We study periodic solutions to the Navier-Stokes equations. The transition phase of a dynamic Navier-Stokes solution to the periodic-in-time state can be excessively long and it depends on parameters like the domain size and the viscosity. Several methods for an accelerated identification of the correct initial data that will yield the periodic state exist. They are mostly based on space-time frameworks for directly computing the periodic state or on optimization schemes or shooting methods for quickly finding the correct initial data that yields the periodic solution. They all have a large computational overhead in common. Here we describe and analyze a simple averaging scheme that comes at negligible additional cost. We numerically demonstrate the efficiency and robustness of the scheme for several test-cases and we will theoretically show convergence for the linear Stokes problem.

中文翻译：

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一种有效逼近时间周期流问题的平均方案

我们研究 Navier-Stokes 方程的周期解。动态 Navier-Stokes 解到周期性时间状态的过渡阶段可能过长，这取决于域大小和粘度等参数。存在几种用于加速识别将产生周期性状态的正确初始数据的方法。它们大多基于用于直接计算周期状态的时空框架或基于优化方案或拍摄方法来快速找到产生周期解的正确初始数据。它们都有一个共同的计算开销。在这里，我们描述和分析了一个简单的平均方案，其额外成本可以忽略不计。