A hybrid method for insoluble surfactant dynamics

In this paper, we develop a hybrid method for insoluble surfactant dynamics. While the Navier-Stokes equations are solved by an Eulerian method with level set describing the interfaces, the surfactant transport is tracked by a single-layer Lagrangian particle method. Consequently, this hybrid method inherits the ability in handling topology changes from the level-set method and high computational efficiency from the Eulerian method. On the other hand, the Lagrangian particle method ensures mass conservation and does not require topology information (connectivity). To prevent clustering of Lagrangian particles, a novel remeshing approach is proposed. It not only enables the generation of particle distributions adaptive to interface geometries, especially for extremely large deformation and strong stretching, but also provides an accurate reconstruction of concentration fields on the interface with mass conservation. Furthermore, by proposing an adaptive remeshing control, we optimize the remeshing frequency to balance computational costs and accuracy. Conservation, accuracy, and convergence of the present hybrid method are validated with 2-D and 3-D test cases.