Graphics Reference
In-Depth Information
Another issue with FLIP is that it is limited to first-order accuracy,
despite being free of numerical dissipation. This appears to be quite ad-
equate for treating velocity, smoke concentration, temperature, etc., but
not
adequate for advecting level sets (from Chapter 6): the nice smooth
surfaces characteristic of level sets depend on either getting high-order ac-
curacy (so that derivatives of
φ
, e.g., the normal field or the curvature
of the surface, are handled accurately) or on strong numerical dissipation
(though of course this leads to other unacceptable errors). Thus, we are
lead to consider one more hybrid particle-grid method, specifically adapted
to level sets.
10.5 The Particle Level Set Method
The particle level set (PLS) method, pioneered by Foster and Fedkiw [Fos-
ter and Fedkiw 01] and fully developed by Enright et al. [Enright et al. 02a,
Enright et al. 02b], is the result of augmenting an Eulerian level set formu-
lation with helper marker particles to track material boundaries, like the
free surface of a liquid.
2
One of the key differences between PLS and other particle-grid hybrid
methods that is helpful to have in mind is that the grid-based level set
function is the fundamental representation of the quantity here, and the
particles are auxiliary. For almost all the other methods in this chapter,
the fundamental representation was the field stored on the particles, and
this was transferred to the auxiliary simulation grid as needed—with the
one exception of the basic particle-in-cell method (
not
FLIP) where the
particles are only helpful auxiliaries in advecting around a grid-sampled
function. In this respect PLS is very similar to basic PIC, albeit with a
much more sophisticated coupling between particles and grid and special
seeding/deletion rules. One of the consequences of this is that PLS only
will work with geometry that
can
be reliably represented on the grid: it is
subject to the same fundamental limits as pure Eulerian methods that we
discussed at the start of this chapter. However, signed distance is one case
where even the most accurate Eulerian methods tend to fall far short of this
limit: pure Eulerian schemes tend to gain accuracy only where the function
is smooth, reducing to first order (and related numerical dissipation) at
2
PLS is not as appropriate for non-conservative boundaries, such as the thin flame
front we saw in Chapter 7, where other processes actively erode or grow the surface in
addition to passive advection. However, in these cases the numerical dissipation that
PLS aims to reduce isn't nearly as objectionable, so regular non-particle methods are
generally just fine.
