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
