高雷诺数湍流壁面流动极端尺度计算的铅笔分布有限差分求解器

IF 3.4 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Rafael Diez Sanhueza, Jurriaan Peeters, Pedro Costa
{"title":"高雷诺数湍流壁面流动极端尺度计算的铅笔分布有限差分求解器","authors":"Rafael Diez Sanhueza,&nbsp;Jurriaan Peeters,&nbsp;Pedro Costa","doi":"10.1016/j.cpc.2025.109811","DOIUrl":null,"url":null,"abstract":"<div><div>We present a computational method for extreme-scale simulations of incompressible turbulent wall flows at high Reynolds numbers. The numerical algorithm extends a popular method for solving second-order finite differences Poisson/Helmholtz equations using a pencil-distributed parallel tridiagonal solver to improve computational performance at scale. The benefits of this approach were investigated for high-Reynolds-number turbulent channel flow simulations, with up to about 80 billion grid points and 1024 GPUs on the European flagship supercomputers Leonardo and LUMI. An additional GPU porting effort of the entire solver had to be undertaken for the latter. Our results confirm that, while 1D domain decompositions are favorable for smaller systems, they become inefficient or even impossible at large scales. This restriction is relaxed by adopting a pencil-distributed approach. The results show that, at scale, the revised Poisson solver is about twice as fast as the baseline approach with the full-transpose algorithm for 2D domain decompositions. Strong and weak scalability tests show that the performance gains are due to the lower communication footprint. Additionally, to secure high performance when solving for wall-normal implicit diffusion, we propose a reworked flavor of parallel cyclic reduction (PCR) that is split into pre-processing and runtime steps. During pre-processing, small sub-arrays with independent 1D coefficients are computed by parallel GPU threads, without any global GPU communication. Then, at runtime, the reworked PCR enables a fast solution of implicit 1D diffusion without computational overhead. Our results show that the entire numerical solver, coupled with the PCR algorithm, enables extreme-scale simulations with 2D pencil decompositions, which do not suffer performance losses even when compared to the best 1D slab configurations available for smaller systems.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"316 ","pages":"Article 109811"},"PeriodicalIF":3.4000,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A pencil-distributed finite-difference solver for extreme-scale calculations of turbulent wall flows at high Reynolds number\",\"authors\":\"Rafael Diez Sanhueza,&nbsp;Jurriaan Peeters,&nbsp;Pedro Costa\",\"doi\":\"10.1016/j.cpc.2025.109811\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We present a computational method for extreme-scale simulations of incompressible turbulent wall flows at high Reynolds numbers. The numerical algorithm extends a popular method for solving second-order finite differences Poisson/Helmholtz equations using a pencil-distributed parallel tridiagonal solver to improve computational performance at scale. The benefits of this approach were investigated for high-Reynolds-number turbulent channel flow simulations, with up to about 80 billion grid points and 1024 GPUs on the European flagship supercomputers Leonardo and LUMI. An additional GPU porting effort of the entire solver had to be undertaken for the latter. Our results confirm that, while 1D domain decompositions are favorable for smaller systems, they become inefficient or even impossible at large scales. This restriction is relaxed by adopting a pencil-distributed approach. The results show that, at scale, the revised Poisson solver is about twice as fast as the baseline approach with the full-transpose algorithm for 2D domain decompositions. Strong and weak scalability tests show that the performance gains are due to the lower communication footprint. Additionally, to secure high performance when solving for wall-normal implicit diffusion, we propose a reworked flavor of parallel cyclic reduction (PCR) that is split into pre-processing and runtime steps. During pre-processing, small sub-arrays with independent 1D coefficients are computed by parallel GPU threads, without any global GPU communication. Then, at runtime, the reworked PCR enables a fast solution of implicit 1D diffusion without computational overhead. Our results show that the entire numerical solver, coupled with the PCR algorithm, enables extreme-scale simulations with 2D pencil decompositions, which do not suffer performance losses even when compared to the best 1D slab configurations available for smaller systems.</div></div>\",\"PeriodicalId\":285,\"journal\":{\"name\":\"Computer Physics Communications\",\"volume\":\"316 \",\"pages\":\"Article 109811\"},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2025-08-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer Physics Communications\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0010465525003133\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Physics Communications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0010465525003133","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0

摘要

我们提出了一种高雷诺数下不可压缩湍流壁面流动的极端尺度模拟计算方法。数值算法扩展了求解二阶有限差分泊松/亥姆霍兹方程的流行方法,使用铅笔分布的平行三对角线求解器来提高大规模的计算性能。在欧洲旗舰超级计算机Leonardo和LUMI上,使用高达800亿个网格点和1024个gpu进行了高雷诺数湍流通道流模拟,研究了这种方法的优点。对于后者,必须承担整个求解器的额外GPU移植工作。我们的结果证实,虽然一维域分解有利于较小的系统,但它们在大尺度上变得低效甚至不可能。通过采用铅笔分发的方法,这种限制被放宽了。结果表明,在规模上,改进的泊松求解器的速度大约是使用全转置算法进行二维域分解的基线方法的两倍。强可伸缩性和弱可伸缩性测试表明,性能的提高是由于较低的通信占用。此外,为了确保求解壁法隐式扩散时的高性能,我们提出了一种重新设计的并行循环还原(PCR)方法,该方法分为预处理和运行时步骤。在预处理过程中,由并行GPU线程计算具有独立一维系数的小子数组,而不需要任何全局GPU通信。然后,在运行时,重新设计的PCR可以快速解决隐式1D扩散,而无需计算开销。我们的研究结果表明,整个数值求解器与PCR算法相结合,可以实现2D铅笔分解的极端尺度模拟,即使与可用于较小系统的最佳1D平板配置相比,也不会遭受性能损失。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A pencil-distributed finite-difference solver for extreme-scale calculations of turbulent wall flows at high Reynolds number
We present a computational method for extreme-scale simulations of incompressible turbulent wall flows at high Reynolds numbers. The numerical algorithm extends a popular method for solving second-order finite differences Poisson/Helmholtz equations using a pencil-distributed parallel tridiagonal solver to improve computational performance at scale. The benefits of this approach were investigated for high-Reynolds-number turbulent channel flow simulations, with up to about 80 billion grid points and 1024 GPUs on the European flagship supercomputers Leonardo and LUMI. An additional GPU porting effort of the entire solver had to be undertaken for the latter. Our results confirm that, while 1D domain decompositions are favorable for smaller systems, they become inefficient or even impossible at large scales. This restriction is relaxed by adopting a pencil-distributed approach. The results show that, at scale, the revised Poisson solver is about twice as fast as the baseline approach with the full-transpose algorithm for 2D domain decompositions. Strong and weak scalability tests show that the performance gains are due to the lower communication footprint. Additionally, to secure high performance when solving for wall-normal implicit diffusion, we propose a reworked flavor of parallel cyclic reduction (PCR) that is split into pre-processing and runtime steps. During pre-processing, small sub-arrays with independent 1D coefficients are computed by parallel GPU threads, without any global GPU communication. Then, at runtime, the reworked PCR enables a fast solution of implicit 1D diffusion without computational overhead. Our results show that the entire numerical solver, coupled with the PCR algorithm, enables extreme-scale simulations with 2D pencil decompositions, which do not suffer performance losses even when compared to the best 1D slab configurations available for smaller systems.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Computer Physics Communications
Computer Physics Communications 物理-计算机:跨学科应用
CiteScore
12.10
自引率
3.20%
发文量
287
审稿时长
5.3 months
期刊介绍: The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信