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Jindra Kosprdova April 20, 2005 06:21

Timestep selection
Hi everybody,

We are solving a flow through an impeller of centrifugal compressor.


The problem was solved for 3 different PHYSICAL TIMESTEP (t1=2E-4,t2=3E-4,t3=2.23E-2).

The history of MAX RESIDUUM was bouncy for the first PHYSICAL TIMESTEP. For the last one the history was monotonic.

When checking solutions we found that all three solutions are the same.

The question is what is the influence of PHYSICAL TIMESTEP on the results of solutions?

What is determinative for the first estimation of the PHYSICAL TIMESTEP?

Thank you a lot,

Jindra and Petr.

Robin April 20, 2005 09:32

Re: Timestep selection
Hi Jindra and Petr,

This is a good observation. The Physical Timestep has no influence on the final solution, only the convergence. Even though you are solving for a steady state, CFX keeps the transient term in the equations to stabilize the equations. This is similar to using an underrelaxation factor, but has a more physical behavior.

Since the solver is fully implicit, there are no timestep restrictions. A larger timestep will generally give you faster convergence, but may be a little unstable. A good tech tip on how to use the timestep is available from the CFX Community Site at

Best regards, Robin

Ian April 20, 2005 09:36

Re: Timestep selection
Assuming it's subsonic the timestep should be anywhere between 0.1/omega to 10/omega, where omega is the angular velocity in rad/s. On the lower end 0.1 should only be used at startup for unstable cases but be increased to 1 for proper convergence.

If the timestep is too small the solution might still have low frequency error and convergence will be slow. Increasing the timstep speeds up convergence and removes low frequency errors to a point where the solver will become unstable. I've found an optimal timestep for subsonic centrifugal compressors to be 2/omega.

Ian April 20, 2005 09:38

Re: Timestep selection
Hey Robin I thought it was against company policy for you to post to CFD Online from work?

John April 20, 2005 16:44

Re: Timestep selection
I guess answering question for cfx users is Robin's job.

We need Robin here. His/Her answers are always simple but clear and helpful.


Jindra a Petr April 21, 2005 02:36

Re: Timestep selection

thanks a lot for your answers. They help.

Jindra and Petr.

Robin April 25, 2005 14:11

Re: Timestep selection
Actually, it's the other way around. The short wavelenght (relative to the mesh) error is always reduced well. The timestep will effect how quickly large wavelength errors are reduced. Large wavelength errors are essentially the transients.

For a single component, values between .1 and 10/omega work well. We have found that for multi-component systems, a larger timestep is needed, on the order of 10 to 100/omega. A small timestep may actually cause the solver to diverge.

Regards, Robin

Bak_Flow April 26, 2005 22:26

Re: Timestep selection

I think that is what he said ..... large time step reduces the large wavelength errors best.

In a time advance under-relaxation to SS method ALL wavelengths are transients. IF the objective is a steady state simulation there is no interest in resolving the high frequency (short wavelength transients) that is why large time steps work fast....would resolving fine features cause divergence...not sure...why would it??

However all non-linear problems have some information that is lagged. And not all inter-equation coupling is active. IF a lot of information (eddy viscosity always, density for compressible flows, mass fluxes at GGI's, etc) then you are limited by the time step you can run.

Mesh quality is also an issue and the discretization scheme.....Hi Res adds another level of non-linearity as well.

Therefore sometimes an upper limit exists....I think that is what Ian was getting at!!!

What do you mean by multi-component....multi-stage?

Be careful to work out the details. ;-)


Robin April 27, 2005 08:57

Re: Timestep selection
Hi Bak_Flow,

Sorry, you're right, he did say low frequency errors. Regarding your question "would resolving fine features cause divergence...not sure...why would it??". If your initial guess is far off, a large timestep can smooth the errors out quickly, effectively removing the large peaks and troughs. If you use too small a timestep, these very large errors may cause the solver to diverge locally.

A practical upper limit may exist for a given problem, above which the solver may diverge or non-linear terms, such as the beta term in the high res scheme, may cause sharp oscillations. But formally, there is no limit since the formulation is fully implicit. There are many cases which have no upper limit and you can increase you timestep infinitely, essentially removing the transient terms from the equations.

By multi-component I mean the same as multi-stage, i.e. several rotating parts, like an entire compressor.


Jindra April 28, 2005 06:41

Re: Timestep selection
Hi Robin, we have no idea what wavelength errors mean. Could you explain it to us. Thanks Jindra a Petr

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