Lattice-boltzmann model with sub-grid-scale boundary conditions

Area of Science:

• Computational fluid dynamics
• Mesoscopic fluid dynamics

Background:

• Accurate simulation of fluid flow requires precise handling of solid-fluid boundaries.
• Existing methods struggle with sub-grid scale boundaries and complex geometries.

Purpose of the Study:

• To develop a lattice-Boltzmann method (LBM) for incorporating solid-fluid boundary conditions at sub-grid scales.
• To achieve second-order accuracy for arbitrary boundary positions and orientations.

Main Methods:

• Introduced a continuous fluid volume fraction parameter at each grid node.
• Developed new LBM rules based on this parameter.
• Ensured conservation of mass and momentum.

Main Results:

• Achieved second-order accuracy for solid-fluid boundaries independent of grid alignment.
• Demonstrated applicability to irregular geometries, including porous media.
• Validated conservation properties of the new boundary rules.

Conclusions:

• The developed lattice-Boltzmann method effectively integrates sub-grid scale solid-fluid boundary conditions.
• The fluid volume fraction approach offers a robust solution for complex geometries.
• The method conserves mass and momentum, enhancing simulation fidelity.