Development of 2-D and 3-D Double-Population Thermal Lattice Boltzmann Models

Authors

  • C. S. Nor Azwadi
  • T. Tanahashi

DOI:

https://doi.org/10.11113/matematika.v24.n.222

Abstract

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. Keywords: Double distribution function; lattice Boltzmann; microscopic velocity; natural convection.

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Published

2008-06-01

Issue

Section

Mathematics