Lattice Boltzmann Simulation of Two- and Three-Dimensional Incompressible Thermal Flows

Abstract

This work is concerned with the application of the thermal lattice Boltzmann method (TLBM) to compute incompressible two- and three-dimensional flows in cavities. Two convection test cases, namely, the laminar flow in a differentially heated square cavity and a cubic cavity, are numerically analyzed through TLBM. The internal energy density distribution function approach with two three-dimensional particle velocity models, namely, the 15-velocity and the 19-velocity, and a two-dimensional model, namely, the nine-velocity, have been used in the present work. Computations are carried out for laminar flows in a differentially heated square cavity and a cubical cavity (Rayleigh numbers = 103 to 105). The boundary conditions used are stable and of good accuracy. To lend credibility to the thermal lattice Boltzmann model square cavity results, they are further compared with those obtained from a finite-difference-based code developed for this purpose.