# LATTICE- BOLTZMANN METHOD FOR SIMULATING TWO-COMPONENT FLUID FLOWS

• D. B. Zhakebayev National Engineering Academy of the Republic of Kazakhstan, Almaty, Kazakhstan
• B. A. Satenova National Engineering Academy of the Republic of Kazakhstan, Almaty, Kazakhstan
• D. S. Agadayeva National Engineering Academy of the Republic of Kazakhstan, Almaty, Kazakhstan

### Abstract

Abstract. 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.
Key words: phase field, binary fluid, surface tension, chemical potential, lattice Boltzmann method.
Published
2020-12-31
How to Cite
ZHAKEBAYEV, D. B.; SATENOVA, B. A.; AGADAYEVA, D. S.. LATTICE- BOLTZMANN METHOD FOR SIMULATING TWO-COMPONENT FLUID FLOWS. International Journal of Mathematics and Physics, [S.l.], v. 11, n. 2, p. 32-40, dec. 2020. ISSN 2409-5508. Available at: <https://ijmph.kaznu.kz/index.php/kaznu/article/view/331>. Date accessed: 23 june 2021. doi: https://doi.org/10.26577/ijmph.2020.v11.i2.05.
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Section
MATHEMATICS