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a problem of incompressible two phases(water and gas) with VOF MethodHi,all
I'm building a 2D simulation program for a two-phase incompressible viscous fluid simulation (water and air) with VOF method. The VOF method I use is the Hirt & Nichols SOLA-VOF scheme but the reconstruction method is PLIC (Young). In a two-phase approach, when the air water interface is no longer considered as a free-surface, but the interface is still reconstructed using the VOF algorithm. The function Fs is used to determine the aggregated density value inside a grid cell, using weighted averaging .The incompressible Navier-Stokes equations without surface tension is solved with variable density and Viscosity considering water and gas. The effective density and Viscosity are computed as rho = rho_liquid*Fs+(1-Fs)*rho_gas Fs is the fraction of the cell that is filled with fluid in VOF. I use the MAC staggered meshes.So density and Viscosity at both cell center and face should be caculated. I ues the program to simulate the break dam over a dry bed ,but it doesn't work because the pressure possion equation isn't convergent after several hundreds steps...It seems that the interface is not accurate(I don't know it is the problem) ..I can figure it out . Give some advise please,thanks very much!! |

First check if your Navier-Stokes solver performs well in monophasic case (same rho, same mu).
Then for large density and/or viscosity ratios instead of using arithmetic mean as you did, use rather harmonic mean: 1/rho = Fs(1/rho_liquid) + (1-Fs)(1/rho_gas) endly check the scheme you use to solve the hyperbolic equation for Fs. It matters a lot ! bad schemes can induce pb of mass conservation and thus pb to solve your pressure equation which is related to that. |

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I will try what you suggest.Thanks for your help very much! |

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Hi , leflix! I have tried what you suggest.In monophasic case,the Navier-Stokes solver performs well . I have used harmonic mean for large density and/or viscosity ratios, it doesn't work because the pressure possion equation isn't convergent after several hundreds steps. It seems that there are some problems with VOF,of which the reconstruction method is PLIC (Young),while the tracking method is Lagrangian method(Gueyffier) instead of Eulerian method(Hirt and Nichols). But I have used the scheme to handle one-phase problem such as generating wave and dam break, considering air is void and getting velocity and pressure of free surface via interpolation. So can you give some adivise? Thank you very much. :) |

Hi Vivien,
Visibly the problem comes from a bad mass conservation. So if your code performs well in the monophasic case, you have to search around two points: 1) is the way the volume fraction Fs is computed 2) is the implementation of your reconstruction method PLIC I think the problem should be there. Which velocity-pressure coupling algorithm do you use ? Have you tried to under-relax the pressure ? |

2 Attachment(s)
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I want to show you some results for more advise~ I use the program to simulate the break dam over a dry bed. In this test( Numerical simulation of breaking waves using a two-phase flow model), a square computation domain with the length and height equal to 22.8 m is set. A water column with the width L and height 2L (L = 5.7 m) is assumed at the left side of the computation domain. And the spatial steps in the horizontal and vertical directions are 0.285，while Δt is 0.0025.When T=200*0.0025=0.5s, the figure of the flow field is Attachment 8788 When T=269*0.0025s, the pressure Possion equation isn't convergent .The figure of the flow field is Attachment 8789 I have used the VOF method to handle one-phase problem such as generating wave and dam break, considering air is void and getting velocity and pressure of free surface via interpolation. And there are no problem with mass conservation.... So I don’t know what the problem is. Can you give me more advice? |

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It is clear on this figure that the interface is not well captured. Quote:
In fact I don't understand well what you are doing when you say that you handle one-phase problem and getting velocity and pressure of free surface via interpolation.... Could you explain? What is the convection scheme you use to compute Fs field? |

Another question what is the velocity-pressure algorithm that you use?
Do you under-relax the pressure? Can you display the isocontour 0.5 of the Fs field? It should coincides with the position of the free surface |

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I have used the VOF to handle one-phase problem considering air is void and getting velocity and pressure of free surface via interpolation. The interopolation is carried out to satisfy the freesurface boundary conditions.That is to say ,the N-S equations are solved in the domain which is full of fluid. In the VOF method, the reconstruction method is PLIC (Young), while the tracking method is Lagrangian method ( D.Gueyffier, J.Li, A.Nadim, R.Scardovelli, S.Zaleski, Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows ) instead of Eulerian method (Hirt and Nichols) .Thank you! |

2 Attachment(s)
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T=200*0.0025s Attachment 8796 T=269*0.0025s Attachment 8797 Thank you! can you give me you email address so that I can discuss with you ?Thank you |

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