AI 中文总结
本研究提出一种分层网格上标记驱动水平集输运的自适应有限元框架，支持动态加密粗化，经多类网格数值实验验证，其精度与均匀离散化相当但成本更低，可集成至多相流求解器。
AI 中文摘要
本研究提出一种新的水平集输运自适应有限元框架，在与两相流界面捕捉方法相关的运动界面输运问题中实现高精度，同时降低计算成本。该框架支持动态加密与粗化，兼容标准有限元数据结构，适用于二维和三维的结构化与非结构化离散化。方法采用基于树的分层网格，通过动态局部加密追踪演化界面，在零水平集周围的窄带集中分辨率，其余区域保持粗离散化。水平集场通过自适应加密网格上的标记输运更新，实现界面预测与演化自适应分层结构构建；同时，反向特征迹线法准确评估平流后的水平集场。两种操作均采用高效的多级标记与点定位算法，识别不同加密层级中的包含单元。对二维、三维结构化与非结构化网格（包括四边形、单纯形、楔形和六面体网格）在经历严重界面变形的数值实验表明，该自适应策略在大幅降低成本的同时，达到与均匀离散化相当的精度，且在高强度自适应下保持良好的守恒性。因此，所提方法提供了高效灵活的框架，可自然集成到基于水平集的多相流求解器中。
英文摘要
This work presents a new adaptive finite-element framework for level-set transport, achieving high accuracy in kinematic interface transport problems relevant to interface-capturing methods for two-phase flows while reducing computational cost. This framework accommodates dynamic refinement and coarsening, and is compatible with standard finite-element data structures. The algorithm is applicable to both structured and unstructured discretizations in two and three dimensions. The method uses a tree-based hierarchical mesh with dynamic local refinement that tracks the evolving interface, concentrating resolution in a narrow band around the zero level set while preserving a coarse discretization elsewhere. The level-set field is updated through marker transport on adaptively refined meshes, enabling interface prediction and the construction of an evolving adaptive hierarchy. Concurrently, backward characteristic tracing provides accurate evaluation of the advected level-set field. Both operations employ an efficient multilevel marker and point-location algorithm to identify containing elements across refinement levels. Numerical experiments on two- and three-dimensional structured and unstructured grids, including quadrilateral, simplicial, wedge, and hexahedral meshes, subjected to severe interface deformations, demonstrate that the adaptive strategy achieves accuracy comparable to uniform discretizations at a substantially lower cost, while maintaining good conservation properties under aggressive adaptivity. Consequently, the proposed approach provides an efficient and flexible framework that can be naturally integrated into level-set-based multiphase flow solvers.
