Finite difference of thermal lattice Boltzmann scheme for the simulation of natural convection heat transfer - Siti Aishah-Awanis, Mohd Yusoff (2009)
In this thesis, a method of lattice Boltzmann is introduced. Lattice Boltzmann method (LBM) is a class of computational fluid dynamics (CFD) methods for fluid simulation. Objective of this thesis is to develop finite difference lattice Boltzmann scheme for the natural convection heat transfer. Unlike conventional CFD methods, the lattice Boltzmann method is based on microscopic models and macroscopic kinetic equation. The lattice Boltzmann equation (LBE) method has been found to be particularly useful in application involving interfacial dynamics and complex boundaries. First, the general concept of the lattice Boltzmann method is introduced to understand concept of Navier-Strokes equation. The isothermal and thermal lattices Boltzmann equation has been directly derived from the Boltzmann equation by discretization in both time and phase space. Following from this concept, a few simple isothermal flow simulations which are Poiseulle flow and Couette flow were done to show the effectiveness of this method. Beside, numerical result of the simulations of Porous Couette flow and natural convection in a square cavity are presented in order to validate these new thermal models. Lastly, the discretization procedure of Lattice Boltzmann Equation (LBE) is demonstrated with finite difference technique. The temporal discretization is obtained by using second order Rungge-Kutta (modified) Euler method from derivation of governing equation. The discussion and conclusion will be presented in chapter five.