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Direct Simulation of the Motion of Particles in Flowing Liquids Web site Dr. Joseph's online book: Interrogations of Direct Numerical Simulation of Solid-Liquid Flows

Direct Numerical Simulation and Modeling of Solid-Liquid Flows

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 numerical simulation.

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 existed—mathematical analysis and experiments—there 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 established."

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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