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PLICVOF with a Conservative formulation at high density ratio 

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February 9, 2018, 04:54 
PLICVOF with a Conservative formulation at high density ratio

#1 
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Abhishek
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Greetings!
I am trying to develop a Two Phase VOF solver with a conservative formulation. I have successfully implemented the following:


February 9, 2018, 05:36 

#2 
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Basically what you have to do is not to use the average density for the interface density in the mass flux. Rather use a mass flux, which is calculated from the mass fluxes of the two phases:
if the face densities for the two phases are and , the face normal velocity is , the face are is , the overall volume flux on the face is . Now, the volume flux for the second phase is known from the PLIC reconstruction, because that is what you need PLIC for. This means you can calculate the volume flux for the first phase from these numbers: Now just use these two volume fluxes to calculate the mass flux using the density for the two phases on the face seperately: This procedure worked very well for me. I can't give you a reference though, because I kind of came up with it myself. However, I am fairly sure someone has done and published it before. Last edited by beer; February 9, 2018 at 10:27. 

February 9, 2018, 08:46 

#3 
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Abhishek
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Hello! Thanks for the reply. Are you suggesting that the density at the faces should be calculated using the amount of both fluids present in the volume (face velocity*dt)*A?


February 9, 2018, 10:28 

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No, sorry I should have stated that. You should calculate the face density for each phase seperately. I edited my answer above.


February 11, 2018, 22:44 

#5 
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Abhishek
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Sorry but i still dont get what you are trying to say. Where do i need to use the mass flux?
Last edited by abhishek13; February 13, 2018 at 02:46. 

February 12, 2018, 03:38 

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Nikhil
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Dear Abhishek,
This is caused due to disparity in Gamma (specific heat ratio calculation) Please refer the following paper, https://www.sciencedirect.com/scienc...21999115005021 titled "Preventing numerical oscillations in the fluxsplit based finite difference method for compressible flows with discontinuities". As this paper is highly condensed you might have to cross refer the references for more details. Regards, 

February 15, 2018, 04:07 

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February 15, 2018, 10:23 

#8 
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Saideep
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Might be of use. A simple way is to filter the volume fraction several times so that you dont see a sharp jump in the fluid properties but a gradual jump. This is something that the software "Gerris Flow Solver" using PLICVOF does.
However, I did find that for some density ratios (air water) keeping the viscosity ratio as 1, the solver really struggles. 

Tags 
conservative form, twophase fluid, volume of fluid 
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