2nd Edition

Fluid Simulation for Computer Graphics

By Robert Bridson Copyright 2016
    276 Pages 22 B/W Illustrations
    by A K Peters/CRC Press

    276 Pages 22 B/W Illustrations
    by A K Peters/CRC Press

    A practical introduction, the second edition of Fluid Simulation for Computer Graphics shows you how to animate fully three-dimensional incompressible flow. It covers all the aspects of fluid simulation, from the mathematics and algorithms to implementation, while making revisions and updates to reflect changes in the field since the first edition.

    Highlights of the Second Edition

    • New chapters on level sets and vortex methods
    • Emphasizes hybrid particle–voxel methods, now the industry standard approach
    • Covers the latest algorithms and techniques, including: fluid surface reconstruction from particles; accurate, viscous free surfaces for buckling, coiling, and rotating liquids; and enhanced turbulence for smoke animation
    • Adds new discussions on meshing, particles, and vortex methods

    The book changes the order of topics as they appeared in the first edition to make more sense when reading the first time through. It also contains several updates by distilling author Robert Bridson’s experience in the visual effects industry to highlight the most important points in fluid simulation. It gives you an understanding of how the components of fluid simulation work as well as the tools for creating your own animations.

    THE BASICS

    The Equations of Fluids
    Symbols
    The Momentum Equation
    Lagrangian and Eulerian Viewpoints
    Incompressibility
    Dropping Viscosity
    Boundary Conditions

    Overview of Numerical Simulation
    Splitting
    Splitting the Fluid Equations
    Time Steps
    Grids
    Dynamic Sparse Grids
    Two Dimensional Simulations

    Advection Algorithms
    Semi-Lagrangian Advection
    Boundary Conditions
    Time Step Size
    Diffusion
    Reducing Numerical Diffusion

    Level Set Geometry
    Signed Distance
    Discretizing Signed Distance Functions
    Computing Signed Distance
    Recomputing Signed Distance
    Operations on Level Sets
    Contouring
    Limitations of Level Sets
    Extrapolating Data

    Making Fluids Incompressible
    The Discrete Pressure Gradient
    The Discrete Divergence
    The Pressure Equations
    Projection
    More Accurate Curved Boundaries
    The Compatibility Condition

    Smoke
    Temperature and Smoke Concentration
    Buoyancy
    Variable Density Solves
    Divergence Control

    Particle Methods
    Advection Troubles on Grids
    Particle Advection
    Transferring Particles to the Grid
    Particle Seeding
    Diffusion
    Particle-in-Cell Methods

    MORE TYPES OF FLUIDS

    Water
    Marker Particles and Voxels
    More Accurate Pressure Solves
    Topology Change and Wall Separation
    Volume Control
    Surface Tension

    Fire
    Thin Flames
    Volumetric Combustion

    Viscous Fluids
    Stress
    Applying Stress
    Strain Rate and Newtonian Fluids
    Boundary Conditions
    Implementation

    MORE ALGORITHMS

    Turbulence
    Vorticity
    Vorticity Confinement
    Procedural Turbulence
    Simulating Sub-Grid Turbulence

    Shallow Water
    Deriving the Shallow Water Equations
    The Wave Equation
    Discretization

    Ocean Modeling
    Potential Flow
    Simplifying Potential Flow for the Ocean
    Evaluating the Height Field Solution
    Unsimplifying the Model
    Wave Parameters
    Eliminating Periodicity

    Vortex Methods
    Velocity from Vorticity
    Biot-Savart and Streamfunctions
    Vortex Particles

    Coupling Fluids and Solids
    One-Way Coupling
    Weak Coupling
    The Immersed Boundary Method
    General Sparse Matrices
    Strong Coupling

    Background
    Vector Calculus
    Numerical Methods

    Derivations
    The Incompressible Euler Equations

    Biography

    Robert Bridson