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j.patel March 4, 2014 10:45

Volume of Fluid method for multiple fluid flows

Currently i am working on multiphase/multifluid flows by using Volume of Fluid method ( with interface capturing no interface reconstruction is involved ). Till now my problem limited to only two fluid by defining volume fraction 1 and 0 for respective fluid. But now i need to extent my two fluid formulation to multiple fluids (more than two fluid having more than one interface). Could anyone suggest me how to take the values volume fractions for more than two fluid for instance three fluids, i have searched for the literatures but did not found relevant one. Please suggest me some useful literatures for the same.


som87 March 4, 2014 12:27

Try searching "SOLA-VOF", I can assure that you wont be disappointed :)

Once you understand that, try reading this one (for three bubble of free surface i.e. three different phase/interface :-

j.patel March 5, 2014 11:28

Thanks for your response, i have gone through the SOLA-VOF and the paper you refereed, in the paper they have simulated multi air bubbles in the water. Therefore, more than one interface exists but having only two phase (i.e. air and water), hence only two volume fraction ( 0 and 1), Please correct me if i have misunderstood. In my case i am interested in more than two fluids, so more then two values of volume fraction and most importantly how to calculate density and viscosity in single continuum model with fluid property jump at the interface, for 2 fluid model i have used following relation:

rho = VF*rho1 + (1-VF)*rho2

index 1 and 2 for fluid 1 and fluid 2 and VF is volume fraction. There are some literatures for multi material interface based on onion skin model but very less description on implementation. Kindly help me for this regard.

thank you,

som87 March 5, 2014 11:59


phi1(x,y)=1 for fluid 1
= [0,1] at the interface between fluid 1 & fluid 2
=0 for fluid 2 & fluid 3

phi2(x,y)=1 for fluid 2
= [0,1] at the interface between fluid 2 & fluid 3
=0 for fluid 3 & fluid 1

phi3(x,y)=1 for fluid 3
= [0,1] at the interface between fluid 3 & fluid 1
=0 for fluid 1 & fluid 2

phi123(x,y)=0 for fluid 1,2,3
=1 for two-fluid interface
=[0,1] if our cell has all 3 fluid within

note1:- [0,1] here indicates 0<function<1
note2:- here phi(s) are our so called volume fraction

Cant we apply the scheme now:)?

j.patel March 7, 2014 10:18

Thanks for your detailed explanation of multi fluid implementation in VOF method. It helps me to better understand the paper you refereed, now i will try to implement two fluid formulation into multi fluid.


som87 March 7, 2014 10:33

cheers, glad I could help(^_^)

chinaduck March 7, 2014 23:13

Hello, My name is Peter,
I am working on the VOF now(air and water only). My code is based on the SIMPLE method. But my code now can only deal with low density ratio flow. Once the density ratio become large, the computed velocity is wrong, the magnitude of the velocity could be more than 100 m/s. I have no idea what causes this. Could anyone give me some suggestion? I am new in VOF. Thanks.

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