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This article reviews the mathematical and computer modeling of the process of ternary fluid mixture separation by free energy based phase field Lattice Boltzmann equations method. The process under study is considered in a limited area having the shape of a rectangle. Three different sets of fluid components with different structures are specified. The mathematical model constructed to describe this process is based on the Navier-Stokes equation for an incompressible fluid and the Cahn-Hilliard equation. The numerical model is built on the basis of LBM using the D2Q9 model. Numerical experiments were performed for two scenarios: (1) - investigate the model without gravity, in order to determine the patterns of the surface tension effect and (2) - investigate the model with gravity force. Numerical results showed a spinodal separation depending on the initial fractions of fluid concentrations. The results obtained determine the adequacy of the constructed model for a three-component fluid. [ABSTRACT FROM AUTHOR]

In this work, a model of binary fluids with different densities and viscosities based on the solution of the Navier-Stokes equations, the continuity and the Cahn-Hilliard equation is developed. The process of influence of surface tension and interface thickness on the phase fields of fluids is investigated. The numerical results of the study are obtained on the basis of a phase field model using the lattice Boltzmann method (LBM). The LME uses two sets of distribution functions for incompressible flow: one for tracking the pressure and velocity fields and the other for the phase field. The use of the pressure distribution function can significantly reduce the effect of numerical errors in calculating the interfacial force. A several 2D tests are carried out to demonstrate the validation, which included droplet problem and the Raleigh- Taylor instability. It is shown that the proposed method allows tracking the interface with high accuracy and stability. [ABSTRACT FROM AUTHOR]

The paper is concerned with numerical modelling of the homogeneous magnetohydrodynamic turbulence decay based on large eddy simulation (LES). The modelling of the turbulent process is based on the solution of a filtered unsteady three-dimensional Navier-Stokes equation and on the equation of magnetic field strength. A dynamic model has been applied to derive the main equations. The problem is solved numerically: the equation of motion is solved by a modified method of fractional steps using compact schemes; the equation for pressure is solved by the Fourier method with a combination of matrix factorization; the equation for magnetic field is solved by the method of fractional steps. The variation of the kinetic and magnetic energies of turbulence with time was obtained depending on the medium conductivity properties. Patterns are defined for micro- and macro-scale turbulence, longitudinal and transverse correlation functions as well as for the Taylor micro-scale Reynolds number for velocity and magnetic field. [ABSTRACT FROM AUTHOR]