A Simple Implementation of the Semi-Lagrangian Level-Set Method

作者：Shi, Weidong; Xu, Jian-Jun^*; Shu, Shi

来源：Advances in Applied Mathematics and Mechanics, 2017, 9(1): 104-124.

DOI：10.4208/aamm.2015.m1305

• Semi-Lagrangian method
• level-set method
• interface motion
• two-phase flow
• bubble/droplet dynamics
• block-structured adaptive mesh

Semi-Lagrangian (S-L) methods have no CFL stability constraint, and are more stable than the Eulerian methods. In the literature, the S-L method for the level-set re-initialization equation was complicated, which may be unnecessary. Since the re-initialization procedure is auxiliary, we propose to use the first-order S-L scheme coupled with a projection technique to improve the accuracy at the grid points just adjacent to the interface. Standard second-order S-L method is used for evolving the level-set convection equation. The implementation is simple, including on the block-structured adaptive mesh. The efficiency of the S-L method is demonstrated by extensive numerical examples including passive convection of interfaces with corners/kinks/large deformation under given velocity fields, a geometrical flow with topological changes, simulations of bubble/droplet dynamics in incompressible two-phase flows. In terms of accuracy it is comparable to the other existing methods.

• 出版日期2017-2
• 单位湘潭大学; 中国科学院重庆绿色智能技术研究院