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

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.