This book is designed to give the reader a practical introduction to fluid simulation for graphics. The field of fluid dynamics, even just in animation, is vast and so not every topic will be covered, and many wonderful papers will sadly be passed over in the hope of distilling the essentials; this is far from a thorough survey. The focus of this book is animating fully three-dimensional incompressible flow—from understanding the math and the algorithms to actual implementation. However, there is also a small amount of material on height field simplifications which are important for efficiently modeling large bodies of water.

In general I try to follow Einstein’s dictum, “everything should be made as simple as possible, but not simpler.” Constructing a fluid solver for computer animation is not the easiest thing in the world—there end up being a lot of little details that need attention—but is perhaps easier than it may appear from surveying the literature. I will also provide pointers to some more advanced topics here and there.

I would especially like to thank my former Ph.D. supervisor, Ron Fedkiw, who got me started in graphics and taught me so much; my coauthors and students, many of whom also read and commented on draft versions of this book; Marcus Nordenstam and Double Negative for many productive visits spent developing much of this book for feature film production; Jim Hourihan and Tweak Films for a fantastic visit and continuing conversations; Matthias M¨uller-Fischer and Eran Guendelman who co-taught the SIGGRAPH course from which this book grew; and Alice Peters and A K Peters for making this a reality.