The chapter shows that to study the three-dimensional flows arising from the complex effect of vibration on Newtonian fluids, it is best to use a topological method of computer modeling. For reliability and clarity of the numerical modeling results obtained, FlowVision software and SUSU supercomputer resources were used. The calculation results showed the superiority of the new controlled vibrojet method over the traditional process of mixing liquid media. The calculations of flows rates were performed. The conditions for the formation of internal submerged toroidal flows and counter-swirling jets inside these flows are revealed. The simulation results made it possible to determine the control parameters of the process, to describe the functionality and technological capabilities of the computer-controlled vibrojet mixer. Its design is based on a fundamentally new method of controlled vibration mixing of multicomponent mixtures and solutions used in the chemical, pharmaceutical, food, engineering, and mining industries. As a result, practical technology has received a tool for digital processing of the mixing process.