The multiphase lattice Boltzmann models face two main challenges: deviation terms \cite{ref1} in the recovered momentum equation and numerical stability at large density ratios, Reynolds numbers, and Weber numbers, which remain difficult to address simultaneously. This paper proposes three regularized recursive multiphase lattice Boltzmann models to address the two challenges. They can eliminate the deviation terms in the recovered momentum equation and adopt different pressure schemes. Detailed numerical tests are conducted to test their numerical stability and accuracy performance. The three models exhibit good numerical stability in an extensive range of density and viscosity ratios, significantly better than the single-relaxation-time multiphase lattice Boltzmann model with deviation terms in the recovered momentum equation. In addition, it is found that the dissipation terms in the pressure scheme should be consistent with the continuous pressure equation, which is decoupled with density and viscosity variations, to obtain correct velocity profiles for transient flow with large density and viscosity variations. The regularized recursive multiphase lattice Boltzmann model with a consistent pressure scheme can achieve superior numerical stability and accuracy.

Multiphase lattice Boltzmann,Regularized,Numerical stability,Pressure scheme,Third-order equilibrium moment