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Philip May 31, 2011 03:00

Does MULES::implicitsolve allow for Courant numbers > 1?

although there are several threads concerning the time step size for MULES VOF (in interFoam and/or interDyMFoam) I have not found a definitive answer whether you (I/OpenFOAM) can safely increase the time step size, or that anyway the max Courant number should still remain < 1?



akidess May 31, 2011 05:09

No, you are still bound by the PISO algorithm to Co < 1. However, using explicit MULES you are bound by the capillary wave length, which usually gives a time step criterion dt << (Co < 1). MULES implicit somewhat relaxes that time step criterion.

Philip May 31, 2011 05:37

Hi Akidess,

thanks for this fast reply. I am an openfoam beginner and I did not know that all PISO (so all transient Navier-Stokes) calculations were limited by Co < 1. Do you know why this is so? Apart from losing accuracy for larger steps, I am not aware of stability issues with eg backward Euler time integration and SIMPLE (or PISO).



akidess May 31, 2011 05:54

The restriction is not OpenFOAM specific, but tied to the PISO algorithm itself. If you read the derivation of the algorithm, there is a step where it is assumed that the velocity only slightly changes between time steps. This is the reason why PISO does not require relaxation and usually converges within 2-3 iterations. With SIMPLE you don't have the same time step restriction, but you'll have to do a lot more work to get a converged solution for a given time step.

You can read more about this in the original paper of the PISO algorithm:
R. I. Issa, Solution of the implicitly discretised fluid flow equations by operator-splitting, Journal of Computational Physics, Volume 62, Issue 1, January 1986, Pages 40-65, ISSN 0021-9991, DOI: 10.1016/0021-9991(86)90099-9.

Philip May 31, 2011 06:25

Hi again,

Thanks. I will look up the original article of Issa.
I found a similar discussion under the title "Courant number and implicit treatment thread":

that make things a bit clearer. At this moment I still wonder if this has been tried: Looping (within a time step) over the momentum solver + corrections does not allow for a larger time step?


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