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NOT JUST ANOTHER FINE MESH; VORTICES AND SUPERCOMPUTING
by Kate Caponi NCSA Science Writer

When you watch from the ground as an airplane take off, the process looks smooth. If you were riding in that plane, you would see and feel vibrations in the wings and body, a physical inkling of some of the forces working for and against the aircraft as it leaves the earth's surface. These forces reflect the influence of the air making its complicated path around the moving airplane. If you could see the actual airflow, you'd notice millions of little eddies--like tiny tornadoes--skimming the metal and affecting the drag and smoothness of the ride.

The need to predict the forces at play drives turbulent fluid motion studies. Numerical computation of how fluids move around the surface of given objects is crucial to the analysis and design of airplanes, automobiles, engines, computer chips, submarines, and many other technologies. In recent years, design teams in government and industry have invested millions of dollars in software capable of solving practical flow problems.

However, traditional models of turbulent fluid flow are unreliable and can be costly to implement. New capabilities in the prediction of turbulent fluid flow are needed if the full potential of computational fluid dynamics is to be exploited. Peter Bernard, professor of mechanical engineering at the University of Maryland, College Park, and a team of researchers from the company VorCat, Inc., have used more than 60,000 hours on the University of Kentucky's HP Superdome, NCSA's Titan Linux cluster, and Boston University's IBM P-Series supercomputer to develop advanced, grid-free techniques in modeling turbulent flow.

Modeling meshes According to Bernard, traditional turbulence models are often difficult to apply successfully in new applications with complex physical features. "This reflects the uncertainty in how turbulent flow processes are modeled," he says. "It is also difficult to provide a priori numerical meshes that correctly resolve essential flow features. Moreover, special care is needed in solving the highly non-linear partial differential equations appearing in the traditional models."

The availability of supercomputers has spawned the development of a more physically realistic alternative to traditional turbulence modeling, called a large eddy simulation (LES). "In this approach," says Bernard, "turbulent flow is modeled at a small scale and the large scale is computed from the small."

However, despite some significant progress to date, it has proven difficult for researchers to develop small-scale models that reliably produce accurate predictions of complex flows on the large scale. In addition, if LES is to become more useful for real-world applications, the construction of numerical meshes that properly reflect underlying flow conditions near physical boundaries must be automated. Such capabilities are important for reducing the effects of numerical diffusion in which the true solution is distorted due to the lack of enough local mesh points to resolve sharp features of the flow field.

For these reasons, mesh generation is one of the top two or three issues in the computational fluid dynamics industry. Bernard says, "The mesh you produce may not have adequate resolution at the points where it is needed. It can sometimes take months to develop a mesh that will work properly for you."

Modeling turbulence for the real world For Bernard's team, the solution is to use supercomputing resources to solve practical turbulent fluid flow problems using grid-free vortex methods in which the computational elements are vortex tubes. He says, "Vortex tubes are physical objects that are similar to little tornadoes. They move around, interact, and stretch. Our models gain accuracy and efficiency over traditional LES methods because the best way to model a physical vortex is with a numerical representation of a vortex. It's a whole new way of simulating turbulence--and because you don't have to worry about developing a mesh, it is easier to use when looking at complicated flows."

In addition to being grid-free and eliminating meshing problems, vortex methods have a number of inherent advantages that are particularly well-suited to modeling turbulent flow. Among these is the self-adaptivity of vortex elements. The vortices actually multiply in the regions where enhanced resolution is needed. Moreover, sharp features of the flow remain sharp, and vortex methods open up a new, more physically appropriate means of modeling small-scale flow phenomena.

One specific turbulent fluid flow problem that Bernard and the VorCat team are working on is a phenomenon called the mixing layer, the region between two fluids of different velocities that are flowing next to each other. The researchers are using the vortex method to look at what happens when you place particles of different sizes in the mixing layer. Bernard says, "Depending on the properties of the particles, they either get sucked in or thrown out of the large-scale mixing layer vortices in a very dramatic fashion."

Another problem that the researchers are looking at is flow past the Ahmed and Morel bodies that serve as prototypes of the kind of flows faced in the automotive industry. These models of simplified car bodies demonstrate how turbulence and drag from airflow are affected when you change the slant of the back window. The vortex method naturally supplies a population of vortices in the regions where the forces at play are most complex, making their model of the car more accurate with less effort than many mesh-based methods.

Such capabilities are important to industry because the answers provided by numerical simulations can form the basis for design. For instance, to see how you might control the flow over wings so as to affect the way a plane flies, you can experiment with surface characteristics that are beneficial. A wing's surface is not flat metal--it is covered with bumps and indentations that cause chaotic airflow. When the plane is taking off, chaotic airflow is desirable because it reduces drag. However, if the plane is flying level, that same chaotic airflow can cause drag. The task of designers is to determine where to put the bumps and dents on the aircraft's wings for maximum fuel efficiency and the ability to climb at a steep angle.

Arvin Shmilovich, associate technical fellow at The Boeing Company, says, "The promise in grid-free methods such as the one being pursued by VorCat lies in the opportunity they provide in achieving substantial economic gains in the form of improved vehicle designs, reduced design cycle times, and lower vehicle costs. Not only do the methods simplify or eliminate the laborious grid generation process, but also provide turbulence modeling that performs reliably under a wide range of flow conditions and without user intervention."