The fluid flow and heat transfer problems encountered in industry applications span into different scales and there are different numerical methods for different scales problems. Multiscale methods are needed to solve problems involving multiple scales. In this dissertation, multiscale methods are developed by combining various single scale numerical methods, including lattice Boltzmann method (LBM), finite volume method (FVM) and Monte Carlo method. Two strategies exist in combing these numerical methods. For the first one, the whole domain is divided into multiple subdomains and different domains use various numerical methods. Message passing among subdomains decides the accuracy of this type of multiscale numerical method. For the second one, various parameters are solved with different numerical methods. These two types of multiscale methods are both discussed in this dissertation. In Chapters 3 and 4, the whole domain is divided into two subdomains and they are solved with LBM and FVM respectively. This LBM-FVM hybrid method is verified with lid driven flows and natural convections. In Chapter 5, a LBM-FVM hybrid method is proposed to take both advantages of LBM and FVM: velocity field and temperature file are solved with LBM and FVM respectively. MCM has advantages in solving radiative heat transfer, and LBM-MCM hybrid method is proposed in Chapter 6. Numerical investigation for melting problems are carried on in this dissertation. The key point in solving the melting problem is how to obtain the interface location. To overcome the disadvantages in the now existing numerical methods, an interfacial tracking method is advanced to calculate the interface location. In Chapter 7, low Prandtl fluid natural convections are solved with LBM to discuss the oscillation results. Based on these results, low Prandtl number melting problems are solved using LBM with interfacial tracking method in Chapter 8. High Prandtl number melting problems in a discrete heated enclosure are solved using FVM with interfacial tracking method in Chapter 9. To take both advantages of LBM and FVM, melting problems are solved with LBM-FVM hybrid method in chapter 10, while interfacial tracking method is advanced by porous media assumptions in fluid flow field simulation process. Problems in Chapters 3-10 are all in two-dimensional and three-dimensional problems are more general than them in the realistic applications. Double LBM-MRT model for threedimensional fluid flow and heat transfer is proposed and three types of natural convections in a cubic cavity are discussed in Chapter 11. For the first two types of cubic natural convections, the present results agreed very well with the benchmark solutions or experimental results in the literature. The results from the third type exhibited more general three-dimensional characters. Three-dimensional melting problems are solved with the proposed double LBM-MRT model with interfacial tracking method in Chapter 12. Numerical results in three conduction melting problems agree with the analytical results well. Taking Chapter 11 results in consideration, the double LBM-MRT model with interfacial tracking method is valid to solve three-dimensional conduction or convection controlled melting problems. Two convection melting problems in a cubic cavity are also solved. With a lower Rayleigh number, the convection effects are weaker; side wall effects are smaller; melting process carries on slower.

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.

All relevant advanced heat and mass transfer topics in heat conduction, convection, radiation, and multi-phase transport phenomena, are covered in a single textbook, and are explained from a fundamental point of view.

This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a variety of hardware platforms, including multi-core processors, clusters, and graphics processing units. Students and scientists learning and using the LB method will appreciate the wealth of clearly presented and structured information in this volume.

Lattice Boltzmann method (LBM) is a relatively new simulation technique for the modeling of complex fluid systems and has attracted interest from researchers in computational physics. Unlike the traditional CFD methods, which solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive propagation and collision processes over a discrete lattice mesh.This book will cover the fundamental and practical application of LBM. The first part of the book consists of three chapters starting form the theory of LBM, basic models, initial and boundary conditions, theoretical analysis, to improved models. The second part of the book consists of six chapters, address applications of LBM in various aspects of computational fluid dynamic engineering, covering areas, such as thermo-hydrodynamics, compressible flows, multicomponent/multiphase flows, microscale flows, flows in porous media, turbulent flows, and suspensions.With these coverage LBM, the book intended to promote its applications, instead of the traditional computational fluid dynamic method.

Introducing the Lattice Boltzmann Method in a readable manner, this book provides detailed examples with complete computer codes. It avoids the most complicated mathematics and physics without scarifying the basic fundamentals of the method.

This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems. With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programmers and researchers.