A Simple Implementation of the Semi-Lagrangian Level-Set Method (Advances in Applied Mathematics and Mechanics, 2018)
Semi-Lagrangian (S-L) methods have no CFL stability constraint, and aremore stable than the Eulerian methods. In the literature, the S-L method for the level-setre-initialization equation was complicated, which may be unnecessary. Since there-initialization procedure is auxiliary, we propose to use the first-order S-L schemecoupled with a projection technique to improve the accuracy at the grid points justadjacent to the interface. Standard second-order S-L method is used for evolvingthe level-set convection equation. The implementation is simple, including on theblock-structured adaptive mesh. The efficiency of the S-L method is demonstratedby extensive numerical examples including passive convection of interfaces with corners/kinks/largedeformation under given velocity fields, a geometrical flow withtopological changes, simulations of bubble/ droplet dynamics in incompressible two-phaseflows. In terms of accuracy it is comparable to the other existing methods.