Revisiting a class of modified pseudopotential lattice Boltzmann models for single-component multiphase flows

Abstract

Since its emergence, the pseudopotential lattice Boltzmann (LB) method has been regarded as a straightforward and practical approach for simulating single-component multiphase flows. However, its original form always results in a thermodynamic inconsistency, which, thus, impedes its further application. Several strategies for modifying the force term have been proposed to eliminate this limitation. In this study, four typical and widely used improved schemes—Li's single-relaxation-time (SRT) scheme [Li et al., “Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows,” Phys. Rev. E 86, 016709 (2012)] and multiple-relaxation-times (MRT) scheme [Li et al., “Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model,” Phys. Rev. E 87, 053301 (2013)], Kupershtokh's SRT scheme [Kupershtokh et al., “On equations of state in a lattice Boltzmann method,” Comput. Math. Appl. 58, 965 (2009)], and Huang's MRT scheme [Huang and Wu, “Third-order analysis of pseudopotential lattice Boltzmann model for multiphase flow,” J. Comput. Phys. 327, 121 (2016)]—are systematically analyzed and intuitively compared after an extension of the MRT framework. The theoretical and numerical results both indicate that the former three schemes are specific forms of the last one, which thus help further understand the improvements of these pseudopotential LB models for achieving thermodynamic consistency. In addition, we modified the calculation of the additional source term in the LB evolution equation. Numerical results for stationary and moving droplets confirm the higher accuracy.