This paper analyzes a parareal approach based on fractional-step methods for the nonstationary Navier-Stokes equations. As an efficient parallel computing framework, the coarse propagator often determines the performance of the parareal algorithm. We present a parareal algorithm using the fractional-step method, a very efficient time discrete scheme for the Naiver-Stokes equations, as the coarse propagator for the Navier-Stokes equations. Then we give the specific stability and convergence analysis of this specific parareal algorithm. Finally, numerical experiments are done to show efficiency and illustrate the theoretical results.

中文翻译：

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不可压缩纳维-斯托克斯方程的分步副实数算法分析

本文分析了一种基于分步法的非平稳纳维-斯托克斯方程的拟实数方法。作为一种高效的并行计算框架，粗传播器往往决定了parareal算法的性能。我们提出了一种使用分数步法的准实数算法，这是一种非常有效的 Naiver-Stokes 方程的时间离散方案，作为 Navier-Stokes 方程的粗传播器。然后我们对该具体的副实数算法进行了具体的稳定性和收敛性分析。最后，进行数值实验以显示效率并说明理论结果。