A mass-conserved fractional step axisymmetric lattice Boltzmann flux solver for incompressible multiphase flows with large density ratio

Most conventional axisymmetric multiphase lattice Boltzmann methods involve complicated external source terms to model the axisymmetric effect. Besides, the break of mass conservation for each phase and the limitation of the simulated density ratio are still critical issues. To remove these drawbacks, a mass-conserved fractional step axisymmetric multiphase lattice Boltzmann flux solver is developed for flows with a large density ratio. We aim to naturally combine the developed modified Cahn-Hilliard equation with a small mass correction term, the lattice Boltzmann flux solver, and the fractional step method together for the simulation of the axisymmetric multiphase flows. The governing equations in the axisymmetric framework are split into the predictor and corrector steps. The predictor step without considering the axisymmetric effect and the mass correction term is solved by the finite-volume multiphase lattice Boltzmann flux solver based on the local application of the lattice Boltzmann method. Then, the corrector step is performed to include the axisymmetric effect and the mass correction term. Specifically, the numerical implementation of the mass correction term is designed in the axisymmetric framework. Several axisymmetric multiphase cases, including the Laplace law, the droplet oscillation, merging spherical bubbles, and micro-droplet impacting on a dry hydrophobic plate, have been adopted to demonstrate the accuracy and reliability of the proposed method. The results of the Laplace law and the droplet oscillation show that for one time step, solving the modified Cahn-Hilliard equation by our method can save about 46% of the computational time as compared with the fifth-order upwind scheme.