A consistent and conservative Phase-Field method for multiphase incompressible flows

Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M.

doi:10.1016/j.cam.2022.114116

Title: A consistent and conservative Phase-Field method for multiphase incompressible flows

Journal Article · 03 February 2022 · Journal of Computational and Applied Mathematics

DOI: https://doi.org/10.1016/j.cam.2022.114116 · OSTI ID:1976901

Huang, Ziyang ^[1];

^[2];

^[2]

Purdue Univ., West Lafayette, IN (United States); Univ. of Michigan, Ann Arbor, MI (United States); OSTI
Purdue Univ., West Lafayette, IN (United States)

In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the consistency of mass and momentum transport are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the “optimal” coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the consistency of reduction of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Finally, numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios.

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Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: National Science Foundation (NSF); US Army Research Office (ARO); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0021142

OSTI ID:: 1976901

Journal Information:: Journal of Computational and Applied Mathematics, Journal Name: Journal of Computational and Applied Mathematics Journal Issue: C Vol. 408; ISSN 0377-0427

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
consistent scheme
large-density ratio
mass conservation
mathematics
momentum conservation
multiphase incompressible flows
phase-field model

Title: A consistent and conservative Phase-Field method for multiphase incompressible flows

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