Evaluation of two different types D2QA microscopic velocity models at low rayleigh number heat transfer - Pylliscia Sumbok, Ak Adan (2009)
The aim of this thesis is to study the methods of the lattice Boltzmann equations in order to be apply in two types of D2Q4 model in thermal fluid flow problems. LBM has been found to be useful in application involving interfacial dynamics and complex boundaries. These methods utilize the statistical mechanics of simple discrete models to simulate complex physical systems. The theory of lattice Boltzmann method in nine and four velocity model are reviewed. The isothermal and thermal equation have been derived from the Boltzmann equation by descretiziton on both time and phase space. In this isothermal problem, a few simple isotherml flow simulation will be done by using the nine velocity model. The concepts of distribution function are considered beside the theory of Boltzmann equations. Then the derivations of Navier-Stokes equation from the Boltzmann equations are also presented. Some simulation results are performed, to highlight the important features of the isothermal LB model. The application of lattice Boltzmann scheme in thermal fluid problem is investigated in chapter 3. By using the derivation of the discretised density distribution function, a 4-velocity model is applied to develop the internal energy distribution function. This model is validated to simulate the porous couette flow problem for thermal fluid flow problems. The performance for both types D2Q4 microscopic model is demonstrated in the simulations of porous thermal couette flow and natural convection flow in a square cavity. The simulation of thermal fluids flow is applied to two different types of four-velocity model that are Azwadi model and old model. The same simulation test is performed for both types and the accuracy and stability analysis of both models are stated. These models are compared and discussed to ensure its validity.