Analysis of the typical unified lattice Boltzmann models and a comprehensive multiphase model for convection-diffusion problems in multiphase systems.

Abstract

The present paper analyzes the typical unified lattice Boltzmann (LB) models for different convection-diffusion (CD) problems in multiphase systems. The CD problems in multiphase systems can be roughly classified into three groups: CD problems with a continuous scalar value and a continuous flux, a discontinuous scalar value and a continuous flux, a continuous scalar value and a discontinuous flux. The characteristics of the corresponding unified LB models for the three kinds of CD problems are analyzed and the equivalence between the LB models based on different perspectives or numerical schemes is revealed. Finally, a comprehensive multiphase LB model (CMLBM) capable of solving different isotropic and anisotropic CD problems in multiphase systems is proposed. Four typical CD problems in multiphase systems are calculated to validate the CMLBM; the results show that it performs well against the typical isotropic and anisotropic CD problems in multiphase systems.