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Park May 4, 2001 02:48

Volume fraction cal. in SIMPLE
from VOF beginner

I want to know the method about calculations of volume fraction in SIMPLE method. SIMPLE is a implicit method. Do I have to make implicit form of void fraction equation ? Can I use explicit method ? if it possible, which one is better ?

and I have another question. In broken-dam problem, how can I satisfy profit boundary condition (especially pressure...) ?

kind regards.

Kike May 4, 2001 04:42

Re: Volume fraction cal. in SIMPLE
Dear "VOF beginner"

There is no relationship between VOF and SIMPLE; which is not an implicit method, but Semi Implicit Method for Pressure Linked Equations.

SIMPLE is a iterative general method to derive pressure equation from NS and continuity eqs. for imcompressible fluids (almost any book of FM have an explanation of it). Now a days there is a "family" of SIMPLE like methods for this problem (SIMPLEST, SIMPLEC, SIMPLER).

VOF is a general method to track interfaces in FV for two phases incompressible fluids. It uses a scalar marker transport eq. to represent the region occupied by each phase (say liquid with scalar=1, gasesous with scalar=0).

If you use VOF, you will update every time step in every cell the values of each fluid properties and to move the interface you need the velocity field, so the resolution of interface dynamic is linked to solution of fluid field, and viceversa.

In VOF you should move the interface from cell to cell, and therefore, you should use explicit schemes to track the interface through the domain. You must to preserve the CFL criterium to avoid interface displacement greater than a cell length, and it will forces you to calculate velocity in an explicit way.

I had used SIMPLEST for pressure calculation in conjunction with explicit Yanenko's Fractional Step Method and PLIC (Picewice Linear Interface Contruction - VOF family) method to tracking the interface. It works and I had very nice agreement with experiments in liquid sheet atomization and droplets formation.


VOF user

pyhsieh May 4, 2001 09:22

Re: Volume fraction cal. in SIMPLE
Hi, Kike,

I am interested in using PLIC-VOF (in 3D). Could you please post some references that describe the details how to implement PLIC in 3D? How is curvature calculated?

Do you know of any site that I can get a source code?



Newbie May 4, 2001 11:39

Re: Volume fraction cal. in SIMPLE
Hi kike Is it possible to apply the VOF in the absence of velocity fields? I need to calculate a shape of a drop in static conditions and I wonder if I can use VOF methodology.


Bubba May 4, 2001 11:55

Re: Volume fraction cal. in SIMPLE
If you want to use an SIMPLE method then you will have to set time critieria for it since

1) VOF is solved explicitly 2) time limits with surface tension 3) Viscous time limits

So to answer your question I think explicit is the way to go.

Bubba May 4, 2001 12:05

Re: Volume fraction cal. in SIMPLE
Yes it is possible to apply VOF in absence of a velocity field. A situation which comes to mind is the simulation of a spherical drop in a gravity free environment (Brackbill,1992). This situation illistrates the most problematic source you will have in your research. Surface Tension. If you are doing a problem in which surface tension is important...

Then don't use VOF use either a LevelSet method or a surface tracking method. These methods can estimate your curvature much better!!!!!!!!!!!!!

Some advances have been made with the surface tension in regards to "spurious currents" but not enough...

Newbie May 4, 2001 12:35

Re: Volume fraction cal. in SIMPLE
Thanks for your answer Bubba, Its very instructive. I would like to ask you about some references on the methods you propose, because for me the curvature prediction is important. Also if you know some codes who implement them.



Bubba May 4, 2001 14:55

Re: Volume fraction cal. in SIMPLE
Tryggvason (old homepage) Interface Tracking ---------------------------------------------

Zaleski (I see Kike with the same e-mail extension) ---------------------------------------------------

Look at Popinet's thesis.

Level Set.... Look through list of reports --------------------------------------------

I personally would not recommend a commercial code for applications with air-water (significant surface tension force) since they typically use CSF with SOLA-VOF. However I have seen a publication recently from someone using the Parallel version of CFX simulating rising bubbles, so it may have been improved. check here under "computer simulations of multi phase flows."

Kike May 10, 2001 05:43

Re: Volume fraction cal. in SIMPLE
Dear N

I am sorry to ansuwer you so late. Yes, it is formally possible, but useless from my point of view.

VOF method is specially usefull to track moving and quite distorted interfaces with fracture and reconnection. If it is not your case you can use, as Bubba say, a surface tracking method.

If you consider surface tension and you apply the CFS method (Brackbil) or the method employed by SURFER (Zaleski), both based on VOF scalar field, then you should add a new term into the momentum eq. and you will have "parasite currents" ie. a small magnitude velocity field, and its related problems.

I think the references Bubba had gave you are good enough to choose a way to start. I specially recomend you to read the content of the PhD Thesis of my colleagues S. Popinet (for surface markers method) and D. Gueyffier (3D VOF).

Best regards


Kike May 10, 2001 05:58

Re: Volume fraction cal. in SIMPLE
Dear pyhsieh

I am sorry to ansuwer you so late. I don't know any published reference for PLIC in 3D, but you can read the PhD. dissertation of my colleague D. Gueyffier from Prof. Zaleski web page:

It is specially dedicated to VOF-PLIC and Surface Tension in 3D. You can also get the e-mail address of Prof. Zaleski from this page and get in contact with him to talk about the source code (he is the head researcher of our group and author of SURFER).

Best whishes


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