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 - <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>