Fluids: Liquids and Gases - Computer Animation: Algorithms and Techniques - page 271

The rendering phase uses standard volumetric graphics techniques to produce an image based on the
densities projected onto the image plane. Illumination of a cell from a light source through the volume
must also be incorporated into the display procedure.
The disadvantage of this approach is that if a static data structure for the cellular decomposition is
used, the extent of the interesting space must be identified before the simulation takes place in order to
initialize the cells that will be needed during the simulation of the gas phenomena. Alternatively, a
dynamic data structure that adapts to the traversal of the gas through space could be used, but this
increases the complexity of the simulation.

Particle-based method
In the particle-based method, particles or globs of gas are tracked as they progress through space, often
with a standard particle system approach ( Figure 8.18 ). The particles can be rendered individually, or
they can be rendered as spheres of gas with a given density. The advantage of this technique is that it is
similar to rigid body dynamics and therefore the equations are relatively simple and familiar. The equa-
tions can be simplified if the rotational dynamics are ignored. In addition, there are no restrictions
imposed by the simulation setup as to where the gas may travel. Particles are assigned masses, and
external forces can be easily incorporated by updating particle accelerations and, subsequently, veloc-
ities. The disadvantage of this approach is that a large number of particles are needed to simulate a
dense expansive gas and that to display the surface of a liquid, the boundary between and fluid and
nonfluid must be reconstructed from the particle samples. Recent techniques generalize on the idea
of using rigidly defined particles to include a particle that represents a distribution of fluid mass in
the surrounding area.

Hybrid method
Some models of gas trace particles through a spatial grid. Particles are passed from cell to cell as they
traverse the interesting space ( Figure 8.19 ) . The display attributes of individual cells are determined by
the number and type of particles contained in the cell at the time of display. The particles are used to
carry and distribute attributes through the grid, and then the grid is used to produce the display.

8.2.2 CFD equations
In developing the CFD calculations, the volume occupied by a small ( differential ) fluid element is ana-
lyzed. Differential equations are created by describing what is happening at this element. ( Figure 8.20 ) .

a i ( t )

v i ( t dt )

v i ( t )

a i ( t dt )

FIGURE 8.18
Particle-based method.