@Article{AAMM-9-1364, author = {Shi , WeidongXu , Jianjun and Shu , Shi}, title = {An Adaptive Semi-Lagrangian Level-Set Method for Convection-Diffusion Equations on Evolving Interfaces}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2017}, volume = {9}, number = {6}, pages = {1364--1382}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0052}, url = {http://global-sci.org/intro/article_detail/aamm/10183.html} }