Three-dimensional simulation of the dynamics of deformable droplets of an emulsion using the boundary element method and the fast multipole method on heterogeneous computing systems

The direct simulation of the interaction between a large number of deformable droplets is necessary for a more accurate prediction of the rheological properties and the microstructure of the liquid-liquid systems. The mathematical model for a three-dimensional flow of a mixture of two Newtonian liquids with a droplet structure in an unbounded domain is considered at low Reynolds numbers. An efficient approach to simulate the dynamics of a large number of deformable droplets is proposed. This approach is based on the boundary element method for three-dimensional problems accelerated both via an advanced scalable algorithm FMM and via the utilization of heterogeneous computing architectures (multicore CPUs and graphics processors). This enables the direct simulations of systems consisting of tens of thousands of deformable droplets on PCs, which is confirmed by test and demo computations. The developed method can be used to solve a wide range of problems related to the emulsion flow in micro- and nanoscales.