Pseudo Transient method
 

Hi to all,

I have a doubt about the pseudo transient method. On the Theory guide you can find how this method calculate this time size for each iteration. Now my question is, this time size have relation with courant number? How? Because when you use a coupled implicit method you cant choose a courant number. Wich is the criteria to converge?

If there are some documents or papers, i'd be grateful

Greetings!

Pseudo Transient Method
 

Fluent, and other CFD tools, use implicit relaxation of equations to stabilize the numerical process. However, there are at least two ways to do that. One is by specifying a Courant number. This is different from CFL but definition is similar, hence, called Courant number. The other option is to use a false time marching. This is pseudo-transient. So, instead of CFL, defined in Coupled Solver, is used. So, in a way they are related but used exclusively.

Thank you for you answer!

I found this information too. There you have the relation between CFL and the relaxation factor.

Link: https://www.afs.enea.it/project/nept...underrelax-eqn

Courant number and Time-step
 

Yes, there is relation between implicit relaxation factors and CFL because implicit factors are not defined by the user. User can only either specify CFL or explicit relaxation factors. However, your question was about CFL and time-step. Therefore, I mentioned that as such there is no direct relation but they convey similar information. Pseudo-transient has a physical basis but not CFL.

In resume:

- the pseudo transient method used the under relaxation factor to stabilize the numerical process where this factor is the time step size, right?

- there's not relation beetwen the courant number and the time step used in the under relaxation method.

So, this time step size is used to converge without the criteria of courant number? wich is the criteria in that case, just obtain the residuals?

Thanks for your answers!

Convergence
 

The criteria for convergence are not defined by either time-step or Courant or URFs, implicit or explicit. These are only methods to ensure numerical stability. To check for convergence, residuals and monitors are required. Residuals should always be less than 1 but don't have to be always very small. Smaller residual does not always mean accurate results. For that, field quantities should be monitored.

Thank you very much for you answer, i was confusing concepts, this is very usefull for me.

Greetings and have a good day!