Physically-Based Fluid Modeling using Smoothed Particle Hydrodynamics

Table of Contents
Chapter 2: Particle Systems and Fluid Dynamics



CHAPTER 1

Introduction

One of the most beautiful physical phenomena is the motion of liquid: flowing rivers, dripping oil, coffee pouring and mixing with cream. The complex behavior of the liquid is what makes it so fascinating, but is also why it is one of the most challenging phenomena to model for computer graphics. Fluid in motion has a very dynamic structure. It is always changing shape, often splitting apart and rejoining again. Mimicking this behavior for computer animation requires complex models and efficient rendering. Fluid will not look realistic if rendered using only a few simple polygons. Point rendering is successful in situations such as spray or waterfalls, but rendering methods such as ray tracing or high resolution polygonization are needed for a realistic animation of continuous fluid. The underlying model can be, but is not required to be, physically based. In any case, complex equations are often needed in order to approximate the behavior so that the resulting animation is realistic. With all this complexity there are performance bottlenecks which make an interactive or real-time system difficult to attain.

The intent of the research presented here is the establishment of a new physically based model of fluid motion. The end goals included:

In order to achieve these goals a particle system was developed with dynamics based on a computational fluid dynamics (CFD) model known as Smoothed Particle Hydrodynamics (SPH). Particles represent small volumes of fluid and move in response to natural forces such as gravity and pressure. Most of the intended goals were achieved. This model gives realistic physically based motion. Particles can move at interactive speeds and particles react properly when coming into contact with solid objects in the environment. The algorithm for rendering the fluid as a surface turned out to be a significant performance bottleneck. Future efforts include research into more efficient surface generation techniques, as well as other methods for improving the realism of the fluid animation.

The remainder of this chapter describes previous methods for modeling fluid in computer graphics. Chapter 2 details the background of particle systems and fluid dynamics, the two areas from which this research stems. Chapter 3 discusses the details of the model being presented. Chapters 4 and 5 go into performance results and future work.

1.1. Previous Fluid Modeling Methods

Accurate models of fluid motion based on physical equations exist (i.e. the Navier-Stokes equations) but are far too complex to be of practical use for computer graphics. As a result, graphics research in this area (as in many areas) has focused on finding simpler models which are efficient and approximate motion well enough to give realistic looking results.

Water waves have been modeled using a wide variety of approaches, including stochastic models (Perlin, 1985; Mastin, 1987) and kinematic models (Max, 1981; T'so, 1987). Kass and Miller (Kass, 1990) presented a dynamic model for wave motion using the hydrodynamic equations to animate a height field. They simplified shallow water equations and applied the solution to a two dimensional grid representing the water surface. Spray and foam from breaking waves have been modeled by adding particle systems to kinematic models using height fields (Peachy, 1986) and parametric surfaces (Fournier, 1986). Particle systems have also been used for modeling ship wakes (Goss, 1990) and waterfalls (Sims, 1990).

Coupled particle systems (where particles interact with each other) have been used to create a molecular dynamics model for animating viscous liquids (Miller, 1989; Terzopoulos, 1989; Tonnesen, 1991). In this model particle motion is governed by the simulation of inter-molecular forces between pairs of particles. External forces such as gravity are also used, resulting in macroscopic movement which is similar to that of slime, oil or other viscous fluids.

This paper presents a model based on fluid dynamics instead of molecular dynamics. The approach is similar to that of the molecular dynamics model, but the simulation involves fluid forces instead of molecular forces. A coupled particle system is used where particles interact according to the hydrodynamic equations of motion specified by a particle-based computational fluid dynamics model known as Smoothed Particle Hydrodynamics.

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Chapter 2