Analysis and reconstruction of the multiphase lattice Boltzmann flux solver for multiphase flows with large density ratios.

Abstract

The multiphase lattice Boltzmann flux solver (MLBFS) has been proposed to tackle complex geometries with nonuniform meshes. It also has been proven to have good numerical stability for multiphase flows with large density ratios. However, the reason for the good numerical stability of MLBFS at large density ratios has not been well established. The present paper reveals the relation between MLBFS and the macroscopic weakly compressible multiphase model by recovering the macroscopic equationsof MLBFS (MEs-MLBFS) with actual numerical dissipation terms. By directly solving MEs-MLBFS, the reconstructed MLBFS (RMLBFS) that involves only macroscopic variables in the computational processes is proposed. The analysis of RMLBFS indicates that by combining the predictor step, the corrector step of MLBFS introduces some numerical dissipation terms which contribute to the good numerical stability of MLBFS. By retaining these numerical dissipation terms, RMLBFS can maintain the numerical stability of MLBFS even at large density ratios.