Interface capturing method based on Level Set with octree adaptive mesh technology

doi:10.11949/j.issn.0438-1157.20160421

Abstract

Abstract:

Level Set method is one of the dominant methods to calculate and track evolution of interfaces because it can efficiently handle complex topology change of interfaces and large deformation. This method often suffers from large amount of numerical dissipation and high order accurate numerical discretization in time and space is used to improve mass conservation properties, which leads to an increase of computational overhead. When octree adaptive mesh technology is incorporated into Level Set to capture moving interfaces, the amount of computational meshes and memory usage is reduced and the calculation precision and efficiency are enhanced by adaptive octree mesh refining or coarsening according to interface distance. Because octree mesh is non-uniform and layer numbers of neighbor grids may be different, the WENO formula could not be directly applied to set values of octree grids. A discretization model and a technique of re-initializing distance field were proposed to calculate value of neighbor octree grids as well as to reduce mass loss in Level Set function. Numerical simulation on moving interface in rotation flow field of Zalesak sphere, in shear flow field of sphere and in cast filling process of square cavity benchmark indicated that combination of Level Set method and octree adaptive mesh technology could successfully capture moving interface. The interface-tracking precision was enhanced by refinement of octree meshes and increase of maximum octree mesh layers. When the maximum octree mesh layer was increased from 8 to 9 in the shear flow field, mass conservation of the sphere was obviously improved and numerical dissipation caused by Level Set method was significantly reduced.

Key words: interface capture, numerical simulation, octree mesh technology, Level Set method, adaptive mesh, model, optimization

摘要：

Level Set方法因能有效地处理界面处复杂的拓扑结构变化以及大变形问题，广泛应用于界面追踪领域。在Level Set方法追踪运动界面时引入八叉树网格技术，通过八叉树网格的细化和粗化技术减少计算网格数量和计算内存并提高计算效率和计算精度。因为八叉树网格为非均匀网格，其相邻网格的层数值可能不相同，所以不能直接采用WENO格式离散Level Set函数得到网格处的函数值，进而提出八叉树网格离散模型解决这一问题，并提出基于八叉树网格距离场重新初始化方法减少Level Set方法的质量损失，最后将基于八叉树网格技术的Level Set方法应用于两个给定速度场的运动界面模拟算例以及基准件方腔的铸造充型过程的模拟。模拟结果表明该方法可以提高界面的精度，同时改善质量守恒性。

关键词: 界面追踪, 数值模拟, 八叉树网格技术, Level Set方法, 网格自适应, 模型, 优化

CLC Number:

O351.2

YIN Yajun, LI Yangdong, TU Zhixin, LI Wen, SHEN Xu, ZHOU Jianxin. Interface capturing method based on Level Set with octree adaptive mesh technology[J]. CIESC Journal, 2016, 67(11): 4732-4741.

殷亚军, 李阳东, 涂志新, 李文, 沈旭, 周建新. 基于八叉树自适应网格技术的LevelSet运动界面追踪方法[J]. 化工学报, 2016, 67(11): 4732-4741.

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