Abstract
This paper discusses the use of the Lattice Boltzmann equations method with free energy based on the phase field approach and implemented in the D3Q27 scheme for modeling the dynamics of a three-component fluid flow in a three-dimensional cavity. Based on this method, a program has been created and it has been verified using a test problem that includes modeling the separation of a ternary liquid mixture. The results demonstrate the dependence of the mixture separation on time, the influence of surface tension and gravity. For example, at a high surface tension, the separation of the components occurs faster. Data on the average kinetic energy of the flow and the rate of energy dissipation under various conditions are also presented. In addition, an analysis ofthe performance of the developed software is performed, including a comparison of the serial and parallel versions of the program. Particular attention is paid to the physical aspects of the model: the transition regions between the components are described using a phase parameter changing according to the Cahn-Hilliard equation. The method allows one to model complex structures and predict the time it takes for the system to reach a stable state. The results confirm the correctness and efficiency of the proposed approach for studying the dynamics of multicomponent fluids