%0 Journal Article
%T Development of 2-D and 3-D Double-Population Thermal Lattice Boltzmann Models
%A C. S. Nor Azwadi
%A T. Tanahashi
%J Matematika
%D 2008
%I Universiti Teknologi Malaysia
%X In this paper, an incompressible two-dimensional (2-D) and three-dimensional (3-D) thermohydrodynamics for the lattice Boltzmann scheme are developed. The basic idea is to solve the velocity field and the temperature field using two different 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 effects are negligible. These models are validated by the numerical simulation of the 2-D porous plate Couette flow problem where the analytical solution exists and the natural convection flows in a cubic cavity.
%K Double distribution function
%K lattice Boltzmann
%K microscopic velocity
%K natural convection.
%U http://www.fs.utm.my/matematika/images/stories/matematika/20082416.pdf