Lattice Boltzmann method for convection-diffusion equations with general interfacial conditions.

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Heat and mass transfer

Background:

• Convection-diffusion equations require accurate modeling of interfacial conditions.
• Existing methods struggle with general interfacial conditions like conjugate heat transfer and porous media.
• The lattice Boltzmann method (LBM) offers a promising framework for such problems.

Purpose of the Study:

• To develop a novel interfacial scheme for LBM that handles general interfacial conditions.
• To achieve high-order accuracy for convection-diffusion equations at interfaces.
• To provide a computationally efficient scheme applicable to complex geometries and porous media.

Main Methods:

• An interfacial scheme is developed based on existing LBM boundary schemes for Robin conditions.
• The scheme is designed to handle various interfacial phenomena: conjugate heat/mass transfer, ion diffusion in porous media, and Kapitza resistance.
• The method achieves second-order accuracy on straight interfaces and first-order accuracy on curved interfaces.

Main Results:

• The proposed interfacial scheme successfully models convection-diffusion equations with diverse interfacial conditions.
• Numerical validation demonstrates the scheme's utility and accuracy, supporting theoretical predictions.
• The method exhibits efficiency by involving only current lattice nodes, beneficial for complex problems.

Conclusions:

• The developed interfacial scheme provides an effective and accurate solution for LBM simulations of convection-diffusion equations with general interfacial conditions.
• This approach is particularly valuable for problems involving complex geometries and porous media.
• The scheme's accuracy and computational efficiency offer significant advantages for scientific and engineering applications.