Animating fluids like water, smoke, and fire using physics-based simulation is increasingly important in visual effects, in particular in movies, like The Day After Tomorrow, and in computer games. This book provides a practical introduction to fluid simulation for graphics. The focus is on animating fully three-dimensional incompressible flow, from understanding the math and the algorithms to the actual implementation.
Author(s): Robert Bridson
Publisher: A K Peters
Year: 2008
Language: English
Commentary: index is missing
Pages: 220
Tags: Информатика и вычислительная техника;Компьютерная графика;
Contents......Page 6
Preface......Page 9
I: The Basics......Page 10
1.1 Symbols......Page 11
1.2 The Momentum Equation......Page 12
1.3 Lagrangian and Eulerian Viewpoints......Page 14
1.4 Incompressibility......Page 18
1.6 Boundary Conditions......Page 21
2.1 Splitting......Page 25
2.2 Splitting the Fluid Equations......Page 27
2.4 Grids......Page 29
3.1 Semi-LagrangianAdvection......Page 34
3.2 Boundary Conditions......Page 38
3.3 Time Step Size......Page 39
3.4 Dissipation......Page 42
3.5 Reducing Numerical Dissipation......Page 44
4. Making Fluids Incompressible......Page 47
4.1 The Discrete PressureGradient......Page 48
4.2 The Discrete Divergence......Page 50
4.3 The Pressure Equations......Page 53
4.4 Projection......Page 67
4.5 More Accurate Curved Boundaries......Page 68
4.6 The Compatibility Condition......Page 77
II: Different Types of Fluids......Page 79
5.1 Temperature and Smoke Concentration......Page 80
5.3 Variable Density Solves......Page 83
5.4 Divergence Control......Page 85
6.1 Marker Particles and Voxels......Page 88
6.2 Level SetMethods......Page 92
6.3 Extrapolation......Page 99
6.4 More Accurate Pressure Solves......Page 100
7. Fire......Page 105
7.1 Thin Flames......Page 106
7.2 Volumetric Combustion......Page 109
8.1 Stress......Page 111
8.2 Applying Stress......Page 113
8.3 Strain Rate and Newtonian Fluids......Page 115
8.4 Boundary Conditions......Page 119
8.5 Implementation......Page 120
III: More Algorithms......Page 129
9.1 Vorticity......Page 130
9.2 Vorticity Confinement......Page 134
9.3 Procedural Turbulence......Page 136
10. Hybrid Particle Methods......Page 140
10.1 Particle Advection......Page 142
10.2 Secondary Particles......Page 144
10.3 Vortex Particles......Page 147
10.4 Particle-in-CellMethods......Page 150
10.5 The Particle Level Set Method......Page 153
11.1 One-Way Coupling......Page 157
11.2 Weak Coupling......Page 160
11.3 The Immersed Boundary Method......Page 161
11.4 General Sparse Matrices......Page 162
11.5 Strong Coupling......Page 165
12. Shallow Water......Page 171
12.1 Deriving the Shallow Water Equations......Page 172
12.2 The Wave Equation......Page 176
12.3 Discretization......Page 178
13.1 Potential Flow......Page 180
13.2 Simplifying Potential Flow for the Ocean......Page 183
13.3 Evaluating the Height Field Solution......Page 188
13.4 Unsimplifying the Model......Page 191
13.6 Eliminating Periodicity......Page 194
A.1 Vector Calculus......Page 196
A.2 Numerical Methods......Page 204
B.1 The Incompressible Euler Equations......Page 208
B.2 The Pressure Problem as a Minimization......Page 210
Bibliography......Page 214
