# Variable time stepping method

ecrod
Member

I am running a transient multiphase flow. If I select variable time stepping method in run calculation, I will have the following settings to adjust.

However, If I selected multiphase flow with explicit solution in models settings I will have.

I have a couple questions regarding this subject

- Both menus shows a Courant Number, what the difference between them and which controls time stepping evolution ?
- Sometimes during in simulation I see a message: Global Courant Number [Explicit VOF Criteria] = 1.498235 for instance. I believe this is not a good solution because Courant Number exceeds 1. In this case, how can I control this Global Courant Number to achieve a value less than 1 ? Should I change Global Courant Number in Variable time stepping or in multiphase model ?
- In the manual is said about variable time stepping that the values of 0.8 and 1.2 for minimum and maximum step change factor respectively is a good value to guarantee a smooth transition for time stepping change. I would like a smoother transition, in this case should I increase minimum step change factor for 1 ?
- What happens if I change Global Courant Number in variable time stepping from 2 to 1 ?
- In summary, in this case when a multiphase model and variable time stepping method is select what is the best way to control solution stability ?

Thanks in advance

## Comments

The various Courant Numbers will be defined in the documentation, so I'll leave you to find that.

If you want a smoother transition, think about what those numbers represent: 0.8 and 1.2 Ie 20% up or down in size, if you set the value to be 1 what do you think might happen?

Lastly, variable time stepping is great in theory. In practice, if your model has multiple and/or varying timescales how do you think the stepping will deal with that?

@Rob I had a question. For explicit formulation(conditionally stable), discretising the governing equations and subsequently applying the stability criterion imposes a condition on the time step size(CFL condition). However, since the implicit formulation is unconditionally stable, hence no such condition is imposed on the time step.

Hence, in case one uses the implicit formulation available in fluent, the CFL condition is ruled out, however, there should be a certain limit to the time step in order to acheive a physical solution. Is there an upper limit to the Courant Number for implicit formulation? I know the answer is yes but I needed an approximate value and the conditions governing the same.

Hello,

You should be able to go with a higher value of time step with an Implicit formulation. I'd, however, not go higher than a Courant number of 5, especially for multiphase problems.

Thank you.

Karthik

Thanks @Kremella that helped. But is the upper limit based on intuition or is there any explanation for the same. Although I have limited Courant number to 2 for most of the cases, I would like to understand the factors that govern the upper limit. Would it be different based upon the problem being simulated?

I generally tend to always be conservative (1 to 2.5) irrespective of the problem / application to obtain solutions. It's intuition and perhaps experience.

Karthik

Got it!