# Fast Findings on Fluid Frenzy: Taking turbulence models to a new level

From blood spurting through hearts to winds buffeting cars, fluids swirl and tumble in complex ways that scientists struggle to understand. Now, a new means to efficiently depict fluid turbulence and to calculate its effects promises to influence many branches of science and technology.

For example, using the new method, car designers can compute aerodynamic simulations of full, three-dimensional vehicles at highway speeds quickly enough to incorporate the information into the design of cars, say the technique's developers. With previous methods, designers typically had time only to simulate two-dimensional flows or 3-D models for which the car was portrayed in a simplified form or was moving at a crawl.

Two-thirds of the world's major automakers have begun using the new simulations, says Hudong Chen, chief scientist at EXA Corp. in Lexington, Mass., which creates and sells software based on the new simulation method.

Conventional methods of calculating turbulence treat fluids not as molecular assemblages but as continuous substances. The new approach includes some of the underlying, microscopic nature of fluids, which surprisingly turns out to be advantageous.

The new technique, described in the Aug. 1 *Science*, "should become the method of choice when fast answers are needed for fluid flows of complex geometry," comments David C. Montgomery of Dartmouth College in Hanover, N.H. Such complex flows can occur as heat travels through electronic devices and as plumes of pollutants infiltrate an environment, scientists say.

For more than 2 centuries, scientists have been using mathematical formulations called Navier-Stokes equations to calculate the precise velocity, pressure, and temperature of a fluid at any location and time. Yet those equations are impossible to solve completely in all but the simplest scenarios, in which fluids flow smoothly and steadily. To simulate more realistic flows on computers, scientists have long used approximations of the Navier-Stokes equations, but those simplified models can't duplicate certain important features of the flows. They also demand inordinate amounts of computing power.

The new method relies on a different equation, called the Boltzmann equation, which is typically employed to predict the behaviors of molecules in gases and liquids. More than a decade ago, researchers were surprised to learn that using the Boltzmann equation to calculate simple fluid flows didn't make the simulations more difficult or time consuming to carry out.

"It's the counterintuitive approach," says Steven A. Orszag of Yale University, a coauthor of the *Science* paper and an EXA consultant. "If you start from the very microscopic dynamics, you would think you'd have to compute much too much."

More recently, Orszag, Chen, and their colleagues found a way to include turbulence in their Boltzmann equation–based simulations at little additional computing cost. The trick was to invent a particular mathematical representation of disruption of particle motions by disorderly flows.

That last step was "really a breakthrough from my point of view," comments Roberto Benzi of the University of Rome Tor Vergata, a pioneer in the use of the Boltzmann equation for fluid flows.

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Roberto Benzi

Department of Physics

Universit di Roma "Tor Vergata"

via della Ricerca 1

00173 Roma

Italy

Hudong Chen

EXA Corporation

450 Bedford Street

Lexington, MA 02420

David C. Montgomery

Department of Physics and Astronomy

Dartmouth College

6127 Wilder Laboratory

Hanover, NH 03755-3528

Steven Orszag

Department of Mathematics

Yale University

New Haven, CT 06520