Development and assessment of the interface lattice Boltzmann flux solvers for multiphase flows

Unlike the lattice Boltzmann method (LBM), the lattice Boltzmann flux solver (LBFS) is free from the limitation of uniform meshes, coupled time step and mesh spacing, and high memory cost. Specifically, the existing interface LBFS (LBFS-CH0) is reconstructed by locally applying the Cahn–Hilliard-based (CH-based) LBM with additional artificial terms. In the framework of LBM, the influence of the additional artificial terms has been assessed. Besides, the comparative study of the CH-based and the Allen–Cahn-based (AC-based) LBM shows that the latter has higher accuracy and stability. Though the LBFS is originated from the LBM, their performances may not be exactly the same. In this study, the AC-based and CH-based LBFS (LBFS-AC and LBFS-CH1) models which can accurately recover the phase field equations are developed from the interface LBM models without any additional terms. The gradient term in the LBFS-AC is discretized by the second-order central difference method. Compared with the LBFS-CH0, the LBFS-CH1 can eliminate the additional terms and recover the true CH equation. Then these interface LBFS models are compared to evaluate their performance and the influence of the additional terms. Different from the LBM, it is found that the CH-based LBFS is superior to the AC-based one in terms of the numerical accuracy and stability. In addition, numerical results show that the additional terms have minor effect on the ability to model the phase interface. This study can provide guidance to ensure the accuracy and stability of interface modeling. Taking into account the accuracy, stability and simplicity, we can conclude that the LBFS-CH0 model could be the first choice to simulate the phase interface in the framework of LBFS.