1. The problem I wish to solve is how to accurately simulate a 2-D smoke field using the Lattice-Boltzman Method for Gaseous Phenomena.  

2. My goal is to implement a particle-based system that takes some initial information about a smoke volume/source and outputs a realistic animation of the smoke as it leaves its source.  The animation may be as simple as watching how the smoke moves as it rises through the air from an arbitrary starting point, but it should also act correctly when encountering (colliding with) a stationary or mobile object.  However, the emphasis will be on accurately simulating the movement of the smoke particles from a fixed-camera perspective rather than modeling the full 3-D shape of the smoke volume.

3. Once this part is implemented, the next logical step would be to extend the system to handle a true 3-dimensional modeling of the particle-based smoke volume.  In addition, it would also be nice to explore how to introduce outside forces on the smoke particles, such as simulating a horizontal wind.

4. The first step will be to do the precursor reading on the Navier-Stokes equation and all other concepts that the Lattice-Boltzman Method is based on, such as 'texture splats.'  Making sure I understand how and why this system works will be my starting point.  From there, I can begin working on solving the sub-problems of the system, map out what data structures I need, and create a simple way of visually outputting my results.

5. Here is an initial list of papers that I will be reading:

Lattice-gas automata for the Navier-Stokes equations, 1986 
Toward interactive-rate simulation of fluids with moving using Navier-Stokes equations, 1995
Lattice Boltzmann method for fluid flows, 1998
Texture splats for 3D scalar and vector field visualization, 1993
Lattice Gas Methods for Partial Differential Equations, 1990

Other readings will likely be added to this list as I gain a better idea of where the stumbling blocks are.  For now though, this should be a good starting point.