2. Multi-phase flows

Unlike previous researches, we handles the multi-phase navier-stokes solver which includes the buoyancy and surface tension. Our system is designed to use the merits of Navier-Stokes simulation schemes developed for the computer graphics animation.

Multi-phase Navier-Stokes equation

3. Minimum-stress surface tension

In the multi-phase fluid configuration, we can know that the surface will be constructed like blue lines. First find the stress-zero surface of each cell like red line. Second, make the tendency toward the stress-zero surfaces. These tendencies are equivalent to the surface tension forces and defined on the simulation grids. Finally, we can add them to the velocity as body forces. Then, Navier-Stokes solver will handle this naturally.

Minimum-stress surface tension method	The velocity field induced by the surface tension forces

4. Numerical simulation of buoyancy

We numerically simulated buoyancy effects instead of empolying some experimental equations.
Our method was easily implemented as a part of multi-phase simulation system.

Step A	Step B	Step C ((AVI/1.46MB))

5. Mass conservation

Since our method is partially based on the VOF (volume-of-fluid) scheme, we could explicitly correct the total mass of enclosed fluids after each interface capturing step.

[Test A] Mass conservation step was skipped (AVI/1.41MB)	[Test B] Mass conservation step was used (AVI/1.58MB)

6. Result

Finally we could animate the rising bubbles in liquid within the Navier-Stokes fluid simulation scheme. We empolyed some particles to provide liveliness for the animation scenes. Interfaces were rendered by the vertex-shader techniques.

(AVI/6.37MB)