Simulation of thermal flows by taylor series expansion- and least square-based Lattice Boltzmann method coupling with macroscopic thermal equation

Abstract

In this paper we use the Taylor series expansion- and least square-based lattice Boltzmann method to solve thermal flows. By introducing the "thermal source" into the isothermal lattice Boltzmann equation, and coupling with an explicit evaluatipn of temperature from the macroscopic thermal equation, the macroscopic property of the thermal flows can be obtained. To show the effectiveness of the method presented, the nature convection in the annulus between concentric horizontal circular and square cylinders was simulated and good results were obtained.