Composite materials play an important role in aircraft, space and automotive industries, wind power industry. One of the most commonly used methods for the manufacture of composite materials is the impregnation of dry textiles by a viscous liquid binder. During the process, cavities (voids) of various sizes can be formed and then move in a liquid resin flows in the complex system of channels formed by textile fibers. The presence of such cavities results in a substantial deterioration of the mechanical properties of the composites. As a result, the development and effective implementation of the numerical methods and approaches for the effective 3D simulation of the viscous liquid flow around a rigid structure of different configuration. In the present study, the mathematical model and its effective numerical implementation for the study of hydrodynamic processes around fixed structure at low Reynolds numbers is considered. The developed approach is based on the boundary element method for 3D problems accelerated both via an advanced scalable algorithm (FMM), and via utilization of a heterogeneous computing architecture (multicore CPUs and graphics processors). This enables direct large scale simulations on a personal workstation, which is confirmed by test and demo computations. The simulation results and details of the method and accuracy/performance of the algorithm are discussed. The results of the research may be used for the solution of problems related to microfluidic device construction, theory of the composite materials production, and are of interest for computational hydrodynamics as a whole.