Axisymmetric Central Moment Lattice Boltzmann Method for Multiphase Flows

Multiphase flows involving axial symmetry occur in various applications, which can be simulated more effectively by incorporating such symmetry rather than performing full three-dimensional (3D) computations. With its origins based on kinetic theory and natural parallelization capabilities, lattice Boltzmann methods (LBM) have been of considerable recent interest. Among the different variants of the LBM, the formulations based on central moments have been more promising due to their enhanced numerical stability (see e.g., Hajabdollahi et al., J. Comp. Phys., 2022). We present an axisymmetric central moment LBM using multiple relaxation times for multiphase flows based on a discretization of a modified continuous Boltzmann equation applicable at high density ratios for the fluid motions with surface tension forces and a conservative Allen-Cahn equation for interface capturing. By exploiting axial symmetry, the 3D effects are incorporated into a two-dimensional formulation in a modular fashion via geometric source terms. The latter involves velocity gradients which are obtained locally based on non-equilibrium moments. We present results from simulations of a variety of axisymmetric multiphase flows which demonstrate the accuracy and efficiency of the proposed approach.