CFD-101: The Basics of Computational Fluid Dynamics Modeling

# Relaxation and Convergence Criteria

Numerical methods used to solve the equations for fluid flow and heat transfer most often employ one or more iteration procedures. By their nature, iterative solution methods require a convergence criteria that is used to decide when the iterations can be terminated.

In many cases, iteration methods are supplemented with relaxation techniques. For example, over-relaxation is often used to accelerate the convergence of pressure-velocity iteration methods, which are needed to satisfy an incompressible flow condition. Under-relaxation is sometimes used to achieve numerically stable results when all the flow equations are implicitly coupled together.

## Choosing Relaxation Criteria

The amount of over or under-relaxation used can be critical. Too much leads to numerical instabilities, while too little slows down convergence. Similarly, a poorly chosen convergence criteria can lead to either poor results (when too loose) or excessive computational times (when too tight).

Selecting proper relaxation and convergence criteria can be a difficult and frustrating experience for users of computational fluid dynamics software. The criteria depend on the specifics of the problem being solved, which may change during the evolution of a problem. Unfortunately, there are no universal guidelines for selecting criteria because they depend not only on the physical processes being approximated, but also on the details of the numerical formulation. Many CFD programs have a standard set of recommended criteria, but users must often resort to trial-and-error adjustments to get good results.

## Dynamic Selection of Criteria

FLOW-3D users are exempt from these difficulties because all relaxation and convergence criteria are selected by the program itself. Further, all selections are adjusted dynamically by the program to follow the development of the solution. Of course, users can always override the automatically selected criteria for special cases. One such case would be the use of a very large convergence criteria and no over-relaxation as a way to reach steady-state conditions with less CPU time.