CSC570Q Final Project

Fluid Simulator

(March 14, 2005)

James Skorupski

Graham O’Daniel

Abstract

Generating fluid simulations in real-time is a desirable ability for applications such as video games and cinema. There are a number of approaches available to work with in order to approximate fluids, with each introducing particular drawbacks. Some simulations approximate the surface of a liquid using reflection maps, but do nothing to address the fluid’s collision with objects. Other simulations approximate water through the use of free moving spheres, which when drawn together and proper filters are applied in the graphics pipeline can appear like fluid. The approach we take in this project is one based on Smooth Particle Hydrodynamics, or SPH. SPH focuses on representing a fluid as a mass of particles, with many different forces applied to the particles, both internal and external forces, by using the Navier-Stokes equations for fluid dynamics. By applying a marching cubes implementation to the simulation, a semi-realistic surface can be approximated from the density of particles. Our program also handles collisions on a per-particle basis with implicit surfaces. The particle system and can be extended to large particle systems given adequate computing power.

Features

SPH based particle dynamics with the following forces

Viscosity – resistance to flow of a liquid

Pressure – force exerted on particles from other particles

Gravity – downward force of gravity (held constant in simulation)

Other external forces

Particle collision with implicit surfaces

“Leap-frog” integration method for accurate time steps

Marching cubes (see reference)

Executables

Pentium III or better optimized executable

Pentium IV or Athlon 64 or better optimized executable

Screenshots

User Guide

S toggles the drawing of spatial buckets as yellow cubes.

X toggles the marching cubes algorithm.

The Left arrow rotates the camera clockwise around the center of the scene.

The Right arrow rotates the camera counter clockwise around the center of the scene.

The Up arrow rotates the camera towards the top about the X-axis around the center of the scene.

The Down arrow rotates the camera towards the bottom about the X-axis around the center of the scene.

L toggles the static sphere in the center of the scene.

O decreases the time step used in fixed time steps mode.

P increases the time step used in fixed time steps mode.

N decreases the radius of the static sphere at the center of the scene.

M increases the radius of the static sphere at the center of the scene.

C changes the color of the lighting on the scene.

G changes whether gravity is applied to the particles or not.

A changes whether a rotational force is applied to the particles or not.

Escape quits the program.

Space applies a force to the particles pushing them to the left of the scene.

Future Improvements

v Implement surface tension

v Optimize marching cubes to reuse previous calculations

v More user forces

v Larger particle systems (1000+)

v More implicit surfaces/containers

References

Stewart, Nigel. “GLT OpenGL – C++ Toolkit.” http://www.nigels.com/glt. Last visited 3/12/05.

Muller, Mathias et al. “Particle-Based Fluid Simulation for Interactive Applications.” SIGGRAPH 2003.