Graphics Reference
In-Depth Information
tion for advection. Various authors have looked at further eroding away
the solid or liquid source as it emits gaseous fuel, which is particularly im-
portant for thin objects like sheets of paper—see for example the articles
by Melek and Keyser [Melek and Keyser 03] and Losasso et al. [Losasso
et al. 06]. Whether or not (and where) a solid is emitting gaseous fuel is
usually directly specified by the animator, often modulated by an animated
texture to produce more interesting effects, though procedural models sim-
ulating the spread of fire according to burn rates or temperature thresholds
can also easily be concocted.
7.1 Thin Flames
Nguyen et al. [Nguyen et al. 02] detail an approach to fire, in which the
region where combustion takes place is modeled as an infinitely thin flame
front, i.e., a surface, not a volume. In addition, it's assumed that fuel and
oxidizer are
premixed
before ignition, as in blow torches—while not really
true for other phenomena where the mixing of fuel and oxidizer is an inte-
gral part of the fire (technically known as
diffuse flames
), the simplifying
premixed assumption can still serve just fine for a visually plausible result.
The flame front divides the fluid region into two parts: premixed
fuel/oxidizer on one side and burnt products (and/or background air) on
the other side. To track the flame surface we model it with a level set
φ
sampled on the grid, as we did for water in Chapter 6.
The first problem to address is how to evolve the flame front: at what
speed does it move? If no combustion were taking place, the flame front
would be nothing more than the material interface between the two fluids—
just like the free surface in water simulation. Thus our first velocity term
is simply the fluid velocity: the flame front is advected along with the flow.
For definiteness (this will be important in a moment) we'll use the velocity
of the unburnt fuel,
u
fuel
. However, when combustion is taking place, the
flame front also is “moving:” fuel at the flame surface gets combusted into
burnt products, effectively shrinking the surface inwards. The simplest
model for this is to assume a constant burn speed
S
, the rate at which the
flame surface burns into the fuel region along the normal direction. Nguyen
et al. [Nguyen et al. 02] suggest a default value of
S
=0
.
5
m/s
. Assuming
that
φ
is negative in the fuel region by convention, this gives our level set
equation
∂φ
∂t
+
u
fuel
·∇
φ
=
S.
(7.1)
