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

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Two-phase and multiphase flows

Published online by Cambridge University Press:  11 October 2016

Weidong Shi ,
Jian-Jun Xu  and
Shi Shu
Weidong Shi*
Affiliation:
School of Mathematical and Computational Sciences, Xiangtan University, Xiangtan, Hunan 411105, China Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714, China
Jian-Jun Xu*
Affiliation:
Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714, China
Shi Shu*
Affiliation:
School of Mathematical and Computational Sciences, Xiangtan University, Xiangtan, Hunan 411105, China
*
*Corresponding author. Email:weidongshi123@xtu.edu.cn (W. Shi), xujianjun@cigit.ac.cn (J. Xu), shushi@xtu.edu.cn (S. Shu)
*Corresponding author. Email:weidongshi123@xtu.edu.cn (W. Shi), xujianjun@cigit.ac.cn (J. Xu), shushi@xtu.edu.cn (S. Shu)
*Corresponding author. Email:weidongshi123@xtu.edu.cn (W. Shi), xujianjun@cigit.ac.cn (J. Xu), shushi@xtu.edu.cn (S. Shu)
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Abstract

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.

Keywords

Semi-Lagrangian methodlevel-set methodinterface motiontwo-phase flowbubble/ droplet dynamicsblock-structured adaptive mesh.

MSC classification

Secondary: 65M06: Finite difference methods 65M20: Method of lines 76T10: Liquid-gas two-phase flows, bubbly flows
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 1 , February 2017 , pp. 104 - 124
Copyright
Copyright © Global-Science Press 2017 

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