Fourth-order analysis of force terms in multiphase pseudopotential lattice Boltzmann model

Pseudopotential lattice Boltzmann model (LBM) for multiphase flow has been widely studied 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.