A simple diffuse interface immersed-boundary scheme for binary flows with curved boundaries

In this paper, a simple diffuse interface immersed-boundary scheme is developed for binary flows with curved boundaries under the frame of Euler-Lagrangian meshes. By this mean, the wetting boundary conditions (WBC) for stationary and moving curved boundaries can also be dealt in a similar manner as the flat boundaries. The main idea is cultivated by introducing two virtual layers of Lagrangian grid inside and outside the exact curved boundary with one interval of two neigboring lagrangian points, and the WBC is realized by the order parameters at the Lagrangian points, which are interpolated from the Euler grids. This scheme has the advantage of simple implication, it can successfully accommodate both the stationery and complex moving curved boundaries along with good accuracy and mass conservation property. A lattice Boltzmann method (LBM) framework is developed to incorporate the proposed immersed-boundary scheme. To test the present method, several binary flow problems are simulated. The numerical results are compared with theoretical and experimental results from literature which showed that the method can easily and efficiently simulate two-phase flows on the curved surfaces with high accuracy and mass conservation properties.