Please cite this article in press as: Y. Wu, et al., Fourth-order analysis of force terms in multiphase pseudopotential lattice Boltzmann model, Computers and Mathematics with Applications (2018), https://doi.org/10.1016/j.camwa.2018.07.022. Computers and Mathematics with Applications ( ) – Contents lists available at ScienceDirect Computers and Mathematics with Applications journal homepage: www.elsevier.com/locate/camwa Fourth-order analysis of force terms in multiphase pseudopotential lattice Boltzmann model Yongyong Wu a, b , Nan Gui a , Xingtuan Yang a , Jiyuan Tu a, b , Shengyao Jiang a, * a Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Tsinghua University, Beijing, 100084, China b School of Engineering, RMIT University, Melbourne, VIC 3083, Australia article info Article history: Received 12 January 2018 Received in revised form 8 June 2018 Accepted 9 July 2018 Available online xxxx Keywords: Pseudopotential lattice Boltzmann model Multiphase-relaxation-time (MRT) Fourth-order analysis Density ratio Force terms abstract Pseudopotential lattice Boltzmann model (LBM) for multiphase flow has been widely stud- ied due to its conceptual simplicity and computational efficiency. Additional interaction force terms are proposed to adjust mechanical stability condition for thermodynamic consistency in pseudopotential force. However, the additional force terms introduce a new non-physical effect in fourth-order macroscopic equation, which causes a variation of density ratio with different relaxation times in the multiphase-relaxation-time (MRT) LBM. In this work, a fourth-order analysis of force term in MRT LBM is presented to identify the fourth-order terms in recovered Navier–Stokes equations. Through the higher-order analysis, two methods are proposed to eliminate this effect. A series of numerical tests of planar interface and droplet are conducted to validate the analyses. © 2018 Elsevier Ltd. All rights reserved. 1. Introduction The lattice Boltzmann model (LBM) has been developed into an effective approach for computational fluid dynamics (CFD) in recent decades [1,2]. Especially for multiphase flow, LBM has been applied to simulate extensive science and engineering problems, such as phase-change heat transfer, droplet microfluidic, interface deformation and fuel cells [3–7]. In multiphase LBM, there are four major categories of multiphase models [7]: the color-gradient model [8], the pseudopotential model [9,10], the free-energy model [11], and the phase-field model [12,13]. Recently, the pseudopotential LBM and phase-field LBM have been studied extensively in recent researches at large density ratios and relatively high Reynolds numbers [7,14–17]. In addition, the stabilized entropic LBM is developed with enhanced numerical stability [18], and it is used to control the dynamics at liquid–vapor interface in multiphase LBM [19,20]. The pseudopotential LBM introduces an interaction force to mimic the fluid interaction. The inter-particle force not only gives a non-monotonic equation of state (EOS) for phase transition, but also yields a non-zero surface tension [7,21]. Consequently, the phase segregation between different phases can be achieved automatically without interface capturing and tracking methods. If the original SC EOS is used, the pseudopotential LBM can give a Maxwell-construction density ratio at equilibrium state [22], i.e. thermodynamic consistency. However, this SC EOS is not proper to describe a variety of practical fluids in science and engineering applications. Another approach of incorporating arbitrary EOS is the strategy introduced by He and Doolen [23], as well as Yuan and Schaefer [24]. Although this approach is convenient and promising to incorporate general EOSs, subsequent researches found a drawback of thermodynamic inconsistency emerges in this method [25,26]. Some new force schemes were proposed to achieve lower temperatures and approach thermodynamic consistency, such as * Corresponding author. E-mail addresses: guinan@mail.tsinghua.edu.cn (N. Gui), shengyaojiang@sina.com (S. Jiang). https://doi.org/10.1016/j.camwa.2018.07.022 0898-1221/© 2018 Elsevier Ltd. All rights reserved.