Hi,

Could anyone tell me where I can find, preferably online, information regarding the use of relaxation parameters and how the variation of these can affect solution convergence. I am modelling a fully unsteady, cavitation model. I also model without unsteadiness. I do not solve the Energy equation. ANy help, even books, papers etc would be appreciated.

The number of convergence promoting actions are discussed in PHOENICS Encyclopaedia.
For the general recommendations relating to relaxation parameters look at here.

Regards

Sergei Zhubrin

If you use TDMA, first of all, increase number of cycle to solve energy equation. Monitor residuals of all the variables to find which one fails. As you know relaxation parameters changes between 0 and 1.0. Make an sensitivity analysis concerning relaxation parameters on your own problem.It will be tedious but it may help much.Perhaps, your relaxation parameters very close to 1.0 so that you have convergence problem.Solution steps from one iteration to another should be small enough to reach the solution at first trials of getting solution. For example, take relaxation parameters for velocity components 0.2 and keep them others close to 0.8 then check whether your program converge or not.You may see that as they become closer to 1.O CPU time will decrease at the expense of convergence problem. As far as I know from my experience (3D full furnace steady state simulation), cfd solutions are sensitive to relaxation parameters. Nuray Kayakol

hi J,

relaxation is a general term and it will be tough to give suggestions based on your question. The basic idea is to slow-down/speed-up (under/over relaxation) the correction to a variable.

Quite obviously, the under-relaxation parameter plays the role of a time-step when solving steady equations. The standard Von-neumann stability analysis can be performed in the case of an under-relaxed system in a way that is analogous to an unsteady system. Generally there must be information relating to the particular context in which you are using under/over relaxation.

Patankar's book "computational heat transfer and fluid flow" has some discussion on under/over relaxation.

regards, chidu...