## Fluids

#### CFL Number in Eulerian Multiphase Flow

• FS2020
Subscriber

Hi all,

I am calculating an instationous water-air two-phase-flow with the eulerian-multi-phase model. The Volume Fraction Formulation is explicit and the time stepping method is calculated variable with a global Courant Number (CFL) of 1. While fluent is calculating the solution i can read in the Console: "Global Courant Number [variable Time Step Criteria]" (with the value of 1) and "Global Courant Number [Explicit VOF Criteria]" (with a value around 0.4). What is the difference between theses two CFL-Numbers?

Moreover I have read in the Fluent User-Guide that it is recommended to choose the CFL-Number as 2 and I am wondering if the Solution is even physical? I thought we need for a accurate time discetisation a cfl number equal or less than one?

Thank you so much for your help!

• DrAmine
Ansys Employee

One is flux based and other one is based on the formulation used in the VOF panel.

CFL<2 impliying 8 sub-steps for VOF explicit reconstruction if default VOFR CFL is kept to 0.25. That is fair enough. Fluent Pressure Based Solver is not explicit solver only the volume fraction can be solved in explicit fashion.

• FS2020
Subscriber

Thanks for your answer!
To be shure that I understand it right, I have a few more questions to this topic. Where is the difference between the VOF reconstruction equation and the continuity equation?

The conservation equations will be solved implicit for every global time step (resulting from CFL = 2) and the VOF reconstruction equation will be solved explicit with a much smaler time-"sub-step" (CFL = 0.25). Am I right so far? Which of these equations will be solved first and how is it possible to solve the VOF equation without knowing the results of the conservation equations (e.g. velocity, ... ) for this (small) time step?

I understand that the Global Courant Number [variable Time Step Criteria] results from this equation: CFL = u*delta t / delta x, but could you explain how the Global Courant Number [Explicit VOF Criteria] is calculated in the console? I do not understand why this CFL number is sometimes much smaler then the variable-time-step-Criteria-CFL and after a number of time steps both CFL-numbers have the same value.

Thank you very much!

• DrAmine
Ansys Employee

1) Yes.VOF equation is solved /Advected at the end.

2) The way the explicit one is calculated is documented. The variable one is based as I said on flux. The other one does depend on what kind you select.

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