Boundary condition at a two-phase interface in the lattice Boltzmann method for the convection-diffusion equation

Area of Science:

• Computational fluid dynamics
• Numerical methods
• Partial differential equations

Background:

• The lattice Boltzmann method (LBM) is a powerful numerical technique for simulating fluid flows and related phenomena.
• Accurately implementing internal boundary conditions, especially at interfaces between phases with different transport properties, poses a significant challenge in conventional LBM.
• Satisfying flux continuity at these interfaces during transient analysis is particularly difficult.

Purpose of the Study:

• To develop and validate a new boundary scheme for the lattice Boltzmann method (LBM) that accurately enforces internal boundary conditions at interfaces.
• To overcome the inherent difficulties in achieving flux continuity at interfaces with differing transport properties in transient LBM simulations.
• To analyze the accuracy and parameter dependence of the proposed scheme.

Main Methods:

• A modified lattice Boltzmann method (LBM) approach was developed by altering the collision operator and streaming process.
• Asymptotic analysis was employed to investigate the behavior and accuracy of the scheme concerning adjustable parameters.
• Numerical simulations of two specific convection-diffusion problems were conducted.

Main Results:

• The proposed boundary scheme successfully realizes internal boundary conditions at interfaces between phases with different transport properties.
• The scheme achieves second-order accuracy with respect to the lattice interval when appropriate parameter values are chosen.
• Numerical results for test problems show excellent agreement with analytical solutions, validating the scheme's effectiveness.

Conclusions:

• The presented boundary scheme offers a robust and accurate solution for handling internal boundary conditions in LBM for convection-diffusion equations.
• The modifications to the LBM collision and streaming processes effectively address the challenge of flux continuity at interfaces.
• The scheme's second-order accuracy and validated performance make it a valuable tool for complex multiphase flow simulations.