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 partial differential equations (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.
Many challenges exists 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.
In this project, the PIs develop novel exascale numerical schemes for PDEs, especially those describing turbulent flows, that exploit asynchrony from the mathematical to the 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 will be able to trade-off accuracy and performance in a quantitative and predictable manner. The approach includes (i) rigorous mathematical studies of stability and accuracy based on numerical analysis and dynamical systems, which will also provide a framework for the development of new schemes and quantify its uncertainty, (ii) development of specific elements in a scalable library for parallel computing to enable portable implementations on current and future machines, and (iii) physics based modeling of numerical perturbations in realistic flows.
The tools, techniques and simulation data in this project will be integrated in the PIs' educational efforts through graduate mentoring, undergraduate research and as material for courses in high-performance computing, fluid dynamics and dynamical systems taught by the PIs.
