KR16: What is the meaning of VOF Courant number and Global Courant number in FLUENT and how are they related?
When ANSYS FLUENT performs a time-dependent VOF calculation, the time step used for the volume fraction calculation will not be the same as the time step used for the rest of the transport equations. ANSYS FLUENT will refine the time step for VOF automatically, based on your input for the maximum Courant Number(C) allowed near the free surface. In Variable time stepping method, FLUENT will refine the time step for transport equations, based on your input for the Global courant number (CFLglobal). In fixed time stepping method, Global courant number varies and it is printed in the Fluent console window at every time step.
The Courant number(C) is a dimensionless number that compares the time step in the VOF calculation to the characteristic time of transit of a fluid element across a control volume:
C = ∆t / ∆tchar (1)
Where ∆t is the time step size used for the VOF calculations, and ∆tchar is the Characteristic time.
In the region near the fluid interface, ANSYS FLUENT calculates the ratio of cell volume over the net outgoing volume flow rate from each cell, which represents the time it would take for the fluid to empty out of the cell. The smallest such time is used as the characteristic time, i.e.,
∆tchar = Min[cell volume/Σ(volume flow rate on each cell face) ]
= Min (∆xcell/νfluid) (2)
Based upon this characteristic time and your input for the maximum allowed Courant Number (C) in the Multiphase models panel, a time step (∆t )is computed for use in the VOF calculation.
VOF time step , ∆t = C ∆tchar (3)
For example, if the maximum allowed Courant number is 0.25 (the default), the time step will be chosen to be at most one-fourth the minimum transit time for any cell near the interface.
Global Courant number:
The Global Courant number(CFLglobal) is a dimensionless number that compares the time step in the transport equations to the characteristic time of transit of a fluid element across a control volume:
CFLglobal = ∆tglobal / ∆tchar (4)
Where ∆t global is the global time step size used for the transport equations, and ∆tchar is the Characteristic time.
Based upon this characteristic time and your input for the maximum allowed Global Courant Number (CFLglobal) in the Variable time stepping panel, a time step (∆t global) is computed for use in the transport equation calculation.
Global time step, ∆tglobal = CFLglobal ∆tchar (5)
The Global Courant number and Courant number can be related in the following manner:
CFLglobal = C ∆tglobal / ∆t (6)
Number of VOF sub time steps = ∆tglobal / ∆t = CFLglobal / C (7)
The default value of the Global Courant number is 2, but smaller value may be required for more accurate solution and more stable numerical calculation.
Note: ∆ stands for delta. This charcter is not showing up in the Siebel