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 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.