Fluid Simulation for Computer Graphics 2nd Edition by Robert Bridson ISBM 135196884X 9781351968843

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ISBN 10:      135196884X
ISBN 13: 978-1351968843
Author:      Robert Bridson

Fluid Simulation for Computer Graphics 2nd Table of contents:

Part I: Foundations

Chapter 1: The Equations of Fluids

• 1.1 Symbols
• 1.2 The Momentum Equation
• 1.3 Lagrangian and Eulerian Viewpoints
  • 1.3.1 An Example
  • 1.3.2 Advecting Vector Quantities
• 1.4 Incompressibility
• 1.5 Dropping Viscosity
• 1.6 Boundary Conditions

Chapter 2: Overview of Numerical Simulation

• 2.1 Splitting
• 2.2 Splitting the Fluid Equations
• 2.3 Time Steps
• 2.4 Grids
• 2.5 Dynamic Sparse Grids
• 2.6 Two Dimensional Simulations

Chapter 3: Advection Algorithms

• 3.1 Semi-Lagrangian Advection
• 3.2 Boundary Conditions
• 3.3 Time Step Size
  • 3.3.1 The CFL Condition
• 3.4 Diffusion
• 3.5 Reducing Numerical Diffusion

Chapter 4: Level Set Geometry

• 4.1 Signed Distance
• 4.2 Discretizing Signed Distance Functions
• 4.3 Computing Signed Distance
  • 4.3.1 Distance to Points
  • 4.3.2 Loop Order
  • 4.3.3 Finding Signed Distance for a Triangle Mesh
• 4.4 Recomputing Signed Distance
• 4.5 Operations on Level Sets
• 4.6 Contouring
• 4.7 Limitations of Level Sets
• 4.8 Extrapolating Data

Chapter 5: Making Fluids Incompressible

• 5.1 The Discrete Pressure Gradient
• 5.2 The Discrete Divergence
• 5.3 The Pressure Equations
  • 5.3.1 Putting It In Matrix-Vector Form
  • 5.3.2 The Conjugate Gradient Algorithm
  • 5.3.3 Incomplete Cholesky
  • 5.3.4 Modified Incomplete Cholesky
  • 5.3.5 Domain Decomposition
• 5.4 Projection
• 5.5 More Accurate Curved Boundaries
  • 5.5.1 The Finite Volume Method
  • 5.5.2 Area Fractions
  • 5.5.3 Tiny Fractions Considered Harmful
  • 5.5.4 Velocity Extrapolation
• 5.6 The Compatibility Condition

Chapter 6: Smoke

• 6.1 Temperature and Smoke Concentration
• 6.2 Buoyancy
• 6.3 Variable Density Solves
• 6.4 Divergence Control

Chapter 7: Particle Methods

• 7.1 Advection Troubles on Grids
• 7.2 Particle Advection
• 7.3 Transferring Particles to the Grid
• 7.4 Particle Seeding
  • 7.4.1 Smoothly Varying Emission
  • 7.4.2 Sharp Regional Emission
• 7.5 Diffusion
• 7.6 Particle-in-Cell Methods

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Part II: More Types of Fluids

Chapter 8: Water

• 8.1 Marker Particles and Voxels
• 8.2 More Accurate Pressure Solves
• 8.3 Topology Change and Wall Separation
• 8.4 Volume Control
• 8.5 Surface Tension

Chapter 9: Fire

• 9.1 Thin Flames
• 9.2 Volumetric Combustion

Chapter 10: Viscous Fluids

• 10.1 Stress
• 10.2 Applying Stress
• 10.3 Strain Rate and Newtonian Fluids
• 10.4 Boundary Conditions
• 10.5 Implementation
  • 10.5.1 Explicit Treatment
  • 10.5.2 Implicit Treatment
  • 10.5.3 Variational Form of Implicit Integration
  • 10.5.4 Implicit Viscosity with Free Surfaces

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Part III: More Algorithms

Chapter 11: Turbulence

• 11.1 Vorticity
• 11.2 Vorticity Confinement
• 11.3 Procedural Turbulence
  • 11.3.1 Fourier Synthesis
  • 11.3.2 Noise
• 11.4 Simulating Sub-Grid Turbulence

Chapter 12: Shallow Water

• 12.1 Deriving the Shallow Water Equations
  • 12.1.1 Assumptions
  • 12.1.2 Velocity
  • 12.1.3 Height
  • 12.1.4 Boundary Conditions
• 12.2 The Wave Equation
• 12.3 Discretization

Chapter 13: Ocean Modeling

• 13.1 Potential Flow
• 13.2 Simplifying Potential Flow for the Ocean
• 13.3 Evaluating the Height Field Solution
• 13.4 Unsimplifying the Model
• 13.5 Wave Parameters
• 13.6 Eliminating Periodicity

Chapter 14: Vortex Methods

• 14.1 Velocity from Vorticity
• 14.2 Biot-Savart and Streamfunctions
• 14.3 Vortex Particles
  • 14.3.1 Tracking Smoke
  • 14.3.2 Buoyancy
  • 14.3.3 Mollification
  • 14.3.4 Undoing the Inviscid Assumption
  • 14.3.5 Jumping to 3D
  • 14.3.6 Speeding Up Biot-Savart
  • 14.3.7 Solid Boundaries
  • 14.3.8 Vortex-in-Cell

Chapter 15: Coupling Fluids and Solids

• 15.1 One-Way Coupling
• 15.2 Weak Coupling
• 15.3 The Immersed Boundary Method
• 15.4 General Sparse Matrices
• 15.5 Strong Coupling

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