A phase-field-based multiple-relaxation-time lattice Boltzmann method for incompressible multiphase flows with density and viscosity contrasts

Abstract

In this work, we present a unified framework of phase-field-based multiple-relaxation-time lattice Boltzmann (MRT-LB) method for incompressible multiphase flows with density and viscosity contrasts where a block-lower-triangular relaxation matrix is introduced. The present framework includes the classic MRT-LB model and central-moments-based LB model (CLBM, a particular version of the MRT-LB model). The governing equations of incompressible multiphase flows can be reproduced precisely through the direct Taylor expansion method at the second-order of expansion parameters. In this work, the pressure p is re-estimated, and we prove that the present pressure expression is suitable for classic MRT model, CLBM and various lattice structures with an accuracy of O(Δt2+ΔtMa2). In addition, the model construction and analysis are all carried out in the velocity space. As a result, the present model has a similar structure to the traditional Bhatnagar-Gross-Krook (BGK) model. Therefore the process of their analysis and implementation is also similar. We then test the present model by five classic physical problems. The results show that the present model is found to be accurate and has better numerical stability over the BGK model, and has the ability to simulate multiphase flow problems with large density ratio (1000).