Taming Turbulence

This chaos, or "turbulence," is difficult for scientists to simulate on computers, but understanding it is critical in the design of aerodynamically sound aircraft, automobiles, and watercraft.

Computerized prediction of turbulence is especially challenging in the case of an arbitrarily shaped body moving through a compressible fluid that has low viscosity, such as air. "In these applications, the numerical model is as unstable as the fluid itself," states SAIC's Hong Luo. In his award-winning research, Luo has applied several numerical techniques in a novel way to overcome the instabilities of this complex computational fluid dynamics problem.

The goal of computer simulation is to reach a steady-state solution. In other words, variables are stepped forward in time until their values become constant. This specific application requires two field equations: one that models fluid flow, the other that models turbulence. The two equations are executed one after the other at each time step. While the fluid flow equations reach a steady state quickly and easily, turbulence equations are more complicated and rarely converge to a steady state. In regions very close to the surface of objects, wild variations in turbulence values cause numerical instability. Using traditional methods, the turbulence variables eventually assume negative values, which extinguish the solution process.

Together with Joseph Baum and Rainald Löhner, Luo has created a simple and elegant antidote to the inherent instability of turbulence simulation. The team's algorithm guarantees that the turbulence variables remain positive by solving for the logarithms of the variables, which are by definition greater than zero. This approach dramatically reduces the range of values, further stabilizing the process.

Because the flow and turbulence equations are coupled, Luo had to force the turbulence equation to converge to a steady state at the same rate as the flow equation. To do this, he employed an efficient "point-implicit" technique to advance the turbulence equation in time, such that each point in space is not explicitly defined but is instead defined by its relationships with other variables. The point-implicit approach requires fewer time steps than the explicit method and less manipulation than a purely implicit approach, in which all points are interrelated.

After testing the method on a variety of turbulent flow problems, the numerical results were in good agreement with both theoretical and experimental data. Luo's method has proven itself to be a viable and robust algorithm for simulating highly turbulent flows over complex geometries. The new method is versatile as well. The scientists coupled the two equations loosely so that new turbulence models can be interchanged easily and different numerical techniques can be used to solve the flow and turbulence equations.

Luo's paper, "Computation of Compressible Flows using a Two-equation Turbulence Model on Unstructured Grids," was published in the International Journal of Computational Fluid Dynamics. The research was sponsored by the Defense Threat Reduction Agency.