An Axisymmetric Lattice Boltzmann Model for Simulation of Taylor Couette Flows between Two Concentric Cylinders

Recently, Halliday et al. presented an idea by inserting the “source” terms into the two-dimensional (2D) lattice Boltzmann equation (LBE) so that the emergent dynamics of the lattice fluid can be transformed into the cylindrical polar system. This paper further extends the idea of Halliday et al. to include the effect of azimuthal rotation. The terms related to the azimuthal effect are considered as inertia forces. By using our recently developed Taylor-series-expansion and least-square-based lattice Boltzmann method (TLLBM) for the transformed LBE and a second order explicit finite difference method for the azimuthal moment equation, Taylor–Couette flows between two concentric cylinders with the inner cylinder rotating were simulated. To show the performance of the proposed model, the same problem was also simulated by the three-dimensional (3D) LBM. Numerical results showed that the present axisymmetric model is much more efficient than the 3D model for an axisymmetric flow problem.