Development of 2-D and 3-D double-population thermal lattice boltzmann models

Abstract

In this paper, an incompressible two-dimensional (2-D) and three- dimensional (3-D) thermohydrodynamics for the lattice Boltzmann scheme are de- veloped. The basic idea is to solve the velocity ¯eld and the temperature ¯eld using two di®erent distribution functions. A derivation of the lattice Boltzmann scheme from the continuous Boltzmann equation for 2-D is discussed in detail. By using the same procedure as in the derivation of the discretised density distribution function, it is found that new lattice of four-velocity (2-D) and eight-velocity (3-D) models for internal energy density distribution function can be developed where the viscous and compressive heating e®ects are negligible. These models are validated by the numerical simulation of the 2-D porous plate Couette °ow problem where the analytical solution exists and the natural convection °ows in a cubic cavity.