Lattice boltzmann models for heat transfer and anisotropic flows

Abstract

Fluid flows and associated heat and mass transfer problems are governed by several nonlinear second-order partial differential equations for which the analytical solutions are hard to obtain. Therefore, the numerical simulations are very useful in the research of the flow and heat transfer problems. In the last decade of the 20th century, a relatively new computational fluid dynamic (CFD) method, so called the lattice Boltzmann method (LBM) was proposed. The method is coding and meshing friendly and is rapidly developing in recent years. In this thesis, three new methods for the flow and heat transfer based on the LBM are presented. First, we give a counter-extrapolation approach to calculate the heat and mass transfer problems between conjugate interfaces with the interfacial discontinuity. By applying the finite difference approximation and extrapolation, the conjugate interface problem can be separated into two individual heat and mass transfer problems with Dirichlet boundaries, and the Dirichlet boundary problems can be solved by applying the LBM (or other CFD methods). Secondly, we consider the inlet and outlet treatment of periodic thermal flow. The periodic features of fully developed periodic incompressible thermal flows will be carefully examined by applying the LBM. The distribution modification (DM) approach and the source term (ST) approach are proposed, which can be both used for periodic thermal flows with constant wall temperature (CWT) and surface heat flux boundary conditions. The last method is a rectangular lattice Boltzmann model for anisotropic flows based on coordinate and velocity transformation. Unlike the other existing rectangular models which tuned the lattice Boltzmann algorithm to fit the rectangular or cuboid lattice grids, this method applies the general lattice Boltzmann method to solve the transformed system over regular square lattice grids. All these methods have been carefully examined in several simulations by comparing the LBM results to those of analytical solutions and previous publications using different numerical techniques. The results of the first and second methods are satisfactory. However, the result of the last method for the rectangular lattice Boltzmann model suffers numerical instability and inaccuracy. The reason has been analyzed, and a possible reform has also been suggested. The future research topics for each method have been proposed as well.