Theoretical and numerical study on the well-balanced regularized lattice Boltzmann model for two-phase flow

Area of Science:

• Computational fluid dynamics
• Multiphase flow modeling
• Numerical methods

Background:

• Standard lattice Boltzmann equation (LBE) simulations for multiphase flows suffer from spurious interface velocities and inconsistent density properties.
• Existing methods require improvements to accurately capture complex two-phase flow phenomena.

Purpose of the Study:

• To develop and validate a novel well-balanced regularized lattice Boltzmann (WB-RLB) model with third-order Hermite expansion for enhanced two-phase flow simulations.
• To address limitations of existing LBE models, specifically spurious velocities and density inconsistencies.

Main Methods:

• Incorporation of Guo's equilibrium distribution function and modified force term into the LBE regularization with trapezoidal integration.
• Theoretical analysis and numerical simulations comparing WB-RLB with WB-LBE and SOMDS, using stationary droplet, droplet coalescence, phase separation, and contact angle test cases.
• Evaluation of force balance accuracy using isotropic central scheme (ICS) and second-order mixed difference scheme (SOMDS).

Main Results:

• The WB-RLB model, particularly with third-order expansion (WB-RLB3), demonstrates superior accuracy and stability compared to WB-LBE.
• SOMDS shows higher accuracy in force balance than ICS, validated by stationary droplet simulations.
• All tested models accurately captured equilibrium states even at high density ratios (1000:1); WB-RLB showed improved numerical stability in dynamic cases.

Conclusions:

• The developed WB-RLB model offers excellent numerical accuracy and stability for both static and dynamic two-phase interface problems.
• Adjusting third-order moment relaxation parameters further enhances WB-RLB model performance.
• While accurate for contact angles, the well-balance property requires further validation near three-phase junctions.