# SEM and VOF

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 May 16, 2001, 15:17 SEM and VOF #1 Mehdi BEN ELHADJ Guest   Posts: n/a What is the difference between SEM and VOF ?

 May 18, 2001, 05:35 Re: SEM and VOF #2 Kike Guest   Posts: n/a Hi, Medhi Formally there is no difference. SEM (Scalar Equation Method) is the name of VOF inside PHOENICS. Nevertheless, there are some differencies between SEM and the original VOF in the way to calculate the convective flux (see Hirt and Nichols "Voulme of Fluid VOF method for the dynamics of free boundaries", J. Comp. Phys. 39, 201-225, 1981). PHOENICS SEM employs a second order flux limiter van Leer scheme and the authors of original VOF have proposed a combination between first order up-stream and down-stream schemes. The differences can be seen in results in favor of the original combination proposed by Hirt and Nichols. The results will be much more accurate if you employ some other method to track the interface (PLIC, for instance) and an ADI algorithm (Yanenko or Strang) to integrate the scalar transport equation in PHOENICS. I know it work well for 2D and 3D cases inside PHOENICS. Regards Kike

 May 20, 2001, 06:21 Re: SEM and VOF #3 Mehdi BEN ELHADJ Guest   Posts: n/a In SEM method, the transient convection of a scalar variable is described by the following equation: dF/dt + div(F*v) = 0 dF/dt + d(F*v)/dx1 + d(F*v)/dx2 + d(F*v)/dx3 = 0 (1) The scalar variable F is used as a marker according to which the fluid properties are set: F = 0.0 - fluid 1 F = 1.0 - fluid 2 In VOF method, the transient convection of a scalar variable is described by the following equation: dF/dt + v1*d(F)/dx1 + v2*d(F)/dx2 + v3*d(F)/dx3 = 0 (2) So, I think there is a difference of linearity forms between equations (1) and (2) ?

 May 21, 2001, 07:45 Re: SEM and VOF #4 Kike Guest   Posts: n/a Dear Medhi Take the eq. dF/dt + [v(dot)grad]F = 0 where v=(v1,v2,v3), grad=(d/dx,d/dy,d/dz) and (dot) means scalar product. Now integrate it over a control volume Vc. The second term becomes, a surface integral over the surface which limits the volume Vc. For this term you can write vol_int[v(dot)gradF dV] = sur_int[vF(dot)n dS] where n is the normal vector to the surface which limits Vc, ie. n=(n1,n2,n3) (or n=(nx,ny,nz) if you want) and dS is a diferential of surface. Now solve the surface integral OVER each of your cell faces and, if you use the PHOENICS notation (w=west, e=east, n=north, s=south, h=high and l=low), you will have something like this: sur_int[vF(dot)n dS]= vw*Fw*Sw-ve*Fe*Se + vn*Fn*Sn-vs*Fs*Ss + vh*Fh*Sh-vl*Fl*Sl This is the procedure that PHOENICS employs to solve the scalar marker transport eq. in SEM and this is exactly the same procedure that VOF method employs. Take into consideration that you have this products at cell faces and you should approximate them by the values of F which are defined in cell centers. Now PHOENICS programmers choose to apply a second order van Leer scheme to determine the value of the fluxes in each face. On the other hand, Hirt and Nichols have chosen a combination of the first order upstream and downstream schemes according the orientation of the interface by respect to the convection face. This is the difference, at least, the biggest difference I found between both schemes. Try to prove that both eqs. (1) and (2) ARE THE SAME if you have a divergency free velocity field. So, I dont understand your words "there is a difference of linearity forms". Could you tell me where have you seen your equation (1) inside the PHOENICS code? or What is the reference (paper, communication, technical note, etc) in which you have seen the equation (1)? Regards Kike

 May 21, 2001, 15:47 Re: SEM and VOF #5 Mehdi BEN ELHADJ Guest   Posts: n/a You will find equation (1)at: THE SCALAR EQUATION METHOD FOR FREE SURFACE FLOWSTHE SCALAR EQUATION METHOD) http://www.cham.co.uk/phoenics/d_pol...ecs/semlec.htm Thank you Enrique.

 June 18, 2001, 06:46 Re: SEM and VOF #6 Ahmed Guest   Posts: n/a (GALA) Gas And Liquid Algorithm is incorprated in Phoenics when using SEM, can this be applicable to liquid liquid system. What is the best practice in this case.

 June 18, 2001, 08:31 Re: SEM and VOF #7 Kike Guest   Posts: n/a Dear Ahmed GALA is used to avoid the inclusion of density into the continuity eq. So if your two fluids (even if they are liquids) are no miscible I recommend you to use it. Nevertheless, if you have mixture (molecular diffusion) between them you shoud try to include the eq. for the mixture fraction (MIXF) where MIXF=1 at one liquid and MIXF=0 into the other. In that case the density is calculated as a function of the mixture fraction and the continuity eq. is keeeped in its original form. In my oppinion it is the best practice in these cases. Regards Kike

 December 17, 2001, 12:32 Re: SEM and VOF ------- surface tension. #8 Ahmed Guest   Posts: n/a I have not seen surface tension in SEM and VOF. any suggestion to how surface tension calculation could be introduced in SEM models for two phase immiscible displacement models.

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