My research pertains to the design and development of numerical
methods for problems that have an internal (complex) moving
boundary at which a discontinuity is present.
Some examples are multiphase flows, shock waves, spreading phenomena,
and jetting phenomena. Problems with internal moving boundaries
are prevalent in many applications, but yet are very difficult
to compute since standard grid generation programs cannot handle
a moving boundary in which corners, topological transitions, cusps,
occur.
Multi-phase flows deal with flows that have gas, liquid and solid.
The density ratio of gas to liquid can be 1:1000.
A flow field involving breaking waves is a good example
of a multiphase flow which
has a complex moving boundary separating the air from
water. When a wave breaks, the water has to reconnect with itself.
The flow of liquid jets is another example of a multiphase flow
that has a complex internal moving boundary.
As a liquid jet is forced thru a nozzle and into air, it breaks
up into satellite drops. Underwater explosions is yet another
example of flows that have a complex internal moving boundary.
In underwater explosions, an explosive gas is released under
high pressure. The boundary separating the explosive gas
from the surrounding liquid can become quite complex if an
explosion is released near a solid boundary.
My current research projects are underwater explosions/implosions,
microscale jetting devices, vapor bubble growth and collapse,
spreading phenomena, Non-Newtonian flow (e.g. in
bubble formation, extrusion processes and jetting devices),
and shock/vortex interaction.
These applications exist in industry and defense. The
numerical methodology used falls in the class of
level set methods, volume-of-fluid
methods, adaptive mesh refinement, and spectral methods. Computer
programs range from small self contained Fortran codes to large
codes involving C++ and Fortran. Platforms range from Pentium computers
running linux to an IBM supercomputer.