Multi-scale physics-informed neural networks for solving high Reynolds number boundary layer flows based on matched asymptotic expansions

• Published in: Theoretical and applied mechanics letters Vol. 14; no. 2; p. 100496
• Main Authors: Huang, Jianlin, Qiu, Rundi, Wang, Jingzhu, Wang, Yiwei
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2024; Elsevier
• Subjects: Boundary layer; Fluid dynamics; Multi-scale; Physics-informed neural networks (PINNs); Physics-informed neural networks (PINNs); Multi-scale; Fluid dynamics; Boundary layer
• DOI: 10.1016/j.taml.2024.100496
• ISSN: 2095-0349

•Proposed a multi-scale physics-informed neural networks scheme for solving high Reynolds number boundary layer flows.•Applied the matched asymptotic expansions to ensure the continuity of the whole domain solutions after dividing.•Demonstrated the effectiveness of multi-scale physics-informed neural networks capturing flow details in different scales. [Display omitted] 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 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.