A kinetic theory-based axisymmetric lattice Boltzmann flux solver for isothermal and thermal swirling flows

Abstract

In this study, an alternative axisymmetric lattice Boltzmann flux solver (LBFS) is proposed within the framework of the kinetic theory-based axisymmetric lattice Boltzmann (LB) model. The macroscopic equations recovered from the axisymmetric LB model are globally resolved by the finite volume method, while numerical fluxes on the cell interface are locally reconstructed from solutions to the axisymmetric LB equation with the second-order of accuracy. Unlike the previous fractional step – axisymmetric LBFS which is based on the standard LB model and contains complicated source terms of various space derivatives, the present scheme originates from the kinetic theory-based lattice Boltzmann equation defined on the cylindrical coordinates which naturally incorporates the axisymmetric effects into the distribution functions and greatly simplifies the source terms involved. As a result, no space derivatives emerge in the source terms, and the corrector step in the previous LBFS model is removed, which yields more compact formulations. Moreover, previous inconsistency between the local reconstruction and the global governing equations is fixed in the present solver, which helps to nurture the computational results. By consolidating the evolutions of the azimuthal velocity and the temperature into the present axisymmetric LBFS, it is particularly suitable for simulations of isothermal and thermal swirling flows. The accuracy and robustness of the proposed scheme are validated through various benchmark tests. Comprehensive comparisons with the results from the previous solver demonstrate that the present solver is quantitatively more accurate than the previous solver, particularly in predicting the pressure distributions.