value; and whether information from solution monitor points have stabilised. Note that these monitor points should be in areas where the flow could be much weaker, and not where the flow could be converged easily, eg just downstream of an inlet.  

The rest of this section discusses some standard ways of trying to understand and improve convergence.