[eric1024]

Hi everyone,

I'm simulating the stokes waves with interfoam which is a solver in openFOAM, and I need to impose the initial conditions. For color function (volume fraction), it is straightforward. However, for the velocity fields, I got stuck, since I could not figure out how the velocity field should be imposed properly, especially for the cell with two phases.

In order to impose the initial condition appropriately, I have read the volume of fluid part in the reference, Description and utilization of interFoam multiphase solver. It said . The subscripts represent liquid phase and gas phase, respectively. denotes the volume fraction of liquid phase. According to this, the initial condition of the velocity field should be the velocity field of liquid phase multiplied by the color function of the cell if gas phase is assumed to be stationary.
Summary : If gas phase is assumed to be stationary, .


Here come another questions : what is ? Is it the velocity field at the cell center? What if the cell center is in the gas phase? Would it be valid?
I read Hirt & Nichols (1981), Volume of fluid (VOF) method for the dynamics of free boundaries. Their code were based on the marker-and-cell (MAC) method. In the work of Harlow & Welch (1965), treatment to veclocity field within a cell containing two phases was mentioned. However, both of the works used staggered grids and finite difference method while interfoam store the velocity fields at cell centers and used finite volume method. (OpenFOAM : phi is on the surface, but I can only found U as the initial condition.)

Therefore, I read a clear note written by Cyprien Soulaine and a more detailed note written by Marguerite Graveleau, and I found that the governing equations of volume of fluid could be derived by volume average. It made me wonder whether the velocity field was volume averaged.
Summary : Some derivations of volume of fluid states that the velocity field is volume averaged.


Last, I read the source code of olaflow. It seems to use the cell center velocity multiplied by the volume fraction of the liquid phase.


Please let me know if I made any mistakes.

[eric1024]

When it comes to the initial condition of color function (volume fraction), it is easy to impose the initial condition.
Just compute the area (2D simulation) or the volume (3D simulation) the fluid phase occupied. Then, divide it by the cell area or the cell volume.


When it comes to the velocity fields, I got some choices.

1. Cell center velocity times the cell color function.
2. Average the velocity field of the cell.

Which is more reasonable? Are both of them bad ideas?


Thank you for reading my question.