Direct numerical simulations (DNS) are an indispensable tool for understanding the fundamental physics of turbulent flows. Because of their steep increase in computational cost with Reynolds number ($R_{\lambda }$), well-resolved DNS are realizable only on massively parallel supercomputers, even at moderate $R_{\lambda }$. However, at extreme scales, the communications and synchronizations between processing elements (PEs) involved in current approaches become exceedingly expensive and are expected to be a major bottleneck to scalability. In order to overcome this challenge, we developed algorithms using the so-called Asynchrony-Tolerant (AT) schemes that relax communication and synchronization constraints at a mathematical level, to perform DNS of decaying and solenoidally forced compressible turbulence. Asynchrony is introduced using two approaches, one that avoids synchronizations and the other that avoids communications. These result in periodic and random delays, respectively, at PE boundaries. We show that both asynchronous algorithms accurately resolve the large-scale and small-scale motions of turbulence, including instantaneous and intermittent fields. We also show that in asynchronous simulations the communication time is a relatively smaller fraction of the total computation time, especially at large processor count, compared to standard synchronous simulations. As a consequence, we observe improved parallel scalability up to 262144 processors for both asynchronous algorithms.

直接数值模拟（DNS）是了解湍流基本物理原理必不可少的工具。由于雷诺数（（${\mathrm{[R}}_{\lambda }$），即使在中等水平的超级计算机上，解析度很高的DNS也只能在大规模并行超级计算机上实现 ${\mathrm{[R}}_{\lambda }$。然而，在极端规模上，当前方法中所涉及的处理元件（PE）之间的通信和同步变得极其昂贵，并且有望成为可伸缩性的主要瓶颈。为了克服这一挑战，我们开发了使用所谓的异步容忍（AT）方案的算法，该算法在数学水平上放松了通信和同步约束，以执行DNS衰减和螺线管可压缩湍流。使用两种方法引入异步，一种方法避免同步，而另一种方法避免通信。这些分别导致在PE边界处的周期性和随机延迟。我们表明，两种异步算法都能准确地解决湍流的大尺度和小尺度运动，包括瞬时场和间歇场。我们还表明，与标准同步仿真相比，在异步仿真中，通信时间占总计算时间的比例相对较小，尤其是在处理器数量较大时。结果，我们观察到两种异步算法的并行可扩展性均提高到262144个处理器。