TY - JOUR
T1 - An Adaptive Semi-Lagrangian Level-Set Method for Convection-Diffusion Equations on Evolving Interfaces
AU - Shi , Weidong
AU - Xu , Jianjun
AU - Shu , Shi
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1364
EP - 1382
PY - 2017
DA - 2017/09
SN - 9
DO - http://doi.org/10.4208/aamm.OA-2016-0052
UR - https://global-sci.org/intro/article_detail/aamm/10183.html
KW - Convection-diffusion equation, semi-Lagrangian method, level-set method, block-structured adaptive mesh, finite difference method.
AB - <p style="text-align: justify;">A new Semi-Lagrangian scheme is proposed to discretize the surface
convection-diffusion equation. The other involved equations including the level-set
convection equation, the re-initialization equation and the extension equation are
also solved by S-L schemes. The S-L method removes both the CFL condition and the
stiffness caused by the surface Laplacian, allowing larger time step than the Eulerian
method. The method is extended to the block-structured adaptive mesh. Numerical
examples are given to demonstrate the efficiency of the S-L method.</p>