Evaluation of finite difference based asynchronous partial differential equations solver for reacting flows

Next-generation exascale machines with extreme levels of parallelism will provide massive computing resources for large scale numerical simulations complex physical systems at unprecedented parameter ranges. However, novel methods, scalable algorithms and re-design current state-of-the art solvers are required scaling to these minimal overheads. One such approach partial differential equations based involves computation spatial derivatives possibly delayed or asynchronous data using high-order asynchrony-tolerant (AT) schemes facilitate mitigation communication synchronization bottlenecks without affecting the accuracy. In present study, an effective methodology implementing temporal discretization a multi-stage Runge-Kutta method AT is presented. Together used perform canonical reacting flow problems, demonstrated in one-dimension including auto-ignition premixture, premixed flame propagation non-premixed autoignition. Simulation results show that incur very small errors all key quantities interest stiff intermediate species despite processing element (PE) boundaries. For supersonic flows, degraded accuracy well-known shock-resolving WENO (weighted essentially non-oscillatory) when relaxed also discussed. To overcome this loss accuracy, AT-WENO derived tested on linear non-linear equations. Finally detonation wave delays PE