Use of relaxation factors in CFD analysis
USE OF RELAXATION FACTOR IN CFD ANALYSIS
Relaxation factors play a vital role in determining the rate of convergence for CFD simulation. For instance, for a stable solution with respect to combustion modeling lower relaxation factors are required. When the relaxation factor is less than one it is said to be under relaxed and it is called over relaxed when the relaxation factor is more than one. Relaxation factor is always a constant and it is multiplied to the algebraic equations to alter the path of the iteration. Usually some system of equations does not converge easily. It takes a lot of memory and time for them to converge without the introduction of relaxation factors. This expense of memory and time also costs other resources like manpower to monitor the iteration.
Relaxation method in fluid mechanics:
Most of the problems in fluid mechanics are solved using point iterative techniques such as Gauss-Jordan technique or Gauss-Seidel method. When the under relaxed values are applied to the successive iterations of the above mentioned methods the convergence rate of the solution increases. The real challenge is to determine the best relaxation factor which is only possible by a trial and error method. The optimum value of the relaxation factor is purely mesh dependent and is specific to a particular problem. However, it will be advantageous if we can select a relaxation parameter which minimizes the number for iterations required while conserving the stability of the solution as well.
Consequences of using relaxation factors:
When inappropriate relaxation factors are used the solution vectors oscillate violently and the results obtained are not useful for interpretation. The residuals obtained from the iterations must converge to zero with successive iterations, if does not converge then it is understandable that a relevant relaxation factor must be introduced.
Difficulties in introducing relaxation factors:
Occasionally, an user may make changes in the under-relaxation factors and resume the iteration, only to find that the residuals have increased. A cautious approach is to save a case file before making any changes to the relaxation factors, and to give the solution algorithm a few iterations to adjust to the new variables. Typically, any change in the under-relaxation factors brings about a slight increase in the residuals, however these increases usually disappear as the solution progresses. If the residuals jump by a few orders of magnitude, one should consider halting the iteration and returning to the last best data file saved.