{"title":"层流数值计算中基于MUSCL的增强保持自由流有限差分法","authors":"Tianen Guan, Zijia Huang, Chunguang Xu","doi":"10.1007/s00162-025-00745-1","DOIUrl":null,"url":null,"abstract":"<div><p>The implementation of the finite-difference method in curvilinear coordinates necessitates coordinate transformations, where violations of the Geometric Conservation Law (GCL) lead to loss of freestream preservation. This failure mechanism typically manifests as numerical instability or spurious physical artifacts in simulations. In this paper, we developed a freestream-preserving Monotone Upstream-centered Scheme for Conservation Laws (MUSCL) to solve viscous problems on perturbed grids. The geometrically induced errors are eliminated with the satisfaction of GCL. The central difference method is used for the computation of viscous flux terms, and the least squares method is introduced to enhance the accuracy and robustness of this scheme for solving subsonic viscous problems. The results of several viscous numerical tests demonstrate the reliable freestream-preserving property of the new method compared to MUSCL.</p></div>","PeriodicalId":795,"journal":{"name":"Theoretical and Computational Fluid Dynamics","volume":"39 3","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Enhanced freestream-preserving finite difference method based on MUSCL for numerical computation of laminar flow\",\"authors\":\"Tianen Guan, Zijia Huang, Chunguang Xu\",\"doi\":\"10.1007/s00162-025-00745-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The implementation of the finite-difference method in curvilinear coordinates necessitates coordinate transformations, where violations of the Geometric Conservation Law (GCL) lead to loss of freestream preservation. This failure mechanism typically manifests as numerical instability or spurious physical artifacts in simulations. In this paper, we developed a freestream-preserving Monotone Upstream-centered Scheme for Conservation Laws (MUSCL) to solve viscous problems on perturbed grids. The geometrically induced errors are eliminated with the satisfaction of GCL. The central difference method is used for the computation of viscous flux terms, and the least squares method is introduced to enhance the accuracy and robustness of this scheme for solving subsonic viscous problems. The results of several viscous numerical tests demonstrate the reliable freestream-preserving property of the new method compared to MUSCL.</p></div>\",\"PeriodicalId\":795,\"journal\":{\"name\":\"Theoretical and Computational Fluid Dynamics\",\"volume\":\"39 3\",\"pages\":\"\"},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2025-06-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical and Computational Fluid Dynamics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00162-025-00745-1\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Computational Fluid Dynamics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00162-025-00745-1","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
Enhanced freestream-preserving finite difference method based on MUSCL for numerical computation of laminar flow
The implementation of the finite-difference method in curvilinear coordinates necessitates coordinate transformations, where violations of the Geometric Conservation Law (GCL) lead to loss of freestream preservation. This failure mechanism typically manifests as numerical instability or spurious physical artifacts in simulations. In this paper, we developed a freestream-preserving Monotone Upstream-centered Scheme for Conservation Laws (MUSCL) to solve viscous problems on perturbed grids. The geometrically induced errors are eliminated with the satisfaction of GCL. The central difference method is used for the computation of viscous flux terms, and the least squares method is introduced to enhance the accuracy and robustness of this scheme for solving subsonic viscous problems. The results of several viscous numerical tests demonstrate the reliable freestream-preserving property of the new method compared to MUSCL.
期刊介绍：
Theoretical and Computational Fluid Dynamics provides a forum for the cross fertilization of ideas, tools and techniques across all disciplines in which fluid flow plays a role. The focus is on aspects of fluid dynamics where theory and computation are used to provide insights and data upon which solid physical understanding is revealed. We seek research papers, invited review articles, brief communications, letters and comments addressing flow phenomena of relevance to aeronautical, geophysical, environmental, material, mechanical and life sciences. Papers of a purely algorithmic, experimental or engineering application nature, and papers without significant new physical insights, are outside the scope of this journal. For computational work, authors are responsible for ensuring that any artifacts of discretization and/or implementation are sufficiently controlled such that the numerical results unambiguously support the conclusions drawn. Where appropriate, and to the extent possible, such papers should either include or reference supporting documentation in the form of verification and validation studies.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
