Macroscopic axisymmetric lattice Boltzmann method (MacAxLAB)

Abstract The author has recently proposed a macroscopic lattice Boltzmann method (MacLAB) for the Navier–Stokes equations. The method is formulated for the first time to retain the streaming step by removing the collision step in the two integral steps of the standard lattice Boltzmann method. It relies on one fundamental parameter of lattice size δ x in the model. This leads to a revolutionary and precise minimal “Lattice” Boltzmann method, which directly uses physical variables as boundary conditions with less required storage for more accurate and efficient simulations. In this paper, the MacLAB is further developed for solving incompressible axisymmetric flow equations (MacAxLAB). The model is validated through simulations of a 3D unsteady Womersley flow and two 3D steady cylindrical cavity flows. The numerical results have compared with other numerical ones and available analytical solutions; it shows that the MacAxLAB is applicable and accurate for modelling incompressible axisymmetric flow.