ABSTRACT

E ulerian approaches to fluid simulation require sampling the space thatthe fluid is acting in, rather than sampling the fluid itself. Because Eulerian approaches begin by subdividing space, they typically require bounding the region

over which a fluid simulation is done. This is in contrast to Lagrangian methods,

where particles are free to move anywhere in space. In this section we present

how this can be done using a uniform spatial grid, as described in Section 6.3.1.

Assuming a gridded representation of space, we first lay the foundations for doing

numerical computing over this grid, using finite difference representations of the

differential operators appearing in the Navier-Stokes equations. We then describe

two approaches for sampling fields onto the grid, and build on this to describe the

two most popular simulation schemes built on this structure, the semi-Lagrangian

and FLIP methods.