发表机构
University of Leeds（利兹大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出黎曼流形上不可压缩纳维-斯托克斯方程的本征有限元方法，验证其能量稳定性与准确性，对比表面有限元法等，表明其高效透明且可扩展至高维流形。
AI 中文摘要
我们提出了一种针对黎曼流形上不可压缩纳维-斯托克斯方程的本征有限元格式，推导了对应的弱形式，并证明了向后欧拉离散化具有能量稳定性。该框架在多个代表性流形上得到验证，特别关注流动的长期行为及其向以基林向量场表示的稳态解的收敛性。我们与表面有限元方法以及基林向量场的对应特征值格式进行了全面比较，数值结果表明，本征格式相较于嵌入型表面有限元格式是一种准确、计算高效且几何透明的替代方案，同时可自然扩展至高维黎曼流形。
英文摘要
We present an intrinsic finite element formulation for the incompressible Navier--Stokes equations on Riemannian manifolds. We derive the corresponding weak formulation and prove that the backward Euler discretisation is energy stable. The proposed framework is validated on several representative manifolds, with particular attention paid to the long-time behaviour of the flow and its convergence to steady-state solutions represented by Killing vector fields. Comprehensive comparisons are performed with the surface finite element method and a corresponding eigenvalue formulation for Killing vector fields. The numerical results demonstrate that the intrinsic formulation provides an accurate, computationally efficient, and geometrically transparent alternative to embedded surface finite element formulations, while naturally extending to higher-dimensional Riemannian manifolds.
