A corrected open boundary framework for lattice Boltzmann immiscible pseudopotential models

The pseudopotential lattice Boltzmann method is a prominent approach for simulating multiphase flows, valued for its physical intuitiveness and computational tractability. However, existing immiscible pseudopotential methods for modeling dynamic multi-component immiscible fluid systems involving open boundaries face persistent challenges, notably the influence of spurious currents on interface formation and breakup, as well as the effects of inlet and outlet boundary configurations on simulation stability. Therefore, this paper proposes a corrected open boundary framework based on multiple-relaxation-time for the immiscible pseudopotential model. Our method includes three key improvements: (1) For the accurate recovery of macroscopic quantities at the inlet boundary, correction coefficients are introduced to reconstruct the distribution function; (2) Based on real-time mass flow rates at the inlet and outlet, the outlet boundary velocity is adjusted to ensure global mass conservation in the computational domain; (3) The relaxation coefficient related to numerical stability is adjusted based on the viscosity of two-phase fluids to reduce spurious currents. To validate the reliability of the proposed corrected method, four benchmark cases were simulated: Laplace tests and Taylor deformation, two-phase Poiseuille flow, migration of droplets in microchannels, as well as droplet generation in T-shaped and co-flow devices. The results demonstrate that the corrected method reduced the average spurious currents at the phase interface by 65.8% and controlled the average mass deviation of the fluid system at around 3.5%. In addition, the morphology of the droplets differs by less than 5% compared to the benchmark examples and experiments.