Abstract:

Recent advances in simulation methods for three-dimensional computer animation have led to a significant increase in realism and have benefited the digital entertainment industry. We will discuss two methods for improving the realism in fluid simulations: (1) The improved BFECC advection that increases the dynamic in simulated fluid motion and (2) a volume control technique that prevent the loss of fluid volume. We will demonstrate these advances on simulations of smoke, liquid, bubbles, rigid bodies, and foam. More detailed summaries of these two methods are provided below. We will also discuss future opportunities afforded by the symbiotic relation between scientific computing and computer animations.

The BFECC (Back and Forth Error Compensation and Correction) was recently developed for interface computation using a level set method. We show that BFECC can be applied to reduce dissipation and diffusion encountered in a variety of advection steps, such as velocity, smoke density, and image advections on uniform and adaptive grids and on a triangulated surface. BFECC 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. When applied to level set evolution, BFECC reduces volume loss significantly. We demonstrate the benefits of this approach on image advection and on the simulation of smoke, bubbles in water, and the highly dynamic interaction between water, a solid, and air. We also apply BFECC to dye advection to visualize vector fields.

Liquid and gas interactions often contain 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 slow 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 trace 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.