Multiphase lattice Boltzmann flux solver with conservative Allen-Cahn model for modeling high-density-ratio flows

Abstract

In this paper, the Allen-Cahn-Multiphase lattice Boltzmann flux solver (AC-MLBFS) is proposed as a new and effective numerical simulation method for multiphase flows with high density ratios. The MLBFS resolves the macroscopic governing equations with the finite volume method and reconstructs numerical fluxes on the cell interface from local solutions to the lattice Boltzmann equation, which combines the advantages of conventional Navier–Stokes solvers and lattice Boltzmann methods for simulating incompressible multiphase flows while alleviating their limitations. Previous MLBFS-based multiphase solvers performed poorly in mass conservation, which might be caused by the excessive numerical diffusion in the Cahn-Hilliard (CH) model used as the interface tracking algorithm. To resolve this problem, the present method proposes using the conservative Allen-Cahn (AC) model as the interfacial tracking algorithm, which can ease the numerical implementation by removing high order derivative terms and alleviate mass leakage by enforcing local mass conservation in the physical model. Numerical validations will be carried out through benchmark tests at high density ratios and in extreme conditions with large Reynolds or Weber numbers. Through these examples, the accuracy and robustness as well as the mass conservation characteristics of the proposed method are demonstrated.