Jianlin Huang , Rundi Qiu , Jingzhu Wang , Yiwei Wang
{"title":"Multi-scale physics-informed neural networks for solving high Reynolds number boundary layer flows based on matched asymptotic expansions","authors":"Jianlin Huang , Rundi Qiu , Jingzhu Wang , Yiwei Wang","doi":"10.1016/j.taml.2024.100496","DOIUrl":null,"url":null,"abstract":"<div><p>Multi-scale system remains a classical scientific problem in fluid dynamics, biology, etc. In the present study, a scheme of multi-scale Physics-informed neural networks (msPINNs) is proposed to solve the boundary layer flow at high Reynolds numbers without any data. The flow is divided into several regions with different scales based on Prandtl’s boundary theory. Different regions are solved with governing equations in different scales. The method of matched asymptotic expansions is used to make the flow field continuously. A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale. The results are compared with the reference numerical solutions, which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows. This scheme can be developed for more multi-scale problems in the future.</p></div>","PeriodicalId":46902,"journal":{"name":"Theoretical and Applied Mechanics Letters","volume":"14 2","pages":"Article 100496"},"PeriodicalIF":3.2000,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2095034924000072/pdfft?md5=3c2bcd1109464bcab55e4a3bad910e96&pid=1-s2.0-S2095034924000072-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Applied Mechanics Letters","FirstCategoryId":"1087","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2095034924000072","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
Multi-scale system remains a classical scientific problem in fluid dynamics, biology, etc. In the present study, a scheme of multi-scale Physics-informed neural networks (msPINNs) is proposed to solve the boundary layer flow at high Reynolds numbers without any data. The flow is divided into several regions with different scales based on Prandtl’s boundary theory. Different regions are solved with governing equations in different scales. The method of matched asymptotic expansions is used to make the flow field continuously. A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale. The results are compared with the reference numerical solutions, which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows. This scheme can be developed for more multi-scale problems in the future.
期刊介绍:
An international journal devoted to rapid communications on novel and original research in the field of mechanics. TAML aims at publishing novel, cutting edge researches in theoretical, computational, and experimental mechanics. The journal provides fast publication of letter-sized articles and invited reviews within 3 months. We emphasize highlighting advances in science, engineering, and technology with originality and rapidity. Contributions include, but are not limited to, a variety of topics such as: • Aerospace and Aeronautical Engineering • Coastal and Ocean Engineering • Environment and Energy Engineering • Material and Structure Engineering • Biomedical Engineering • Mechanical and Transportation Engineering • Civil and Hydraulic Engineering Theoretical and Applied Mechanics Letters (TAML) was launched in 2011 and sponsored by Institute of Mechanics, Chinese Academy of Sciences (IMCAS) and The Chinese Society of Theoretical and Applied Mechanics (CSTAM). It is the official publication the Beijing International Center for Theoretical and Applied Mechanics (BICTAM).