Forcing term in single-phase and Shan-Chen-type multiphase lattice Boltzmann models

Area of Science:

• Computational fluid dynamics
• Fluid mechanics
• Statistical physics

Background:

• Incorporating bulk forcing terms into lattice Boltzmann equations (LBE) is crucial for simulating complex fluid flows.
• Existing LBE forcing schemes exhibit varying performance, particularly in multiphase flow scenarios.

Purpose of the Study:

• To comparatively analyze five popular bulk forcing schemes for the lattice Boltzmann equation.
• To identify the strengths and weaknesses of these schemes, especially in multiphase flow simulations.
• To evaluate their accuracy in predicting surface tension and phase behavior.

Main Methods:

• Comparative analysis of five distinct LBE forcing schemes.
• Numerical simulations of the two-dimensional unsteady Taylor-Green vortex flow.
• Incorporation of schemes into Shan-Chen-type multiphase lattice Boltzmann models.
• Investigation of surface tension and coexisting phase densities under varying conditions.

Main Results:

• All five schemes show comparable accuracy for single-phase flow.
• The original Shan-Chen forcing scheme demonstrates inaccuracies in surface tension prediction for two-phase flow, dependent on relaxation time.
• The He et al. scheme provides accurate surface tension values independent of relaxation time.
• Including next-nearest neighbor interactions improves the matching of coexisting phase densities.

Conclusions:

• The choice of forcing scheme significantly impacts the accuracy of multiphase LBE simulations.
• The He et al. scheme is recommended for accurate surface tension modeling in Shan-Chen LBM.
• Next-nearest neighbor interactions are important for achieving thermodynamic equilibrium in multiphase simulations.