A Boundary Method for Incompressible Fluid Flow

The animation of fluids is a topic of great interest in the computer animation community. The common familiarity with real-world fluid motion and the difficulty in achieving this motion combines to make the problem exceptionally challenging — everyone knows what fluid should look like, but animating it convincingly by hand is difficult. To achieve realistic fluid motion, researchers have been generating fluid simulations using computational fluid dynamics and rendering the output. This physics-based animation produces plausible fluid motion with much less effort required by the animator. This project is a novel method of fluid simulation for animation. The main focus is on maintaining fluid incompressibility, so that the volume of fluid remains constant. This is achieved by using a pseudo-pressure which forces the velocity field of the fluid to be divergence-free. This pressure is obtained by solving an integral of least squares problem. In this project, this least squares problem is solved both on a finite-difference grid, and using a new explicit surface representation. The two main contributions of this work are thus: verification of the least squares pressure solve on a finite difference grid, and a new surface-only fluid simulator, which aims to reduce the dimensionality of the problem by one.