### Summary 
This paper describes a stable method for solving for velocities of fluid flow. 
### Problem
The problem addressed in this paper is how to get a stable solution for fluid flow with arbitrarily large time steps
### Methods used 
This paper takes a staged approach to the Navier-Stokes equation: 

du/dt = -(u * del)(u) - (1/rho) * del(p)  + v * del2(u) + f

* Any exterior forces are added (this takes care of the last term, f)
* The field velocities are advected with a semi-Lagrangian scheme (this takes care of the first term, -(u * del)(u) )
* Solve the diffusion term implicitly ( v * del2(u) )
* Project the resultant velocity field onto its divergence-free component (this is equivalent to solving - (1/rho) * del(p) )

### Key Ideas
Semi-Lagrangian advection: 
Starting from each point in the Eulerian field, a particle is traced backwards through the velocity field for time dt.  The new velocity is equal to the velocity at the grid location in which the particle's path ends.

Velocity field projection:
According to Some Mathematician, any vector field can be decomposed into the sum of a divergence-free field and a scalar gradient field; w = u + del(q) where q is a scalar field and del * u = 0.  Finding this field can be turned into a Poisson problem, which can be solved discretely just like the diffusion term.