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An efficient numerical method for simulating multiphase flows using a diffuse interface model

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  • Lee, Hyun Geun
  • Kim, Junseok

Abstract

This paper presents a new diffuse interface model for multiphase incompressible immiscible fluid flows with surface tension and buoyancy effects. In the new model, we employ a new chemical potential that can eliminate spurious phases at binary interfaces, and consider a phase-dependent variable mobility to investigate the effect of the mobility on the fluid dynamics. We also significantly improve the computational efficiency of the numerical algorithm by adapting the recently developed scheme for the multiphase-field equation. To illustrate the robustness and accuracy of the diffuse interface model for surface tension- and buoyancy-dominant multi-component fluid flows, we perform numerical experiments, such as equilibrium phase-field profiles, the deformation of drops in shear flow, a pressure field distribution, the efficiency of the proposed scheme, a buoyancy-driven bubble in ambient fluids, and the mixing of a six-component mixture in a gravitational field. The numerical result obtained by the present model and solution algorithm is in good agreement with the analytical solution and, furthermore, we not only remove the spurious phase-field profiles, but also improve the computational efficiency of the numerical solver.

Suggested Citation

  • Lee, Hyun Geun & Kim, Junseok, 2015. "An efficient numerical method for simulating multiphase flows using a diffuse interface model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 423(C), pages 33-50.
    • Handle: RePEc:eee:phsmap:v:423:y:2015:i:c:p:33-50
    DOI: 10.1016/j.physa.2014.12.027
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    1. Karimipour, Arash & Hemmat Esfe, Mohammad & Safaei, Mohammad Reza & Toghraie Semiromi, Davood & Jafari, Saeed & Kazi, S.N., 2014. "Mixed convection of copper–water nanofluid in a shallow inclined lid driven cavity using the lattice Boltzmann method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 150-168.
    2. Lee, Hyun Geun & Kim, Junseok, 2008. "A second-order accurate non-linear difference scheme for the N -component Cahn–Hilliard system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4787-4799.
    3. Vanherpe, Liesbeth & Wendler, Frank & Nestler, Britta & Vandewalle, Stefan, 2010. "A multigrid solver for phase field simulation of microstructure evolution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(7), pages 1438-1448.
    4. Foroughi, Sajjad & Jamshidi, Saeid & Masihi, Mohsen, 2013. "Lattice Boltzmann method on quadtree grids for simulating fluid flow through porous media: A new automatic algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4772-4786.
    5. Lee, Hyun Geun & Choi, Jeong-Whan & Kim, Junseok, 2012. "A practically unconditionally gradient stable scheme for the N-component Cahn–Hilliard system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1009-1019.
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    Cited by:

    1. Nadja Adam & Florian Franke & Sebastian Aland, 2020. "A Simple Parallel Solution Method for the Navier–Stokes Cahn–Hilliard Equations," Mathematics, MDPI, vol. 8(8), pages 1-14, July.

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