An Immersed Boundary Method for Simulating Interfacial Flows with Insoluble Surfactant in Three Dimensions (Communications in Computational Physics, 2018)
In this paper, an immersed boundary (IB) method for simulating the interfacialflows with insoluble surfactant in three dimensions is developed. We consider adoubly periodic interface separating two fluids where the surfactant exists only alongthe evolving interface. An equi-arclength parametrization is introduced in order totrack the moving interface and maintain good Lagrangian meshes, so stable computationscan be performed without remeshing. This surface mesh-control techniqueis done by adding two artificial tangential velocity components into the Lagrangianmarker velocity so that the Lagrangian markers can be equi-arclength distributed duringthe time evolution. As a result, the surfactant equation on the interface must bemodified based on the new parametrization. A conservative scheme for solving themodified surfactant equation has been developed and proved to satisfy the total surfactantmass exactly in discrete level. A series of numerical experiments consisting ofthe validation of Lagrangian mesh control technique, the convergence study, the studyof self-healing dynamics, and the simulations of two-layer fluids under Couette flowhave been conducted to test our present numerical scheme.