This note describes a method used to simulate realistic fluid motion.
The paper first describes the basic Navier-Stokes equation term by
term, which is the accepted physical description of fluid motion.
The introduction of discretized cube grids for simulation instead of
particles and a Lagrangian simulation was a big change that became
pretty standard now. Then the semi-Lagrangian/implicit method presented
by Stam. It uses the "method of characteristics" that implicitly
traces a line backwards along the current velocity field to find the
new velocity. This gives stability that wasn't possible with explicit
methods with large time steps.