In this paper the Micro-Macro Parareal algorithm was adapted to PDEs. The parallel-in-time approach requires two meshes of different spatial resolution in order to compute approximations in an iterative way to a predefined reference solution. When fast convergence in few iterations can be accomplished the algorithm is able to generate wall-time reduction in comparison to the serial computation. We chose the laminar flow around a cylinder benchmark on 2-dimensional domain which was simulated with the open-source software OpenFoam. The numerical experiments presented in this work aim to approximate states local in time and space and the diagnostic lift coefficient. The Reynolds number is gradually increased from 100 to 1,000, before the transition to turbulent flows sets in. After the results are presented the convergence behavior is discussed with respect to the Reynolds number and the applied interpolation schemes.

翻译：本文将微宏观并行时间（Micro-Macro Parareal）算法应用于偏微分方程。该并行时间方法需使用两种不同空间分辨率的网格，以迭代方式计算逼近预设参考解。当算法能在少量迭代内快速收敛时，相较于串行计算可显著缩短运行时间。我们选取二维层流绕圆柱基准问题，并采用开源软件OpenFoam进行数值模拟。本工作旨在通过数值实验逼近局部时空状态及诊断性升力系数。雷诺数从100逐步增至1,000，直至湍流转捩发生前。在呈现结果后，本文针对雷诺数与所采用的插值方案探讨了收敛性行为。