XPS: FULL: DSD: Asynchronous PDE Algorithms for Turbulent Flows at Exascale

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Future exascale computing systems will be available to study important,compute-intensive applications such as multi-physics multi-scale naturalphenomena and engineering systems typically modeled accurately by partialdifferential equations (PDEs).  A prime example is turbulence at high Reynoldsnumbers, typically found in natural and engineering systems, which comprise anextremely wide range of spatial and temporal scales and has thus became a GrandChallenge in scientific computing.Many challenges exists that must be overcome before exascale systemscan be utilized effectively. These include communication betweenprocessing elements as well as global synchronizations both of which willlikely be a main bottleneck when millions of billions of processing elementsare utilized in a simulation.In this project, the PIs develop novel exascale numerical schemes for PDEs,especially those describing turbulent flows, that exploit asynchrony from the mathematical tothe software level. These are based on widely used finite differences, compact differentiation and spectral schemes.Asynchrony offers better performance but also introduces errors in the solution. The new schemes willbe able to trade-off accuracy and performance in a quantitative and predictable manner.The approach includes (i) rigorous mathematical studies of stability andaccuracy based on numerical analysis and dynamical systems, which will alsoprovide a framework for the development of new schemes and quantify itsuncertainty, (ii) development of specific elements in a scalable library for parallelcomputing to enable portable implementations on current and future machines,and (iii) physics based modeling of numerical perturbations inrealistic flows.The tools, techniques and simulation data in this projectwill be integrated in the PIs' educational efforts through graduate mentoring, undergraduateresearch and as material for courses in high-performance computing, fluid dynamics and dynamical systemstaught by the PIs.