FMM/GPU Accelerated BEM Simulations of Emulsion Flow in Microchannels

Modeling of motion of two-phase liquids in microchannels of different shape is needed for a variety of industrial applications, such as enhanced oil recovery, advanced material processing, and biotechnology. Development of efficient computational techniques is required for understanding the mechanisms of many effects in “liquid-liquid” systems, such as the jamming of emulsion flows in microchannels and blood cell motion in capillaries. In the present study, a mathematical model of a three-dimensional flow of a mixture of two Newtonian liquids of a droplet structure in microchannels at low Reynold’s numbers is considered. The computational approach is based on the boundary element method accelerated both via an advanced scalable algorithm (FMM), and via utilization of a heterogeneous computing architecture (multicore CPUs and graphics processors). To solve large scale problems flexible GMRES solver is developed. Example computations are conducted for dynamics of many deformable drops of different sizes in microchannels. The results of simulations and accuracy/performance of the method are discussed. The developed approach can be used for solution of a wide range of problems related to emulsion flows in micro- and nanoscales.