发表机构
The Hong Kong Polytechnic University; Academy of Mathematics and Systems Science, Chinese Academy of Sciences; University of Chinese Academy of Sciences（香港理工大学; 中国科学院数学与系统科学研究院; 中国科学院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种能量稳定的ALE有限元方法，通过补偿切向速度重分布边界节点，解决表面张力驱动的Navier-Stokes自由边界流动，并证明其适定性与能量耗散，数值验证其鲁棒性和网格质量优势。
AI 中文摘要
我们提出了一种能量稳定的任意拉格朗日-欧拉（ALE）有限元公式，用于具有表面张力驱动的自由边界的不可压缩Navier-Stokes流动。关键要素是一种无乘子的补偿切向速度公式，该公式通过离散切向曲率残差重新分布边界节点。控制人工切向速度的松弛参数根据粘性-毛细平衡进行缩放，得到自然选择α=γ0/μ，其中γ0是表面张力系数，μ是动态粘度。我们证明了全离散格式是适定的、能量耗散的，并且与其半离散对应物在时间上一致。数值结果证实了所提出方法在μ和γ0值范围内具有鲁棒性。此外，与BGN方法相比，该方法在小时间步长状态下表现出更优越的网格质量保持能力。
英文摘要
We propose an energy-stable arbitrary Lagrangian-Eulerian (ALE) finite element formulation for incompressible Navier-Stokes flows with surface-tension-driven free boundaries. The key ingredient is a multiplier-free compensated tangential velocity formulation, which redistributes boundary nodes via the discrete tangential curvature residual. The relaxation parameter governing the artificial tangential velocity is scaled according to the viscous-capillary balance, yielding the natural choice $α= γ_0/ μ$, where $γ_0$ is the surface tension coefficient and $μ$ is the dynamic viscosity. We prove that the fully discrete scheme is well-posed, energy-dissipative, and temporally consistent with its semi-discrete counterpart. Numerical results confirm the robustness of the proposed method across a range of $μ$ and $γ_0$ values. Furthermore, the method exhibits superior mesh quality preservation compared with the BGN method, particularly in the small-time-step regime.
