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## Über dieses Buch

Lattice Boltzmann Method introduces the lattice Boltzmann method (LBM) for solving transport phenomena – flow, heat and mass transfer – in a systematic way. Providing explanatory computer codes throughout the book, the author guides readers through many practical examples, such as:

flow in isothermal and non-isothermal lid driven cavities;flow over obstacles;forced flow through a heated channel;conjugate forced convection; andnatural convection.

Diffusion and advection-diffusion equations are discussed with applications and examples, and complete computer codes accompany the coverage of single and multi-relaxation-time methods. Although the codes are written in FORTRAN, they can be easily translated to other languages, such as C++. The codes can also be extended with little effort to multi-phase and multi-physics, if the reader knows the physics of the problem.

Readers with some experience of advanced mathematics and physics will find Lattice Boltzmann Method a useful and easy-to-follow text. It has been written for those who are interested in learning and applying the LBM to engineering and industrial problems and it can also serve as a textbook for advanced undergraduate or graduate students who are studying computational transport phenomena.

## Inhaltsverzeichnis

### Chapter 1. Introduction and Kinetics of Particles

Abstract
There are two main approaches in simulating the transport equations (heat, mass, and momentum), continuum and discrete. In continuum approach, ordinary or partial differential equations can be achieved by applying conservation of energy, mass, and momentum for an infinitesimal control volume. Since it is difficult to solve the governing differential equations for many reasons (nonlinearity, complex boundary conditions, complex geometry, etc.), therefore finite difference, finite volume, finite element, etc., schemes are used to convert the differential equations with a given boundary and initial conditions into a system of algebraic equations. The algebraic equations can be solved iteratively until convergence is insured. Let us discuss the procedure in more detail, first the governing equations are identified (mainly partial differential equation). The next step is to discretize the domain into volume, girds, or elements depending on the method of solution.

### Chapter 2. The Boltzmann Equation

Abstract
Ludwig Eduard Boltzmann (1844–1906), the Austrian physicist whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms and molecules (microscopic properties) determine the phenomenological (macroscopic) properties of matter such as the viscosity, thermal conductivity, and diffusion coefficient. The distribution function (probability of finding particles within a certain range of velocities at a certain range of locations at a given time) replaces tagging each particle, as in molecular dynamic simulations. The method saves the computer resources drastically.

### Chapter 3. The Diffusion Equation

Abstract
Equation 3.1 has second derivative in space, therefore, the diffusion takes place in both directions and requires two boundary conditions. Also, Eq. 3.1 has a first derivative in time, the diffusion is one directional in time, in other words, the diffusion at any point depends on the previous time and no information can be transferred from the future time. Also, it requires an initial condition to solve Eq. 3.1.

Abstract
In this chapter, the physics of advection and advection diffusion will be explained. Lattice Boltzmann method will be discussed for solving different advection–diffusion problems for one and two dimensional cases. Extending the method to three dimension problems is straightforward.

### Chapter 5. Isothermal Incompressible Fluid Flow

Abstract
In the following chapter, fluid flow problems will be explained. Lattice Boltzmann method (LBM) will be discussed to solve different isothermal, two dimensional fluid flow problems. Implementation of different boundary and flow conditions will be detailed. Extending the method for three dimensional problems is straightforward.

### Chapter 6. Non-Isothermal Incompressible Fluid Flow

Abstract
A cold fluid flows through a heated wall channel. The walls of channel are kept at constant temperature. Water flows through a channel of 6.0 cm in height and 120 cm in length. The inlet temperature and velocity of the water are 20°C and 0.006 m/s, respectively. The channel walls are kept at 80°C. Determine the velocity and temperature profiles and rate of heat transfer. Assume that the width of the channel is unity.

### Chapter 7. Multi-Relaxation Schemes

Abstract
Single relaxation scheme is extensively discussed and many problems were solved in the previous chapters. There is a claim that multi-relaxation schemes offer a higher stability and accuracy than the single relaxation scheme. This chapter is devoted to explain the multi-relaxation-time scheme.

### Chapter 8. Complex Flows

Abstract
The source term can be incorporated in LBM as external force, as discussed before. The beauty of LBM in treating multi-phase flows is that there is no need to trace the interface between phase as in the case in NS. Hence, coding of multi-phase is much easier in LBM than in NS solver. In this book, we avoided to discuss this kind of problems for one simple reason. The method is relatively simple to imply but the reader needs background on the physics of the problem, before applying the LBM. Therefore, the complex flow is left to the readers interest. However, I am sure that the reader can easily extend the pervious codes to handle complex phenomena easily provided that the reader understand the underlying physics of the problem.