Alternative extrapolation-based symmetry boundary implementations for the axisymmetric lattice Boltzmann method

Area of Science:

• Computational Fluid Dynamics
• Numerical Methods
• Fluid Mechanics

Background:

• Axisymmetric simulations are crucial in fluid dynamics.
• Traditional lattice Boltzmann (LB) methods face challenges with singularities at symmetry axes.
• Existing boundary implementations can lack accuracy or stability.

Purpose of the Study:

• To develop and validate alternative symmetry boundary implementations for the axisymmetric lattice Boltzmann method.
• To address and eliminate singularities at the symmetry axis (r=0) in LB simulations.
• To enhance the accuracy and numerical stability of axisymmetric LB models.

Main Methods:

• Proposed novel symmetry boundary schemes based on nonequilibrium and direct extrapolation.
• Implemented boundary schemes directly on the symmetry axis.
• Extrapolated postcollision distribution functions and macroscopic variables from inner fluid nodes.

Main Results:

• Successfully avoided singularities during collision and macroscopic variable calculations at the symmetry axis.
• Achieved accuracy consistent with established axisymmetric LB models.
• Demonstrated slightly improved accuracy compared to Guo et al.'s scheme and enhanced numerical stability over specular reflection schemes.

Conclusions:

• The proposed nonequilibrium and direct extrapolation boundary schemes offer effective solutions for axisymmetric LB simulations.
• These new schemes provide a more accurate and numerically stable alternative to existing methods.
• The findings contribute to advancing the capabilities of lattice Boltzmann methods in simulating axisymmetric flows.