Graphics Reference
In-Depth Information
-8-
Viscous Fluids
After briefly discussing viscosity in Chapter 1, we dispensed with it and un-
til now have only looked at inviscid simulations. In fact our major problem
has been that our numerical methods have too much numerical dissipation
which, in the velocity field, looks like viscosity. We now will turn our at-
tention to simulating highly viscous fluids, like molasses, and even variable
viscosity fluids where some parts are more viscous than others (perhaps
due to heating or cooling, or desired animation effects).
8.1 Stress
To properly understand viscosity and avoid some potential mistakes when
handling variable viscosity situations, we need to first understand the con-
cept of stress.
In reality, at least as a first approximation, matter is composed of small
particles with mass that interact by applying forces on each other. However,
since we're not interested in phenomena at that microscopic scale, in fluid
mechanics we make the continuum assumption, that matter is a continuous
field with no discrete particles. One way of thinking about this assumption
is that we're taking the limit as the particles become infinitesimally small
and packed together with infinitesimal space between them. For dynamics
this poses the problem that the masses drop to zero, and for accelerations
to remain bounded the forces must drop to zero too. To get around this,
we measure things in bulk: how much mass there is in a volume of space,
or what the net force is on a volume.
While it makes no sense to ask what the mass of a continuum fluid is
at a point in space (it has to be zero), we can define the density at any
point, which is a useful quantity. By integrating density in a volume we get
the total mass of the volume. Similarly it makes no sense to ask what the
force on a continuum fluid is at a point in space (it has to be zero), but we
can define quantities analogous to density: force densities in a sense, that
when integrated over a region give a net force.
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