Fluid Simulation for Computer Graphics (Hardcover, 2)

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