An alternative implementation of the kinetic theory based axisymmetric lattice Boltzmann model

Abstract

The semi-implicit centered scheme, as an approximated implementation of the trapezium rule based scheme, has proved to be capable of avoiding the discrete lattice effects in our recent forcing scheme analysis for the axisymmetric LB method, and is applied here for an alternative implementation of the kinetic theory based axisymmetric model by Guo et al. In particular, the external force terms and the first-order part of the source terms accounting for the axisymmetric effect are discretized with the semi-implicit centered scheme, while the rest are represented with the trapezium rule. The proposed axisymmetric LB scheme has the advantage of simpler calculations of the macroscopic variables since the zeroth- and the first-order moments of the distribution function are independent of the complicated source terms. Chapman–Enskog analysis in the Appendix demonstrates that axisymmetric Navier–Stokes (N–S) equations are recovered from the proposed model, and the error terms caused by the semi-implicit centered scheme do not affect the overall accuracy of the present model. Moreover, the accuracy and applicability of the proposed axisymmetric LB model are verified by the adopted numerical tests, and the complicated macroscopic variables computations in the Guo et al. model and its derivative models are avoided by the present model.