Optimum convergence parameters of lattice Boltzmann method for predicting effective thermal conductivity

Abstract

Lattice Boltzmann method is widely used in predicting effective thermal conductivity of multi-phase composites due to its prominent performances. In this paper, a comparative study between single-relaxation-time model (BGK model) and two-relaxation-time model (TRT model) for predicting effective thermal conductivity is performed. To this end, the local heat flux scheme of TRT model is derived. The intrinsic drawbacks inherent to BGK model may be effectively cured by TRT model. It is interesting that an optimum convergence parameter exists in TRT model, which may maximize the convergence speed without losing computational accuracy. To determine the optimum convergence parameters, the influences of the microstructure distributions, volume fractions, thermal conductivity ratios and grid numbers are investigated in a systematic manner. For application, an empirical formula is developed to estimate the optimum convergence parameters, which may work for various multi-phase media. Under the guidance of this formula, the convergence speed of TRT model may be thousands of times faster the BGK counterpart. The present work may be readily extended to the predictions of effective electrical conductivity and elasticity modulus.