Fire - Fluid Simulation for Computer Graphics - page 101

This is appropriate particularly for modeling the fireballs due to deflagra-
tion of fuel suspended in the air, whether flammable powder or liquid-fuel
mist. It's also slightly simpler to implement than the preceding thin-flame
model, since level sets are not involved, yet it can still achieve some of the
look of regular flames and thus might be preferred in some instances.
To a standard smoke simulation, which includes temperature T ,smoke
concentration s , and divergence controls, we add another field F , the con-
centration of unburnt fuel in each grid cell. The fuel gets advected along
with the flow as usual, may be additional diffused, and may be seeded at
fuel sources or emitted from boundaries. (In Feldman et al.'s work, fuel
is instead represented as the unburnt mass of discrete fuel particles; we'll
come back to using particle systems in grid-based fluid solvers in Chap-
ter 10.)
To this we add some simple rules. If the temperature T at a grid cell,
following advection and dissipation steps, is above some ignition threshold
T ignition and the fuel concentration F is above zero, we burn some of the
fuel. At the simplest we reduce F by z Δ t ,where z is the burn speed (vol-
ume fraction combusted per second), clamping it to zero to avoid negative
F .LetΔ F be the change in F ; we then increase the smoke concentration
s by some amount proportional to Δ F , increase the temperature T also
proportional to Δ F , and add an amount to the divergence control propor-
tional to Δ F/ Δ t (recall the divergence is percent expansion per unit of
time, thus we need to divide by Δ t ). Note that this rule burns the fuel at
a constant rate z without regard to the availability of oxidizer; Feldman et
al. argue that for suspended particle explosions (coal dust, sawdust, flour,
etc.) oxygen availability in the air is never the limiting factor, and thus
this rule is justified. However, if need be you could limit the rate based on
1 F , the volume fraction left for plain air.

Rendering is based on black-body radiation as in the previous section,
though here we don't have any representation of the “blue core” available
so the rendering possibilities are slightly more limited.

− s −