CFD is a ubiquitous technique central to much of computational simulation such as that required by aircraft design. Solving of the Poisson equation occurs frequently in CFD and there are a number of possible approaches one may leverage. The dynamical core of the MONC atmospheric model is one example of CFD which requires the solving of the Poisson equation to determine pressure terms. Traditionally this aspect of the model has been very time consuming and-so it is important to consider how we might reduce the runtime cost. In this paper we survey the different approaches implemented in MONC to perform the pressure solve. Designed to take advantage of large scale, modern, HPC machines, we are concerned with the computation and communication behaviour of the available techniques and in this text we focus on direct FFT and indirect iterative methods. In addition to describing the implementation of these techniques we illustrate on up to 32768 processor cores of a Cray XC30 both the performance and scalability of our approaches. Raw runtime is not the only measure so we also make some comments around the stability and accuracy of solution. The result of this work are a number of techniques, optimised for large scale HPC systems, and an understanding of which is most appropriate in different situations.

中文翻译：

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CFD 中泊松方程求解方法的比较

CFD 是一种无处不在的技术，是许多计算模拟的核心，例如飞机设计所需的计算模拟。泊松方程的求解在 CFD 中经常发生，并且可以利用多种可能的方法。MONC 大气模型的动力学核心是 CFD 的一个例子，它需要求解泊松方程来确定压力项。传统上，模型的这一方面非常耗时，因此考虑如何降低运行时成本非常重要。在本文中，我们调查了 MONC 中实现的不同方法来执行压力求解。旨在利用大规模、现代、HPC 机器，我们关注可用技术的计算和通信行为，在本文中，我们专注于直接 FFT 和间接迭代方法。除了描述这些技术的实现之外，我们还将在 Cray XC30 的多达 32768 个处理器内核上展示我们方法的性能和可扩展性。原始运行时间不是唯一的衡量标准，因此我们还对解决方案的稳定性和准确性进行了一些评论。这项工作的结果是许多技术，针对大规模 HPC 系统进行了优化，并了解哪种技术最适合不同情况。