## VOF simulation diverges with the error message 'Global courant number is greater than 250.The velocity field is probably diverging'

#### Mesh Requirements:

If volume mesh contains tetrahedral elements, use double precision with node based gradient option (Spatial Discretization). Create uniform mesh. In regions where the mesh is refined, ensure that there is a gradual transition to the coarser mesh. Avoid sudden changes in cell size. The maximum skewness of the volume mesh should be less than 0.95 and maximum aspect ratio of tetrahedral cells should be less than 5. In compressible phase calculations, use of non-conformal interfaces can leads to solution instability and divergence. We should not use non-conformal interfaces in the region of liquid-air interfaces. This is one limitation of VOF with compressible calculations. This limitation becomes magnified when you use MDM with VOF (both are explicit schemes)

Phase: Use compressible phase as primary phase.

Viscous model: Check the Reynolds number and use Turbulence model if needed.

Specified Operating density: Switch on the specified operating density and specify the density of lightest phase.

Implicit body force: Turn on

P-V Coupling: Use SIMPLE for compressible calculation and PISO for incompressible.

URF: Use small values. Pressure-0.2, Density-0.5, Body forces-0.5 Momentum- 0.3, Turbulent kinetic energy- 0.8, Turbulent dissipation rate ¿ 0.8, Turbulent viscosity ¿ 1

Use this command for better patching: (rpsetvar `patch/vof ? #t)

If you face the divergence at the beginning of the simulation, start the simulation with very small time step size, and increase after a few time steps if Global courant number is under control. The global courant number is printed in the Fluent console window at every time step.

The Global courant number depends on the mesh size, velocity field, and the time step size used for the transport equations. If CFL exceeds 2 and keeps on increasing, that means your velocity field is increasing or/and the interface is moving through dense cells, and the time step size used is too high. You need to reduce the time step size to bring the Global courant number under control.

For VOF calculations (using the Explicit scheme), FLUENT allows you to use variable time stepping in order to automatically change the time-step when an interface is moving through dense cells or if the interface velocity is high. If there are frequent velocity jumps in your problem, it is better to use the variable time stepping method to control the CFL under limit. The solution will be stable with the variable time stepping method.

If you use the fixed time step, the CFL may exceed the value 2 whenever there is a velocity jump or when the interface is moving through dense cells, and your results will be time step size dependent. If you continue with the same time step size, the results will not be accurate, and this may even lead to divergence. It is better to use variable time stepping method for this type of problems and for compressible VOF calculations.

Variable time stepping method: Here the input will be CFL. The global courant number is constant and the time step size varies with the velocity field. You should give appropriate value for Global courant number (CFL). Because, the time step size for transport equations are calculated from this CFL. You need to specify the Global courant number, minimum time step size, maximum time step size, minimum step change factor and maximum step change factor.

Global courant number: 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. In some cases, you need to reduce this up to 0.5 for accurate results. This is because the time step size (so, the CFL) should be small enough to get the accurate results. In some cases you may use CFL greater than 2 depending on the problem.

Maximum Time step size: minimum grid size / maximum velocity in the domain

Minimum Time step size: It should be greater than 1e-10. You cannot use time step size less than 1e-10. This is the limitation of VOF Explicit scheme.

Minimum step change factor: The default value is 0.5.

Maximum step change factor: The default value is 5. It is better to reduce this value to 1.5-2 to avoid the sudden increase in time step size.

If still there is a divergence, check your mesh quality, boundary conditions and physics of the problem.-
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