General bounce-back scheme for concentration boundary condition in the lattice-Boltzmann method

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Transport phenomena

Background:

• The convection-diffusion equation governs mass and heat transfer.
• Implementing complex boundary conditions in numerical methods like the lattice Boltzmann method (LBM) is challenging.
• Existing LBM schemes struggle with general boundary conditions, especially in complex geometries.

Purpose of the Study:

• To propose a general bounce-back scheme for implementing concentration and thermal boundary conditions in LBM.
• To enable accurate simulations of convection-diffusion equations with complex boundary conditions, particularly in porous media.
• To analyze the accuracy and behavior of the proposed scheme.

Main Methods:

• Development of a general bounce-back scheme for the lattice Boltzmann method.
• Application of the scheme to implement general concentration boundary conditions (b1(∂Cw/∂n) + b2Cw = b3).
• Numerical simulations for flows with stationary and moving interfaces.
• Analytical study of concentration jump for the halfway bounce-back scheme.

Main Results:

• The proposed scheme successfully implements general concentration boundary conditions.
• Numerical results show excellent agreement with analytical solutions for various flow scenarios.
• The scheme is effective for boundaries with complex geometric structures, such as porous media.
• The analytical study provides insights into the concentration jump phenomenon.

Conclusions:

• The developed bounce-back scheme offers a robust and accurate approach for LBM simulations.
• It provides second-order accuracy for solving convection-diffusion equations with general boundary conditions.
• The scheme is particularly advantageous for problems involving porous media and complex geometries.