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Copyright:
19962010
J.A. Sethian

Motion of Fluid Interfaces
Overview
The motion of fluids, and in particular boundaries between fluids, is
exceedingly complex.
For example, there is no computer code in the world (and no one
is even close) that can predict what happens when milk is poured
into a cup of swirling tea. So many things are going on, such
as turbulence in the tea, density
differences between milk and water, and odd shapes of the bowl (and, of
course, don't forget the effect of the spoon), that focusing
on individual effects is enough of a challenge. As a piece of the puzzle,
imagine an air bubble rising in water, a
thermal of hot air rising on a cold day, or smoke rising out of smokestack.
In each case, the interface between the two fluids will change dramatically
as the fluids move.
As an example, consider a bubble of a fluid of one density, initially circular,
and rising in a fluid of a heavier density. Although the bubble starts off
circular, as it rises it accelerates in the middle, and the sides are caught
up in a pair of swirling vortices.
Light fluid bubble rising in heavier fluid

How fast the bubble rises, how much swirling goes on at the tips, and
how "stable" the boundary is between the two fluids depends on the
density differences, the Reynolds number (related to the friction) of the
two fluids, and the surface tension between the two,
which depends on the
curvature of the interface.

Movie of Rising Thermal
(274K)
Details
The calculation was made using a
level set method
to track the motion of the fluid interface. The surface tension is computed
from the local
curvature as given by the level set function, and is manifested as a source
term in the righthandside of the NavierStokes equations for incompressible
flow. The fluid velocities are computed using Chorin's projection method,
and the level set equation of motion is used to advect the fluid densities.
The density ratio of heavy to light fluid is two to one, and the calculation
is performed on a 512x512 grid.
References

Projection Methods Coupled to Level Set Interface Techniques
,
Zhu, J., and Sethian, J.A.,
J. Comp. Phys., 102, pp. 128138, 1992.
OVERVIEW

A Coupled Level Set Projection Method Applied to Ink Jet
Simulation,
,
Yu, JD., Sakai, S., and Sethian, J.A.,
Interfaces and Free Boundaries,
193, No. 1, pp 275305, 2003,
This paper
List of downloadable publications

