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Hybrid Method for Water and Bubbles

1. Abstract

We propose a hybrid method for simulating multiphase fluids such as bubbly water. The appearance of subgrid visual details is improved by incorporating a new bubble model based on smoothed particle hydrodynamics (SPH) into an Eulerian grid-based simulation that handles background flows of large bodies of water and air. To overcome the difficulty in simulating small bubbles in the context of the multiphase flows on a coarse grid, we heuristically model the interphase properties of water and air by means of the interactions between bubble particles. As a result, we can animate lively motion of bubbly water with small scale details efficiently.

2. Hybrid approach of Eulerian and Lagrangian

We use the Eulerian method to generate the background motions of water and air bodies which are large enough to be captured using a simulation grid which can be managed by a common single-CPU machine. The bubbling details that are too small to be handled on the grid are simulated by SPH particles. We built our system on the particle level-set fluid solver to generate bubble particles modeled by incorporating the escaped particles back into the SPH system as bubbles.

3. The drag force at a bubble surface

Since the density of water is 800 times that of air, the force applied to water by air is insignificant. Conversely, water induces buoyancy, drag and left forces on bubbles. A drag force is applied to the upper portion of the air bubble by buoyancy. Ellingsen and Risso observed that an air bubble injected into water retains its ellipsoidal shape while it rises, implying that the drag force only acts on the upper portion of the air bubble. We control the shape of an air bubbles by the drag force.

4. Interchangeable SPH and Level set

We displayed small-scaled bubble motion based on Lagrangian SPH particles in a grid-based simulation to detect detailed features of the sub-grid. In fact, the cohesion force SPH particles contain enables particles to be merged, yielding high density and creating air bubbles large enough to be depicted in a grid. Though the creation of SPH particles was originally intended to describe details of a sub-grid, the integration of SPH particles larger than subgrid size reduces the simulation accuracy. When the size of SPH particles outgrows that of the sub-grid, we turn to grid-based level set.

5. Swirling Bubbly Water

The effect of surface tension is dynamically and realistically represented within a multiphase fluid simulation. Air bubbles are seeded with 'bubble particles,' which move randomly. These molecule-like movements modify the surface of the air bubbles and generate turbulence in the water. The surface tension between air bubble and water, determined by the composition of the water, remains constant regardless of the size of the bubble, while external forces cause unstable uid motion as the surface tension strives to remain constant, bubbles split and merge. The bubble particles can also compute for the numerical dissipation usually experienced in grid-based fluid simulations, by restoring the lost volume of individual bubbles. The realistic tearing of bubble surfaces is shown in a range of examples.

6. Related Publications

[1] "Bubbles Alive," Jeong-Mo Hong, Ho-Young Lee, Jong-Chul Yoon and Chang-Hun Kim, ACM Transactions on Graphics (In Proceedings of ACM SIGGRAPH 2008), Volume 27, Number 3, Article 48, August 2008.

[2] "Interchangeable SPH and Level set Method in Multiphase Fluids," Ho-Young Lee, Jeong-Mo Hong and Chang-Hun Kim, The Visual Computer, Volume 25, Number 5-7, pp. 713-718, May 2009.

[3] "Simulation of Swirling Bubbly Water using Bubble Particles," Ho-Young Lee, Jeong-Mo Hong and Chang-Hun Kim, The Visual Computer, Volume 25, Number 5-7, pp. 707-712, March 2009.

[4] "Controlling shapes of air bubbles in a multi-phase fluid simulation," Po-Ram Kim, Ho-Young Lee, Jong-Hyun Kim and Chang-Hun Kim, The Visual Computer, Volume 28, Number 6-8, pp. 597-602, June 2012.