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Texas A&M Engineering Experiment Station researchers are part of a team working on a National Science Foundation-funded project researching asynchronous partial differential equations (PDE) algorithms for turbulent flows at exascale. The principal investigator is Dr. Diego Donzis, assistant professor in the Department of Aerospace Engineering. Co-principal investigators are Dr. Raktim Bhattacharya, associate professor, and Dr. Sharath Girimaji, professor, aerospace engineering; and Dr. Nancy Amato, Unocal Professor, and Dr. Lawrence Rauchwerger, professor, Department of Computer Science and Engineering.

Future exascale computing systems will be available to study important, compute-intensive applications such as multi-physics multi-scale natural phenomena and engineering systems typically modeled accurately by PDEs.  A prime example is turbulence at high Reynolds numbers, typically found in natural and engineering systems, which comprise an extremely wide range of spatial and temporal scales and has thus became a Grand Challenge in scientific computing.

However, many challenges exist that must be overcome before exascale systems can be utilized effectively. These include communication between processing elements as well as global synchronizations both of which will likely be a main bottleneck when millions of billions of processing elements are utilized in a simulation.

For this project, the team will develop novel exascale numerical schemes for PDEs, especially those describing turbulent flows that exploit asynchrony from the mathematical to the software level.  These will be based on widely used finite differences, compact differentiation and spectral schemes.  Asynchrony offers better performance but also introduces errors in the solution. The team’s schemes will be able to trade-off accuracy and performance in a quantitative and predictable manner, a feature thought to be critical at exascale.  Their approach includes rigorous mathematical studies of stability and accuracy, which will also provide a framework for the development of new schemes and quantify its uncertainty,  as well as the development of specific elements in a scalable library for parallel computing to enable portable implementations on current and future machines.

The tools, techniques and simulation data in this project will be integrated in the principal investigators’ educational efforts through graduate mentoring, undergraduate research and as material for courses they teach in high-performance computing, fluid dynamics and dynamical systems.