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积分算法（Micro-Macro Parareal）应用于偏微分方程求解。该并行时间方法需要两套不同空间分辨率的网格，通过迭代方式逼近预设的参考解。当算法在少量迭代中实现快速收敛时，与串行计算相比能够缩短计算时间。我们选取二维圆柱绕流层流基准问题，使用开源软件OpenFoam进行数值模拟。本研究开展的数值实验旨在近似计算时空局部状态及诊断升力系数。雷诺数从100逐步增至1000，直至逼近湍流转捩阈值。在呈现计算结果后，本文讨论了雷诺数与所采用插值格式对收敛行为的影响。