Graphics Reference
In-Depth Information
-11-
Coupling Fluids and Solids
We have covered in some detail earlier (Chapter 4) how to incorporate
moving solid-wall boundary conditions in a simulation. The assumption
there was that the solids followed an immutable scripted path: the fluid
can't push back on them to change their motion. This chapter is focused
on providing this two-way coupling.
11.1 One-Way Coupling
However, before going into two-way coupling, let's take a quick look at the
other one-way coupling: solids that take their motion from the fluid, but
don't affect it. This is particularly useful for solids that are much lighter
than the fluid or much smaller than the features of the flow. In fact we have
already seen this, tracing marker particles in the velocity field of the fluid
for smoke animation. Here the position
x
i
of each particle simply followed
the fluid velocity field:
dx
i
dt
=
u
(
x
i
,t
)
.
(11.1)
This is also useful for small objects, or even particle systems representing
foam, drifting in water, perhaps with a step projecting them to stay on the
water surface.
One step up from marker particles are rigid bodies that take their mo-
tion from the fluid. In addition to moving their centers of mass with Equa-
tion (11.1), we need to update their orientations. Recalling the the vorticity
of the flow
ω
=
u
is twice the angular velocity of the fluid at any given
point, we simply integrate the rigid body position using
∇×
1
2
ω
. For example,
using a unit-length quaternion
q
i
to represent the orientation, we could
update it over a time step Δ
t
with
q
i
=
1
,
4
Δ
tω
q
i
,
q
n
+1
i
q
i
=
.
q
i
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