Abstract The simulation of unsteady incompressible fluid flow and heat transfer problems is a huge time-consuming task and has been becoming one of the hottest topics in the fields of computational fluid dynamics and numerical heat transfer. Pure spatial parallelization has been so far the most widely used parallel strategy to speed up unsteady simulations but suffers from the problem of speedup saturation as parallel scale increases. In order to further speed up unsteady simulations and exploit the concurrency in temporal dimension, we propose a novel temporal parallelization strategy, i.e., parallel inverted dual time stepping method, by simply inverting the sequence of the inner loop (pseudo time) and the outer loop (physical time) within the dual time stepping framework. The parallel performance of the proposed method is verified and validated with three steady/unsteady problems. Parallel results of the proposed method agree well with those of the dual time stepping method and the available benchmark solutions. The parallel efficiency of the proposed method is about 96%, 81%, 62%, 51%, 45% for 4, 8, 12, 16, 20 CPU cores, respectively, which is considerably higher than that of the widely used parareal method. The proposed method has potential in further increasing parallel scale as spatial parallelization is saturated.

中文翻译：

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非定常不可压缩流体流动与传热问题的并行反演双时间步长方法

摘要 非定常不可压缩流体流动和传热问题的模拟是一项耗时巨大的任务，已成为计算流体动力学和数值传热领域的热门话题之一。迄今为止，纯空间并行化是最广泛使用的用于加速非稳态模拟的并行策略，但随着并行规模的增加，它会遇到加速饱和的问题。为了进一步加速非稳态模拟并利用时间维度的并发性，我们提出了一种新的时间并行化策略，即并行倒置双时间步进方法，通过简单地反转内循环（伪时间）和外循环的序列（物理时间）在双时间步进框架内。所提出方法的并行性能通过三个稳态/非稳态问题得到验证和验证。所提出方法的并行结果与双时间步长方法和可用的基准解决方案的结果非常吻合。4、8、12、16、20个CPU核，所提方法的并行效率分别约为96%、81%、62%、51%、45%，远高于广泛使用的parareal方法. 随着空间并行化饱和，所提出的方法具有进一步增加并行规模的潜力。这大大高于广泛使用的超现实方法。随着空间并行化饱和，所提出的方法具有进一步增加并行规模的潜力。这大大高于广泛使用的超现实方法。随着空间并行化饱和，所提出的方法具有进一步增加并行规模的潜力。