Graphics Reference
In-Depth Information
-5-
Smoke
5.1 Temperature and Smoke Concentration
The first visual fluid phenomena we will consider is smoke, loosely fol-
lowing the standard reference papers by Foster and Metaxas [Foster and
Metaxas 97] and by Fedkiw et al. [Fedkiw et al. 01], with some additional
capabilities added. Our fluid in this case is the air in which the smoke
particles are suspended. To model the most important effects of smoke,
we need two extra fluid variables: the temperature
T
of the air and the
concentration
s
of smoke particles—what we actually can see. Similar phe-
nomena, such as vapor, can be modeled in much the same way. Generally
we'll try to keep to SI units of Kelvin for temperature and keep
s
anumber
between 0 (no smoke) and 1 (as thick as possible). Also keep in mind that
it's crucial to simulate
all
the air in the simulation, not just the regions
with
s>
0: a lot of the characteristic swirly behavior you see in smoke
depends on enforcing the divergence-free constraint in nearby clear regions
of air.
Before getting to how these variables will influence the velocity of the
air in the next few sections, let's work out how
T
and
s
should evolve. It
should be immediately apparent that temperature and soot particles are
both advected with the fluid, i.e., we'll be using the material derivatives
DT/Dt
and
Ds/Dt
to describe them.
1
This gives us the simplest possible
equations,
DT
Dt
=0
,
Ds
Dt
=0
and will be the first step of a numerical method: when we advect
u
,we
also advect
T
and
s
. Typically we would discretize both variables at cell
centers, where the pressure values lie.
1
The story for temperature, at least, can be rather more complicated when full ther-
modynamics are considered. However, the assumption of incompressible fluid flow ab-
stracts away most of the interaction between heat, pressure, density, etc.
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