@Article{AAMM-9-1,
author = {Weidong, Shi and Xu, Jian-Jun and Shu, Shi},
title = {A Simple Implementation of the Semi-Lagrangian Level-Set Method},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2017},
volume = {9},
number = {1},
pages = {104--124},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2015.m1305},
url = {https://global-sci.com/article/73241/a-simple-implementation-of-the-semi-lagrangian-level-set-method}
}