Simulation of Advection-Diffusion Problems with a Unified Lattice Boltzmann Equation

摘要

A more general advection-diffusion equation, which can describe the mass transport in both single- and two-phase fluid flow is proposed. A field distribution parameter was coupled in a modified governing differential equation, which can be used not only to account for the change of diffusivity in single-phase flow, but also to account for the sharp concentration jump at the interface of two-phase fluid flow. A unified multiple-relaxation-time (MRT) lattice Boltzmann equation (LBE) for simulating the advection-diffusion problems is also proposed. Two test cases with transient and steady conjugate mass transfer problems with straight or curved interfaces were calculated to validate the present method. The results show that the proposed MRT LBE is simple and accurate, and has good numerical stability against large difference in mass diffusivity.