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 levelset re-initialization equation was complicated,which may be unne...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 levelset 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 twophase flows.In terms of accuracy it is comparable to the other existing methods.展开更多
基金This work is partially supported by National natural science fund of China(No.91430213 and No.11571293)Hunan Provincial Innovation Foundation for Postgraduate(No.CX2015B208)。
文摘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 levelset 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 twophase flows.In terms of accuracy it is comparable to the other existing methods.
