A 3-D indirect boundary element method for bounded creeping flow of drops

The simulation of the flow of emulsions in porous media presents formidable challenges, due to the extremely complex evolving geometry. Methods based on boundary integral equations, suitable for creeping flows, reduce the effort dedicated to geometry representation, but can become computationally expensive. An efficient indirect boundary integral formulation representing deformable drops in a bounded Stokes flow, resulting in a set of Fredholm integral equations of the second kind, is presented. The boundary element method (BEM) based on the formulation employs an accurate numerical integration scheme for the singular kernels involved, an effective and accurate curvature and normal calculation method, and an adaptive remeshing method to simulate interfacial deformation of drops. Two benchmark problems are used to assess the accuracy of the method, and to investigate its behavior for large problems. The method is found to provide accurate results combined with well-posedness, making it suitable for use in accelerated fast multipole method algorithms.