Study Of Level-set Method For Computing Two-phase Flows With Surfactant And Its Relevant Issues

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 level-set re-initialization equation was complicated, which may be unnecessary. S-ince 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 geo-metrical flow with topological changes, simulations of bubble/droplet dynamics in incompressible two-phase flows. In terms of accuracy it is comparable to the other existing methods.A new S-L scheme is proposed to discretize the surface convection-diffusion equation. The other involved equations including the the level-set convection e-quation, 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 stiff-ness caused by the surface Laplacian, allowing larger time step than the Eulerian method. The method is extended to the block-structured adaptive mesh. Numer-ical examples are given to demonstrate the efficiency of the S-L method.In the following [1],a level-set method for two-phase flows with soluble surfac-tant is presented. The bulk surfactant concentration convection-diffusion equation defined in the region occupied by bulk fluid, is reformulated as distributional for-m by using the idea of the diffusive domain method. The resulting equation is discretized by using a modified Crank-Nicolson scheme. Based on level-set func-tion, the relevant surface delta and indictor function are approximated. A simple procedure to ensure the conservation of surfactant is given. Convergence of the method is demonstrated numerically. Numerical simulations, including droplet rising driven by buoyant force in 2D, drop breakup and interaction of two drops in a 3D shear flow, show that surfactant play a critical role in two-phase flows.