Asynchronous simulations of reacting flows: a path towards exascale computing

Direct Numerical Simulations (DNS) of turbulent combustion at higher Reynolds numbers with detailed reaction mechanisms and at conditions of practical relevance will require efficient utilization of massive computing resources anticipated on the next-generation exascale machines. However, scaling current solvers to these extreme scales requires novel numerical methods and algorithms to avoid performance penalties due to parallelization. A very promising approach is based on so-called asynchrony-tolerant (AT) schemes that can use delayed or asynchronous data at processor boundaries without degrading numerical accuracy, thereby alleviating communication and synchronization bottlenecks. To study stability we developed a new approach that extends (and also highlights important limitations of) the standard von Neumann analysis. We use these AT schemes for asynchronous simulations of several canonical reacting flow problems including auto-ignition and flame propagation. Effects of delayed data on relevant physical processes and the challenging stiff intermediate species is investigated. To further solve problems with shocks and discontinuities, we devised AT-WENO schemes which are validated with DNS data. These first-of-a-kind AT simulations provide a path towards exascale computing.