Numerical validation of a consistent axisymmetric lattice Boltzmann model

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Fluid mechanics

Background:

• The Lattice Boltzmann Method (LBM) is a powerful numerical technique for simulating fluid flow.
• Existing LBM models often face challenges in accurately capturing axisymmetric flow phenomena.
• Incorporating source terms is crucial for modeling complex fluid dynamics.

Purpose of the Study:

• To numerically evaluate a recently derived axisymmetric lattice Boltzmann model.
• To validate the model's ability to incorporate spatially and temporally varying source terms.
• To confirm the model's accuracy in simulating fluid flow problems.

Main Methods:

• A novel axisymmetric lattice Boltzmann model was developed.
• A Chapman-Enskog analysis was used to derive the source term.
• The model was implemented on a two-dimensional Cartesian lattice.
• Simulations of Hagen-Poiseuille flow and Stokes' flow over a sphere were performed.

Main Results:

• The model successfully incorporated axisymmetric contributions into the Navier-Stokes equations.
• Simulations of Hagen-Poiseuille flow validated the model's accuracy.
• Numerical predictions for the drag coefficient in Stokes' flow closely matched analytical results.
• At higher Reynolds numbers, predictions aligned with empirical formulas.

Conclusions:

• The derived axisymmetric lattice Boltzmann model is a valid and accurate tool for fluid dynamics simulations.
• The model demonstrates excellent agreement with analytical and empirical results across different flow conditions.
• This model offers a promising approach for simulating complex axisymmetric flows.