A Coupled Immersed Interface and Level Set Method for Three-Dimensional Interfacial Flows with Insoluble Surfactant (Communications in Computational Physics, 2018)
In this paper, a numerical method is presented for simulating the 3D interfacial flows with insoluble surfactant. The numerical scheme consists of a 3D immersedinterface method (IIM) for solving Stokes equations with jumps across the interfaceand a 3D level-set method for solving the surfactant convection-diffusion equationalong a moving and deforming interface. The 3D IIM Poisson solver modifies the onein the literature by assuming that the jump conditions of the solution and the fluxare implicitly given at the grid points in a small neighborhood of the interface. Thisassumption is convenient in conjunction with the level-set techniques. It allows standard Lagrangian interpolation for quantities at the projection points on the interface.The interface jump relations are re-derived accordingly. A novel rotational procedureis given to generate smooth local coordinate systems and make effective interpolation.Numerical examples demonstrate that the IIM Poisson solver and the Stokes solverachieve second-order accuracy. A 3D drop with insoluble surfactant under shear flowis investigated numerically by studying the influences of different physical parameterson the drop deformation.