A simplified axisymmetric lattice Boltzmann method for incompressible swirling and rotating flows

Abstract

A simplified axisymmetric lattice Boltzmann method (SALBM) is developed in this paper for effective simulation of incompressible swirling and rotating flows. This model explores an alternative approach of reconstructing an axisymmetric model within the lattice Boltzmann (LB) framework. Essentially, SALBM reconstructs solutions to the macroscopic governing equations recovered from the axisymmetric LB equation through the Chapman-Enskog expansion analysis. Two variations of schemes, which bear different orders of temporal accuracy and are, respectively, suitable for the steady and the unsteady axisymmetric flow problems, can be evolved from SALBM. The proposed schemes reflect direct evolution of macroscopic variables instead of distribution functions, which could reduce the cost in virtual memory. Meanwhile, analytical interpretation of physical boundary conditions is available in SALBM which avoids tedious transformations as required in conventional LB models. Numerical tests further reveal that SALBM performs better than the existing axisymmetric LB models in numerical stability. These merits endow the present SALBM with advantages over previous models and forge its prospect in engineering applications.