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Liu, Yingjie

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    Simulation of Bubbles in Foam With The Volume Control Method
    (Georgia Institute of Technology, 2007) Kim, Byungmoon ; Liu, Yingjie ; Llamas, Ignacio ; Jiao, Xiangmin ; Rossignac, Jarek
    Liquid and gas interactions often produce bubbles that stay for a long time without bursting on the surface, making a dry foam structure. Such long lasting bubbles simulated by the level set method can suffer from a small but steady volume error that accumulates to a visible amount of volume change. We propose to address this problem by using the volume control method. We track the volume change of each connected region, and apply a carefully computed divergence that compensates undesired volume changes. To compute the divergence, we construct a mathematical model of the volume change, choose control strategies that regulate the modeled volume error, and establish methods to compute the control gains that provide robust and fast reduction of the volume error, and (if desired) the control of how the volume changes over time.
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    Simulation of Bubbles and Liquid Films
    (Georgia Institute of Technology, 2006) Kim, Byungmoon ; Liu, Yingjie ; Llamas, Ignacio ; Rossignac, Jarek
    Liquid and gas interactions often contain bubbles surrounded by thin liquid films. Simulation of these liquid films is challenging since they quickly become thinner than the grid resolution, which leads to premature bursting or merging of the bubbles. We prevent this thinning process by applying a disjoining force to the film, obtaining bubbles that last much longer without bursting or merging. The surface tension on the liquid film is the next diffuculty. Since the level set is not differentiable at the center of the thin liquid film, the curvature computed from the level set gradient is noisy, and the thin liquid film ruptures quickly. To prevent this, we compute the surface tension from the local isosurface, obtaining long-lasting liquid films. However, since bubbles stay longer without bursting or merging, the volume loss of each bubble is noticeable. To solve this problem, we modify the pressure projection to produce a velocity field whose divergence is controlled by the proportional and integral feedback. This allows us to preserve the volume or, if desired, to inflate or deflate the bubbles. In addition to premature bursting and volume change, another difficulty is the complicated liquid surface, which increases memory and computational costs. To reduce storage requirement, we collocate the velocity and pressure to simplify the octree mesh. To reduce the computational complexity of the pressure projection, we use a multigrid method.
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    Advections with Significantly Reduced Dissipation and Diffusion
    (Georgia Institute of Technology, 2006) Kim, Byungmoon ; Liu, Yingjie ; Llamas, Ignacio ; Rossignac, Jarek
    Back and Forth Error Compensation and Correction (BFECC) can be applied to reduce dissipation and diffusion in advection steps, such as velocity, smoke density, and image advections. It can be implemented trivially as a small modification of the first-order upwind or semi-Lagrangian integration of advection equations. It provides second-order accuracy in both space and time and reduces volume loss significantly. We demonstrate its benefits on the simulation of smoke, bubbles, and interaction between water, a solid, and air.
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    FlowFixer: Using BFECC for Fluid Simulation
    (Georgia Institute of Technology, 2005) Kim, Byungmoon ; Liu, Yingjie ; Llamas, Ignacio ; Rossignac, Jarek
    Back and Forth Error Compensation and Correction (BFECC) was recently developed for interface computation by using the level set method. We show that it can be applied to reduce dissipation and diffusion encountered in various advection steps in fluid simulation such as velocity, smoke density and image advections. BFECC can be implemented easily on top of the first order upwinding or semi-Lagrangian integration of advection equations, while providing second order accuracy both in space and time. When applied to level set evolution, BFECC reduces volume loss significantly. We combine these techniques with variable density projection and show that they yield a realistic animations of two-phase flows. We demonstrate the benefits of this approach on the image advection and on the simulation of smoke, of bubbles in water, and of a highly dynamic interaction between water, a solid, and air.