Improved axisymmetric lattice Boltzmann scheme

TL;DR

This paper introduces an improved lattice Boltzmann scheme for axisymmetric incompressible flows that simplifies implementation, handles singularities effectively, and maintains compatibility with standard LB methods, validated through multiple flow simulations.

Contribution

It presents a new axisymmetric lattice Boltzmann scheme with a simple source term and effective singularity handling, enhancing ease of implementation and accuracy.

Findings

Numerical results agree well with analytical solutions.

The scheme effectively handles singularities at the axis.

Validated through multiple flow simulations.

Abstract

This paper proposes an improved lattice Boltzmann scheme for incompressible axisymmetric flows. The scheme has the following features. First, it is still within the framework of the standard lattice Boltzmann method using the single-particle density distribution function and consistent with the philosophy of the lattice Boltzmann method. Second, the source term of the scheme is simple and contains no velocity gradient terms. Owing to this feature, the scheme is easy to implement. In addition, the singularity problem at the axis can be appropriately handled without affecting an important advantage of the lattice Boltzmann method: the easy treatment of boundary conditions. The scheme is tested by simulating Hagen-Poiseuille flow, three-dimensional Womersley flow, Wheeler benchmark problem in crystal growth, and lid-driven rotational flow in cylindrical cavities. It is found that the numerical results agree well with the analytical solutions and/or the results reported in previous studies.