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Mathematics to the rescue

Mathematics to the rescue

Preventing space shuttle tragedies and improving the performance of high-speed aircraft are potential benefits of the Center for Numerical Simulation and Modeling’s research on turbulent conditions.

Most people associate turbulence with airplanes. But turbulence is everywhere, says Chaoqun Liu, director of UT Arlington's Center for Numerical Simulation and Modeling. It exists in tornadoes, rivers, even in smoke as it rises.

Dr. Liu

Chaoqun Liu, mathematics professor

Dr. Liu and his team specialize in computational fluid dynamics, using mathematics and computing to model things that flow. They're making the first-ever measurable progress in determining the time and place that a flow transitions from laminar, or non-turbulent, to turbulent, a condition characterized by chaotic change.

That knowledge could help prevent tragedies like the space shuttle Columbia explosion, which took seven lives, including UT Arlington alumna Kalpana Chawla, and dealt a major setback to U.S. space exploration.

Identifying the time and location that flow changes from laminar to turbulent also can reduce submarine noise, improve the performance of high-speed aircraft, and help scientists and engineers better understand underground water flow, Liu says. In fact, since turbulence is everywhere in nature, the impact of the slowly developing knowledge will be infinite.

"Flow transition itself has been an important research topic for hundreds of years," Liu says. "But turbulence is still nature's secret."

To model things that flow, an interdisciplinary research group studies the momentum deficit and its origins. Team members are making progress in determining when a flow transitions from non-turbulent to turbulent.

The mathematics professor and his team have revealed many of those secrets by new direct numerical simulation.

Computational fluid dynamics requires adaptive grid generation, or generating an orthogonal mesh that approximates a geometric domain. The mesh is used on a computer in computational fluid dynamics. The NSM center created unique grids that have proved effective in helping solve the turbulence issue.

Liu's research has amassed a database of 100 terabytes at the vast computing center at UT Austin, an amount reportedly equal to that of the Library of Congress in Washington, D.C. His research group of fewer than a dozen professors, graduate students, and postdoctoral researchers presented seven papers at the annual conference of the American Institute of Aeronautics and Astronautics in January.

"Having that number of papers accepted by the most prestigious aeronautics and astronautics organization in the world is a strong confirmation of the importance of the breakthroughs we have made," Liu says.

The Air Force funds most of the research, which includes the micro vortex generator for high-speed flow control and shock boundary layer interaction. The group has achieved new knowledge and mechanisms that provide a solid foundation for Air Force and NASA engineers to improve high-speed vehicle designs.

The NSM center also aids non-related, ongoing explorations by biomedical researchers in the College of Engineering and by the College of Business and is actively involved in the University's doctoral program in applied mathematics.

- Sue Stevens