A Review of Mesh Adaptation Technology Applied to Computational Fluid Dynamics
Mesh adaptation techniques can significantly impact Computational Fluid Dynamics by improving solution accuracy and reducing computational costs. In this review, we begin by defining the concept of mesh adaptation, its core components and the terminology commonly used in the community. We then categ...
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MDPI AG
2025-05-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/10/5/129 |
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| author | Guglielmo Vivarelli Ning Qin Shahrokh Shahpar |
| author_facet | Guglielmo Vivarelli Ning Qin Shahrokh Shahpar |
| author_sort | Guglielmo Vivarelli |
| collection | DOAJ |
| description | Mesh adaptation techniques can significantly impact Computational Fluid Dynamics by improving solution accuracy and reducing computational costs. In this review, we begin by defining the concept of mesh adaptation, its core components and the terminology commonly used in the community. We then categorise and evaluate the main adaptation strategies, focusing both on error estimation and mesh modification techniques. In particular, we analyse the two most prominent families of error estimation: feature-based techniques, which target regions of high physical gradients and goal-oriented adjoint methods, which aim to reduce the error in a specific integral quantity of interest. Feature-based methods are advantageous due to their reduced computational cost: they do not require adjoint solvers, and they have a natural ability to introduce anisotropy. A substantial portion of the literature relies on second-order derivatives of scalar flow quantities to construct sensors that can be equidistributed to minimise discretisation error. However, when used carelessly, these methods can lead to over-refinement, and they are generally outperformed by adjoint-based techniques when improving specific target quantities. Goal-oriented methods typically achieve higher accuracy in fewer adaptation steps with coarser meshes. It will be seen that various approaches have been developed to incorporate anisotropy into adjoint-based adaptation, including hybrid error sensors that combine feature-based and goal-oriented indicators, sequential strategies and adjoint weighting of fluxes. After years of limited progress, recent work has demonstrated promising results, including certifiable solutions and applications to increasingly complex cases such as transonic compressor blades and film-cooled turbines. Despite these advances, several critical challenges remain: efficient parallelisation, robust geometry integration, application to unsteady flows and deployment in high-order discretisation frameworks. Finally, examples of the potential role of artificial intelligence in guiding or accelerating mesh adaptation are also discussed. |
| format | Article |
| id | doaj-art-77dd5d2066b446b7a9101cff3bd4993b |
| institution | DOAJ |
| issn | 2311-5521 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
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| series | Fluids |
| spelling | doaj-art-77dd5d2066b446b7a9101cff3bd4993b2025-08-20T03:14:46ZengMDPI AGFluids2311-55212025-05-0110512910.3390/fluids10050129A Review of Mesh Adaptation Technology Applied to Computational Fluid DynamicsGuglielmo Vivarelli0Ning Qin1Shahrokh Shahpar2Department of Aeronautics, Imperial College London, London SW7 2AZ, UKDepartment of Mechanical Engineering, University of Sheffield, Sheffield S1 4DT, UKRolls-Royce Plc, Derby DE24 8BJ, UKMesh adaptation techniques can significantly impact Computational Fluid Dynamics by improving solution accuracy and reducing computational costs. In this review, we begin by defining the concept of mesh adaptation, its core components and the terminology commonly used in the community. We then categorise and evaluate the main adaptation strategies, focusing both on error estimation and mesh modification techniques. In particular, we analyse the two most prominent families of error estimation: feature-based techniques, which target regions of high physical gradients and goal-oriented adjoint methods, which aim to reduce the error in a specific integral quantity of interest. Feature-based methods are advantageous due to their reduced computational cost: they do not require adjoint solvers, and they have a natural ability to introduce anisotropy. A substantial portion of the literature relies on second-order derivatives of scalar flow quantities to construct sensors that can be equidistributed to minimise discretisation error. However, when used carelessly, these methods can lead to over-refinement, and they are generally outperformed by adjoint-based techniques when improving specific target quantities. Goal-oriented methods typically achieve higher accuracy in fewer adaptation steps with coarser meshes. It will be seen that various approaches have been developed to incorporate anisotropy into adjoint-based adaptation, including hybrid error sensors that combine feature-based and goal-oriented indicators, sequential strategies and adjoint weighting of fluxes. After years of limited progress, recent work has demonstrated promising results, including certifiable solutions and applications to increasingly complex cases such as transonic compressor blades and film-cooled turbines. Despite these advances, several critical challenges remain: efficient parallelisation, robust geometry integration, application to unsteady flows and deployment in high-order discretisation frameworks. Finally, examples of the potential role of artificial intelligence in guiding or accelerating mesh adaptation are also discussed.https://www.mdpi.com/2311-5521/10/5/129error estimationfeature adaptationadjoint adaptationanisotropic adaptationisotropic adaptationmesh movement |
| spellingShingle | Guglielmo Vivarelli Ning Qin Shahrokh Shahpar A Review of Mesh Adaptation Technology Applied to Computational Fluid Dynamics Fluids error estimation feature adaptation adjoint adaptation anisotropic adaptation isotropic adaptation mesh movement |
| title | A Review of Mesh Adaptation Technology Applied to Computational Fluid Dynamics |
| title_full | A Review of Mesh Adaptation Technology Applied to Computational Fluid Dynamics |
| title_fullStr | A Review of Mesh Adaptation Technology Applied to Computational Fluid Dynamics |
| title_full_unstemmed | A Review of Mesh Adaptation Technology Applied to Computational Fluid Dynamics |
| title_short | A Review of Mesh Adaptation Technology Applied to Computational Fluid Dynamics |
| title_sort | review of mesh adaptation technology applied to computational fluid dynamics |
| topic | error estimation feature adaptation adjoint adaptation anisotropic adaptation isotropic adaptation mesh movement |
| url | https://www.mdpi.com/2311-5521/10/5/129 |
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