SPENDLOVE, James, XU, Xu, HALLIDAY, O.J, SCHENKEL, Torsten and HALLIDAY, Ian (2020). Chromodynamic multirelaxation-time lattice Boltzmann scheme for fluids with density difference. Physical Review E (PRE), 102 (1).
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Spendlove_ChromodynamicMulti-Relaxtaion (VoR).pdf - Published Version
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Abstract
We develop, after Dellar ( P. J. Dellar, Phys. Rev. E. 65, 036309 (2002), J. Comput. Phys.
190, pp351 (2003)), a multiple-relaxation time (MRT), chromodynamic, multi-component lattice
Boltzmann equation (MCLBE) scheme for simulation of isothermal, immiscible fluid flow with a
density contrast. It is based on Lishchuk’s method (J. U. Brackbill, D. B. Kothe and C. Zemach, J.
Comp. Phys. 100, 335-354 (1992), S. V. Lishchuk, C. M. Care and I. Halliday, Phys. Rev. E. 67(3),
036701(2), (2003)) and the segregation of d’Ortona et al. (U. D’Ortona, D. Salin, M. Cieplak, R.
B. Rybka and J. R. Banavar Phys. Rev. E. 51, 3718, (1995)). We focus on fundamental model
verifiability but do relate some of our data to that from previous approaches, due to Ba et al. (Y.
Ba, H. Liu, Q. Li, Q. Kang and J. Sun, Phys. Rev. E 94, 023310 (2016)) and earlier Liu et al. (H.
Liu, A. J. Valocchi and Q. Kang, Phys. Rev. E 85, 046309 (2012)), who pioneered large density
difference chromodynamic MCLBE and showed the practical benefits of a MRT collision model.
Specifically, we test the extent to which chromodynamic MCLBE MRT schemes comply with the
kinematic condition of mutual impenetrability and the continuous traction condition by developing
analytical benchmarking flows. We conclude that our data, taken with those of Ba et al., verify the
utility of MRT chromodynamic MCLBE.
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