The Art of Fluid Animation

【核心代码】

Contents
Preface, xi
Acknowledgments, xix
Author, xxi
C HAPTER 1 ◾ Introduction 1
C HAPTER 2 ◾ Observations, Equations, and Numbers 11
2.1 BEAVERS, CAVE PERSONS, AND FIRE 11
2.2 FROM CAVES TO GREEKS: ARCHIMEDES, GOLD,
AND MEDALS 13
2.3 LONG, CURLY HAIRED MATHEMATICIANS,
THE ABYSS AND THE AIRBRUSH 16
C HAPTER 3 ◾ Euler–Newton Equations or Navier–Stokes
Equations 35
3.1 LEONARDO DA VINCI 35
3.2 EULER AND CONTINUITY 36
3.3 INCOMPRESSIBILITY, CONTINUITY, HELMHOLTZ,
AND HODGE THEORY 44
3.4 EULER AND THE MOTION OF FLUIDS 49
3.5 NEWTON AND VISCOSITY 55
3.6 NAVIER AND STOKES AND THEIR EQUATIONS 64
3.7 BOUNDARIES, BOUNDARIES, BOUNDARIES,
BOUNDARIES, AND BOUNDARIES 69
viii ◾ Contents
C HAPTER 4 ◾ The Early Days of Computational
Fluid Dynamics 81
C HAPTER 5 ◾ Kolmogorov and Turbulence 91
C HAPTER 6 ◾ Introduction to Fluid Animation 97
6.1 DISCRETIZE! BUGS, GRIDS, AND BUGS MOVING
THROUGH GRIDS 98
6.1.1 Bugs 99
6.1.2 Grids 103
6.1.3 Bugs Moving through Grids 107
6.1.4 Semi-Lagrangian 108
6.1.5 PIC 112
C HAPTER 7 ◾ Intermezzi 117
7.1 INTERMEZZO UNO: LINEAR SYSTEMS 118
7.2 INTERMEZZO DUE: THE GENERAL SOLUTION OF
A LINEAR SYSTEM 124
7.3 INTERMEZZO TRE: CIRCULANT MATRICES
AND THE FOURIER TRANSFORM 132
7.4 INTERMEZZO QUATTRO: NUMERICAL SOLUTION
OF LINEAR SYSTEMS 141
C HAPTER 8 ◾ A Simple Fluid Solver 155
8.1 A MATH HORROR FLICK: OPERATOR SPLITTING 159
8.2 CODE PLEASE? 160
8.2.1 Moving Densities 164
8.2.2 Moving Fluids Tat Change Temselves:
Nonlinearity 170
8.3 BUGS CRAWLING ON DONUTS, THE FFT, AND
~60 LINES OF C CODE 176
8.4 FOUR-DIMENSIONAL TURBULENT VECTOR FIELDS
AND TURBULENCE 186
8.5 DECORATING FLUIDS 189
Contents ◾ ix
C HAPTER 9 ◾ The Little Computers Who Can Handle Fluids 195
C HAPTER 10 ◾ The Smart Phones That Can Handle Fluids 199
C HAPTER 11 ◾ Fluid FX: Version 2.0 of Autodesk Fluid 203
C HAPTER 12 ◾ Show Time! MAYA Fluid Effects 205
C HAPTER 13 ◾ Fluids on Arbitrary Surfaces 213
C HAPTER 14 ◾ Control Freaks! How to Make Fluids Do What
We Want 219
14.1 SHOOTING CANNONBALLS IN TWO DIMENSIONS 222
14.2 COMPUTER OPTIMIZERS 223
14.3 THE AD, THE JOINT, AND THE PATH BACK TO THE
OPTIMIZER 233
C HAPTER 15 ◾ Real Experiments, Computer Experiments,
and Validation 239
15.1 SPHERES ARE SUCH A DRAG 240
15.2 CURLY FLOWS BEHIND SPHERES, WAVY FLOWS IN
TUBES, AND TURBULENT PLUMES BETWEEN PLATES 242
15.2.1 Experiment Number One: Curly Flows behind
Spheres 243
15.2.2 Experiment Number Two: Wavy Flows in Tubes 243
15.2.3 Experiment Number Tree: Turbulent Plumes
between Plates 245
C HAPTER 16 ◾ Epilogue: Let’s Call It Quits 249