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PLIC-VOF with a Conservative formulation at high density ratio

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Old   February 9, 2018, 04:54
Post PLIC-VOF with a Conservative formulation at high density ratio
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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:
  • PLIC-VOF in 2D (for coupling with a Naviers Stokes Solver)
  • Non-conservative formulation for a dam-break problem with density ratio of 1000
  • Conservative formulation for a dam-break problem with denstiy ratio of 10
At higher density ratios, while using the conservative formulation, there is an unphysical increase in the velocity near the interface. I know that this is caused by a sudden jump in density which causes an ill-posed matrix while solving for pressure. I would like to know how to rectify the issue to make the conservative solver work at higher density ratios.
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Old   February 9, 2018, 05:36
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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 \rho_{f1} and \rho_{f2}, the face normal velocity is v_f, the face are is A, the overall volume flux on the face is

\dot{V}_{Sum}=v_F*A.

Now, the volume flux for the second phase \dot{V}_2 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:

\dot{V}_1=\dot{V}_{Sum} - \dot{V}_2

Now just use these two volume fluxes to calculate the mass flux using the density for the two phases on the face seperately:

\dot{m}_f=\dot{V}_{f1}*\rho_1 + \dot{V}_2*\rho_{f2}

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.
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Old   February 9, 2018, 08:46
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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?
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Old   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.
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Old   February 11, 2018, 22:44
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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.
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Old   February 12, 2018, 03:38
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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 flux-split 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,
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Old   February 15, 2018, 04:07
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Quote:
Originally Posted by abhishek13 View Post
Sorry but i still dont get what you are trying to say. Where do i need to use the mass flux?
For the discretization of the convection term and for the source term in the pressure correction equation.
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Old   February 15, 2018, 10:23
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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 PLIC-VOF does.

However, I did find that for some density ratios (air water) keeping the viscosity ratio as 1, the solver really struggles.
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