Chromo-dynamic multi-component lattice Boltzmann equation scheme for axial symmetry

SPENDLOVE, James, XU, Xu, SCHENKEL, Torsten, SEATON, M and HALLIDAY, Ian (2020). Chromo-dynamic multi-component lattice Boltzmann equation scheme for axial symmetry. Journal of Physics A: Mathematical and Theoretical, 53 (14), p. 145001.

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Abstract

We validate the chromo-dynamic multi-component lattice Boltzmann equation (MCLBE) simulation for immiscible fluids with a density contrast against analytical results for complex flow geometries, with particular emphasis on the fundamentals of the method, i.e. compliance with inter-facial boundary conditions of continuum hydrodynamics. To achieve the necessary regimes for the chosen validations, we develop, from a three-dimensional, axially-symmetric flow formulation, a novel, two-dimensional, pseudo Cartesian, MCLBE scheme. This requires the inclusion in lattice Boltzmann methodology of a continuously distributed source and a velocity-dependent force density (here, the metric force terms of the cylindrical Navier–Stokes equations). Specifically, we apply our model to the problem of flow past a spherical liquid drop in Re = 0, Ca regime and, also, flow past a lightly deformed drop. The resulting simulation data, once corrected for the simulation’s inter-facial micro-current (using a method we also advance herein, based on freezing the phase field) show good agreement with theory over a small range of density contrasts. In particular, our data extend verified compliance with the kinematic condition from flat (Burgin et al 2019 Phys. Rev. E 100 043310) to the case of curved fluid–fluid interfaces. More generally, our results indicate a route to eliminate the influence of the inter-facial micro-current.

Item Type:	Article
Additional Information:	** From IOP Publishing via Jisc Publications Router ** Licence for this article: http://creativecommons.org/licenses/by/4.0/ **Journal IDs: pissn 1751-8113; eissn 1751-8121 **Article IDs: publisher-id: aab777f; manuscript: ab777f; other: jphysa-112392.r1 **History: published 14-04-2020; open-access 18-03-2020; published_online 18-03-2020; accepted 18-02-2020; revised 13-01-2020; submitted 01-08-2019
Uncontrolled Keywords:	Paper, Statistical physics, lattice Boltzmann, multiphase flows, hydrodynamics
Identification Number:	https://doi.org/10.1088/1751-8121/ab777f
Page Range:	p. 145001
SWORD Depositor:	Colin Knott
Depositing User:	Colin Knott
Date Deposited:	23 Mar 2020 15:22
Last Modified:	18 Mar 2021 02:31
URI:	https://shura.shu.ac.uk/id/eprint/25993

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