Source: http://graphics.ethz.ch/teaching/imagesynthesis_06/miniprojects/p3/index.html

This project is nearly similiar to the goal of our project, Partical Advection. However, the project described takes it much further than we are required to. The flame and smoke is rendered in three dimensions using velocify fields based on 3D Navier-Stokes equations. They use differential fields to not only simulate the the density of the flame, but also temperature. This is a simplification, as they are independant variables. However, it allows them to model a realistic color of fire. Fire is further simulated by not only adding fire to the base, but also giving it an initial velocity. Adding initial velocity adds to the realism of the simulation because it removes the delay of new particles from reaching the top, and helps remove the gathering of particles as they slowly obtain velocity.

For their smoke simulation, the same principles are used as the simulation of fire. Particles are given an initial velocity as they are injected into the base. But, to add realism to the fire, they added light sources and used ray tracing to see through the smoke cloud. Thus, instead of the smoke cloud being a solid object (like our Particle Advection), we can see the edges of the cube that the smoke is filling.

Here are videos the fire and smoke renders:
fire: http://graphics.ethz.ch/teaching/imagesynthesis_06/miniprojects/p3/fire.mpg
smoke: http://graphics.ethz.ch/teaching/imagesynthesis_06/miniprojects/p3/smoke.mpg