Fluids: Liquids and Gases - Computer Animation: Algorithms and Techniques - page 250

CHAPTER

8

Fluids: Liquids and Gases

Among the most difficult graphical objects to model and animate are those that are not defined by a
static, rigid, topologically simple structure. Many of these complex forms are found in nature. They
present especially difficult challenges for those intent on controlling their motion. In some cases, spe-
cial models of a specific phenomenon will suffice. We begin the chapter presenting special models for
water, clouds, and fire that approximate their behavior under certain conditions. These models identify
salient characteristics of the phenomena and attempt to model those characteristics explicitly. Such
approaches are useful for a specific appearance or motion, but for a more robust model, a more rigorous
scientific approach is needed. As far as a computational science is concerned, all of the phenomena
mentioned earlier fall under the classification of fluids and computing their motion is called compu-
tational fluid dynamics (CFD). The basics of CFD are given at the end of this chapter.
Many of the time-varying models described in this chapter represent work that is state of the art. It is
not the objective here to cover all aspects of recent research. The basic models are covered, with only
brief reference to the more advanced algorithms.

8.1 Specific fluid models
Fire, smoke, and clouds are gaseous phenomena that have no well-defined surface to model. They are
inherently volumetric models, although surface-based techniques have been applied with limited suc-
cess. For example, water when relatively still has a well-defined surface; however, water changes its
shape as it moves. In the case of ocean waves, features on the water's surface move, but the water itself
does not travel. The simple surface topology can become arbitrarily complex when the water becomes
turbulent. Splashing, foaming, and breaking waves are complex processes best modeled by particle
systems and volumetric techniques, but these techniques are inefficient in nonturbulent situations.
In addition, water can travel from one place to another, form streams, split into separate pools, and
collect again. In modeling these phenomena for purposes of computer graphics, programmers often
make simplifying assumptions in order to limit the computational complexity and model only those
features of the physical processes that are visually important in the specific situation of interest.

8.1.1 Models of water
Water presents a particular challenge for computer animation because its appearance and motion take
various forms [ 5 ] [ 7 ] [ 17 ] [ 20 ] . Water can be modeled as a still, rigid-looking surface to which ripples
can be added as display attributes by perturbing the surface normal using bump mapping [ 1 ].