A fractional step axisymmetric lattice Boltzmann flux solver for incompressible swirling and rotating flows

• The complicated forcing terms in lattice Boltzmann models are offset by the predictor–corrector scheme.
• It is first time to present the lattice Boltzmann flux solver for simulation of axisymmetric flows.
• Fluxes are evaluated from local reconstruction of lattice Boltzmann solution.
• Overcome disadvantages of conventional lattice Boltzmann solver.
• The azimuthal velocity is also computed by the lattice Boltzmann model.

A fractional step axisymmetric lattice Boltzmann flux solver (ALBFS) is proposed for simulation of incompressible swirling and rotating flows in this paper. The predictor and corrector steps are introduced in the present solver. At first, the governing equations of axisymmetric flows are written as the quasi-two-dimensional forms with external forcing terms. Then in the predictor step, without considering the external forcing terms, the intermediate flow variables are predicted at the cell center by finite volume discretization of the conservative equations recovered by lattice Boltzmann equation (LBE). In this step, the lattice Boltzmann flux solver is presented to evaluate fluxes at the cell interface by local application of lattice Boltzmann method (LBM). The double-distribution-function lattice Boltzmann (LB) models are used to provide the local LBM solution at the cell interface, in which one distribution function is used for the axial and radial velocities while the other is adopted for the azimuthal velocity. In the corrector step, the intermediate flow variables are corrected by the external forcing terms. Compared with conventional axisymmetric LB models, the present work also computes the azimuthal velocity by a LB model and avoids complicated introduction of external forcing terms into the LB model. The reliability and flexibility of present solver are validated by simulations of pipe flow, Taylor–Couette flow and cylindrical cavity flow. The present numerical results agree excellently well with theoretical solution or available data in the literature.