VOF
 

Dear all,

How can the continuity equation be handled for large density difference with VOF method? I noticed that lots of work used divergence-free form of the continuity equation. However it will be invalid when one of the phases is compressible(or there is phase change).

Thanks for any input.

Re: VOF
 

For not so big density diffrence use a Favre averaging formulation if you want to keep using an incompressible code. Otherways if you are dealing with compressible fluids, just use the compressible Navier stokes equations. Theare tons of methods, see Tanehill et al, or Toro, or Ferziger's books, in them you will find lots of schemes.

Re: VOF
 

I think it's not a matter of averaging. Favre averaging does not help.

As a matter of fact, even for incompressible interfacial flows, the divergence-free assumption (inside an interfacial cell) may not be correct (despite used frequently), especially when dealing with large density ratios.

However, for compressible interfacial flows, one of very few works available, has used Godunov method. Also note that in this case, we should add an extra term to conventional "Advection equation" since velocity is not divergence-free.

Take a look at this paper: Pember, R.B., Bell, J.B., Colella, P., Crutchfield, W.Y., and Welcome, M.L., "An adaptive cartesian grid method for unsteady compressible flow in irregular regions", J. Comp. Phys., 120 (1995), pp. 278-304.

It's availbale for download from the following link:

http://www.llnl.gov/CASC/people/pemb...lications.html

Good Luck.