Direct Numerical Simulation and Modeling of Solid-Liquid
Recent advances in computers and software have made possible
exciting new research in science and engineering. These powerful technological
tools are key to the work of Dr. D.D. Joseph and his team in their project
"Direct Numerical Simulation and Modeling of Solid Liquid Flows," which focused
on computing the motion of solids in liquids using what is called direct
Solids in liquids, such as particles in an oil pipeline or sediment
in a river, interact with one another. Dr. Joseph and his team used high-speed
computers and innovative software to create three-dimensional direct numerical
simulations of the interactions of thousands of particles, so that they could
understand and predict their collective behavior.
In the past, this was an inexact science. According to Dr.
Joseph, the project's Principal Investigator (PI) and Regents Professor at the
Department of Aerospace Engineering and Mechanics at the University of
Minnesota, "Prior to the introduction of this method, people would compute
these motions using models, which were left to researchers' imaginations, and
by and large always led to one defect or another."
But thanks to this National Science Foundation-funded
project, researchers were able to study the interaction of the solids in new ways.
"There are certain physical effects, like the rotation of a particle, that
occur in experiments," explains Dr. Joseph. "But in direct numerical
simulation, we can suppress those things or include those things. We can
examine separate physical effects one at a time, so we can do things in
numerical experiments that we can't do in real experiments."
These computations create very large amounts of data, which
Dr. Joseph and his team use in numerous ways. "We can process the data to find
formulas that give rise to an expression for the lift force, or an expression
for the drag, or an expression for the expansion of [chemical reactors called]
fluidized beds as you increase the velocity, or an expression for the lift-off
of the sediment." This has important applications in the chemical process
industry and the field of oil exploration and recovery.
Direct numerical simulations also save time and effort. "The
same methods that we use, we can use in real experiments and we can use in
numerical experiments," says Dr. Joseph. "So it opens up a huge opportunity in
the future for shortcutting actual experimentation with numerical
experimentation." Models can be compared to direct numerical simulations.
Direct numerical simulations can also help suggest new models, and in some
cases, they can replace models entirely.
What makes this aspect of the work particularly exciting,
says Dr. Joseph, is that in addition to the two branches of scientific inquiry
that already existedmathematical analysis and experimentsthere is
now a third: numerical experiments. The original two will "continue to be an
aspect of scientific culture that will produce and produce and produce," says
Dr. Joseph. "But we know all about what they can do. They're not new items. The
boundaries of what can be produced by numerical experiments have not yet been
For this project, Dr. Joseph assembled a team of experts in
fluid mechanics, computational fluid dynamics, and computer science from around
the country. They include Yousef Saad (the project's co-PI), Professor in the
Department of Computer Science and Engineering at the University of Minnesota;
Roland Glowinski, the Cullen Professor of Mathematics and Mechanical
Engineering at the University of Houston; Gene Golub, the Fletcher Jones
Professor of Computer Science at Stanford; and Ahmed Sameh, the Samual Conte
Professor of Computer Science at Purdue. Also involved were a number of
postdocs and graduate students.
Dr. Joseph says, "We've been very successful in this. It
could be said that we are the leading group in this method of direct numerical
simulation of solid-liquid flow."
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