Axisymmetric lattice Boltzmann method revised.

A reformulated lattice Boltzmann model is described for incompressible axisymmetric flows with or without swirling. It is a further development and improvement on the author's axisymmetric lattice Boltzmann method. The main features of the revised scheme are (a) all the macroscopic variables such as velocities are determined in the same formulas as those in the conventional lattice Boltzmann approach to the Navier-Stokes equations and (b) the added sink or source and force terms are simple with no calculation for a derivative. Such features distinguish the present method from the other existing simplified schemes, leading to a simple and efficient model. The scheme is naturally suitable for generic incompressible axisymmetric rotational flows involving more physical phenomena. The numerical solutions to Womersley and cylindrical cavity flows are presented to demonstrate its accuracy and capability.