An improved forcing scheme for high-density-ratio multiphase flows based on the three-dimensional cumulant lattice Boltzmann method

This study presents an improved forcing scheme for high-density-ratio multiphase flow simulations within the three-dimensional cumulant lattice Boltzmann method. By modifying the structurally compatible forcing scheme and conducting rigorous asymptotic analysis of second-order correction terms, we successfully integrate the pseudopotential model with the three-dimensional twenty-seven velocities (D3Q27) cumulant lattice Boltzmann method for high-density-ratio simulations, which is performed for the first time and achieves remarkable density ratios. The proposed scheme concurrently satisfies the macroscopic Navier–Stokes equations and thermodynamic consistency while preserving the core architecture of the original forcing scheme. Enhanced thermodynamic consistency is achieved through optimized correction terms derived from asymptotic analysis. Numerical validation reveals significant stability improvements, attaining minimal reduced temperatures of 0.135 and 0.387 for planar and curved interfaces, respectively, under the pseudopotential model. The scheme achieves a maximum density ratio enhancement exceeding two orders of magnitude compared with existing cumulant-based forcing schemes, demonstrating enhanced numerical stability. The practical utility of the scheme is confirmed through simulations of wettability-driven droplet dynamics and ternary droplet coalescence phenomena. The quantitative agreement between numerically predicted capillary phenomena in square channels and prior experimental correlations further validates the applicability to practical multiphase flow systems. This work establishes a framework for implementing the pseudopotential model within the D3Q27 cumulant lattice Boltzmann method, offering a reference for high-density-ratio flow simulations.