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Summary: Computation of Axisymmetric Suction Flow Through
Porous Media in the Presence of Surface Tension
Hector D. Ceniceros
Department of Mathematics, University of California Santa Barbara, Santa Barbara,
California 93106
and
Helen Si
Oracle Corporation, 500 Oracle Parkway, Redwood Shores California 94065
E-mail: hdc@math.ucsb.edu; hsi@us.oracle.com
The e ect of small surface tension on a class of axi-symmetric
ows with
suction is studied numerically. The dynamic evolution of a blob of incom-
pressible viscous
uid, surrounded by air, and drawn into an interior sink
is considered. The velocity eld of the viscous
uid is assumed to satisfy
Darcy's law and thus, the motion is that of a
ow through porous media.
The
uid interface motion is computed using a highly accurate boundary
integral method. This method combines recent numerical techniques to
achieve eÆcient and high order space and time discretizations for this type
of
ows. Through accurate computations, it is shown that, in the presence
of small surface tension, the dynamic behavior of the axi-symmetric
ows
is very similar to that of the (two-dimensional) Hele-Shaw counterparts.
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