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Volume 9, Issue 1
A Simple Implementation of the Semi-Lagrangian Level-Set Method

Weidong Shi, Jian-Jun Xu & Shi Shu

Adv. Appl. Math. Mech., 9 (2017), pp. 104-124.

Published online: 2018-05

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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.

  • AMS Subject Headings

65M06, 65M20, 76T10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-104, author = {Shi , WeidongXu , Jian-Jun and Shu , Shi}, title = {A Simple Implementation of the Semi-Lagrangian Level-Set Method}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {1}, pages = {104--124}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1305}, url = {http://global-sci.org/intro/article_detail/aamm/12139.html} }
TY - JOUR T1 - A Simple Implementation of the Semi-Lagrangian Level-Set Method AU - Shi , Weidong AU - Xu , Jian-Jun AU - Shu , Shi JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 104 EP - 124 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2015.m1305 UR - https://global-sci.org/intro/article_detail/aamm/12139.html KW - Semi-Lagrangian method, level-set method, interface motion, two-phase flow, bubble/ droplet dynamics, block-structured adaptive mesh. AB -

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.

Weidong Shi, Jian-Jun Xu & Shi Shu. (2020). A Simple Implementation of the Semi-Lagrangian Level-Set Method. Advances in Applied Mathematics and Mechanics. 9 (1). 104-124. doi:10.4208/aamm.2015.m1305
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