An Adaptive Semi-Lagrangian Level-Set Method for Convection-Diffusion Equations on Evolving Interfaces (Advances in Applied Mathematics and Mechanics, 2021)
A new Semi-Lagrangian scheme is proposed to discretize the surfaceconvection-diffusion equation. The other involved equations including the level-setconvection equation, the re-initialization equation and the extension equation arealso solved by S-L schemes. The S-L method removes both the CFL condition and thestiffness caused by the surface Laplacian, allowing larger time step than the Eulerianmethod. The method is extended to the block-structured adaptive mesh. Numericalexamples are given to demonstrate the efficiency of the S-L method.