Force method in a pseudo-potential lattice Boltzmann model

Abstract

Please cite this article in press as: A. Hu et al., Force method in a pseudo-potential lattice Boltzmann model, J. Comput. Phys. (2015), http://dx.Abstract Single component pseudo-potential lattice Boltzmann models have been widely studied due to their simplicity and stability in multiphase simulations. While numerous model have been proposed, comparative analysis and advantages and disadvantages of different force schemes is often lacking. A pseudo-potential model to simulate large density ratios proposed by Kupershtokh et al. [1] is analyzed in detail in this work. Several common used force schemes are utilized and results compared. Based on the numerical results, the relatively most accurate force scheme proposed by Guo et al. [2] is selected and applied to improve the accuracy of Kupershtokh et al.'s model. Results obtained using the modified Kupershtokh et al.'s model [1] for different value of τ are compared with those obtained using Li et al. [3] 's model. Effect of relaxation time τ on the accuracy of the results is reported. Moreover, it is noted that the error in the density ratio predicted by the model is directly correlated with the magnitude of the spurious velocities on (curved) interfaces. Simulation results show that, the accuracy of Kupershtokh et al.'s model can be improved with Guo et al. [2] 's force scheme. However, the errors and τ 's effects are still noticeable * Corresponding author. Tel.: +86 15210623987 E-mail address: anjie@cqu.edu.cn (A. Hu) 2 when density ratios are large. To improve the accuracy of the pseudo-potential model and to reduce the effects of τ , two possible methods were discussed in the present work . Both, a rescaling of the equation of state and multi-relaxation time, are applied and are shown to improve the prediction of the density ratios.

Lattice Boltzmann methods for multiphase flow and phase-change heat transfer

“…Recently, Hu et al have conducted theoretical and numerical analyses of the mixed interaction force given by Eq. (100) and the details can be found in Ref [256][39] in 2013 proposed an improved forcing scheme based on the LB-MRT equation, which utilizes the following forcing term:…”

Third-order analysis of pseudopotential lattice Boltzmann model for multiphase flow

“…This consistency is the reason why we call the present scheme for additional term a consistent scheme. However, in previous works [12,38,39], similar third-order terms, like ∇ · (hFF) (h is a coefficient), are inconsistently recovered and analyzed at the second-order. Note that Q m2 in Q m is still undetermined.…”

“…where R is the gas constant, T is the temperature, and a = 0.4963R 2 T 2 c /p c and b = 0.18727RT c /p c with T c and p c being the critical temperature and pressure, respectively. Moreover, a scaling factor K is also included in the EOS, which can be used to adjust the interface thickness in the simulation [29,39].…”

“…Substituting Eqs. (39) and (41) into Eq. (38), and considering ∇∇ψ 2 = 2∇ψ∇ψ + 2ψ∇∇ψ and ∇ · ∇ψ 2 = 2∇ψ · ∇ψ + 2ψ∇ · ∇ψ, the continuum form pressure tensor can be finally obtained as…”

“…Li et al [12] found that the rationale behind this phenomenon is that different forcing schemes produce different additional terms in the recovered macroscopic equation, which have important influences on the interfacial dynamics for multiphase flow, and then they proposed a forcing scheme to alleviate the thermodynamic inconsistency. Following the similar way, some other forcing schemes have been proposed recently [31,39,40]. As compared to the thermodynamic inconsistency, the nonadjustable surface tension has not received much attention.…”