For the past several years, James D. Gunton, Haowen Xi and Jorge Vinals have used Pittsburgh Supercomputing Center's CRAY Y-MP and C90 to simulate Rayleigh-Benard convection. The Gunton team's simulations have revealed unpredicted chaotic patterns in R-B convection, unveiled new R-B convection structures and paved the way for mathematically accurate, three-dimensional renditions of chaotic behavior.

"We're trying to understand pattern formation and chaotic behavior in nature," says Gunton. "As a result of using supercomputing to simulate R-B convection, we're discovering previously unknown chaos in fluids."

Under long-used experimental parameters, R-B experiments have consistently exhibited the same evolving structures, among them parallel rolls, squares and hexagons (discernible in the convection topography). The initial parameters and the type of fluid govern which kind of pattern will emerge first, but all the patterns are stable and non-chaotic. Given a constant temperature, they maintain their structure over time.

More recently, the Gunton team used the CRAY C90 to monitor the onset of Rayleigh-Benard from a non-convective state. The resulting two-dimensional images reveal a kaleidoscopic pattern of local spirals. Their findings matched those of an independent though simultaneous experimental effort, thus bolstering the veracity of the unpredicted find.

The spirals not only rotate, says Gunton, they move around in the fluid, annihilate each other, grow at the expense of one another and fluctuate in size and number. Gone is the regularity exhibited in the parallel rolls, with the fluid moving in continuous circular waves. Velocities and temperatures vary throughout the fluid. Some portions of it rise and fall faster than others. Everything about the system changes from one moment to the next. It's a crock pot of symmetry turned bubbly cauldron.

The new patterns revealed themselves when experimentalists, and later theorists, devised a means of enlarging the R-B cell, the enclosed setting in which the convection occurs and is observed. Previously, they could examine only a small piece of the convection system, which limited the extent to which pattern activity could evolve. "In order for us to mathematically model bigger cells, we had to solve some very complex equations," says Xi. "It couldn't have been done without supercomputing." The code ran between 300-350 Mflops on the C90 and the researchers have logged approximately 1200 hours on the supercomputers, with 900 more slated for investigations that will produce three-dimensional images of chaos in R-B convection.

"One of the quantities we try to calculate is the upward velocity of the fluid at different points in the system, at different times," says Gunton. "Solving the equations means determining the velocity of the fluid at any given point in the system at any given time. It can't be done without supercomputing."

Physics Department Home Page at Lehigh University

Projects in Scientific Computing, PSC's annual research report.

**References, Acknowledgements & Credits**