A coupled grid based particle and implicit boundary integral method for two-phase flows with insoluble surfactant

Abstract

We develop a coupled grid based particle and implicit boundary integral method for simulation of three-dimensional interfacial flows with the presence of insoluble surfactant. The grid based particle method (GBPM, Leung and Zhao [20]) tracks the interface by the projection of the neighboring Eulerian grid points and does not require stitching of parameterizations nor body fitted moving meshes. Using this GBPM to represent the interface, the surfactant equation defined on the interface is discretized naturally following a new volumetric constant-along-surface-normal extension approach (Chu and Tsai [4]). We first examine the proposed scheme to solve the convection-diffusion equation for the problems with available analytical solutions. The numerical results demonstrate second-order accuracy of the scheme. We then perform a series of simulations for interfacial flows with insoluble surfactant. The numerical results agree well with the theory, and are comparable with other numerical works in literature.