A fractional-step lattice Boltzmann flux solver for axisymmetric thermal flows

ABSTRACT

A fractional-step lattice Boltzmann flux solver is proposed in this work for effective simulation of axisymmetric thermal flows with rotating walls. The predictor and corrector steps are introduced in the solver. In the predictor step, excluding axisymmetric effects, the intermediate flow variables are predicted by the lattice Boltzmann flux solver (LBFS), which applies the finite-volume method to discretize the conservative equations recovered by the standard lattice Boltzmann method (LBM). The fluxes of the LBFS at the cell interfaces are reconstructed by local application of the lattice Boltzmann (LB) model with three distribution functions. These three distribution functions are used respectively for calculating axial and radial velocities, azimuthal velocity, and internal energy. In the corrector step, the intermediate flow variables are corrected by considering the axisymmetric effects. The present method not only retains the simplicity of the LBM but also eliminates the complicated derivation process in the axisymmetric LB model. The reliability of the proposed solver is examined by its application to simulate natural convection in an annulus, the Rayleigh-Benard convection, mixed convection in a vertical tall annulus, and Wheeler’s benchmark problem in crystal growth. The numerical results obtained agree well with the published data.