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格子Boltzmann方法的最新书籍.pdf
Preface
How to Read This Book
Acknowledgements
Contents
Acronyms
Frequently Asked Questions
Getting Started
Capabilities of the LBM
Boundary Conditions
Pressure and Compressibility
Advanced Questions
Part I Background
1 Basics of Hydrodynamics and Kinetic Theory
1.1 Navier-Stokes and Continuum Theory
1.1.1 Continuity Equation
1.1.2 Navier-Stokes Equation
1.1.3 Equations of State
1.2 Relevant Scales
1.3 Kinetic Theory
1.3.1 Introduction
1.3.2 The Distribution Function and Its Moments
1.3.3 The Equilibrium Distribution Function
1.3.4 The Boltzmann Equation and the Collision Operator
1.3.5 Macroscopic Conservation Equations
1.3.5.1 Mass Conservation Equation
1.3.5.2 Momentum Conservation Equation
1.3.5.3 Energy Conservation Equation
1.3.5.4 Discussion
1.3.6 Boltzmann's H-Theorem
References
2 Numerical Methods for Fluids
2.1 Conventional Navier-Stokes Solvers
2.1.1 Finite Difference Method
2.1.1.1 Finite Difference Approximations of Derivatives
2.1.1.2 Finite Difference Methods for CFD
2.1.1.3 Advantages and Disadvantages
2.1.2 Finite Volume Method
2.1.2.1 Finite Volume Approximation of Conservation Equations
2.1.2.2 Finite Volume Methods for CFD
2.1.2.3 Advantages and Disadvantages
2.1.3 Finite Element Methods
2.2 Particle-Based Solvers
2.2.1 Molecular Dynamics
2.2.2 Lattice Gas Models
2.2.2.1 Algorithm
2.2.2.2 Advantages and Disadvantages
2.2.3 Dissipative Particle Dynamics
2.2.4 Multi-particle Collision Dynamics
2.2.4.1 Algorithm
2.2.4.2 Advantages and Disadvantages
2.2.5 Direct Simulation Monte Carlo
2.2.6 Smoothed-Particle Hydrodynamics
2.3 Summary
2.4 Outlook: Why Lattice Boltzmann?
References
Part II Lattice Boltzmann Fundamentals
3 The Lattice Boltzmann Equation
3.1 Introduction
3.2 The Lattice Boltzmann Equation in a Nutshell
3.2.1 Overview
3.2.2 The Time Step: Collision and Streaming
3.3 Implementation of the Lattice Boltzmann Methodin a Nutshell
3.3.1 Initialisation
3.3.2 Time Step Algorithm
3.3.3 Notes on Memory Layout and Coding Hints
3.3.3.1 Initialisation
3.3.3.2 Streaming
3.3.3.3 Updating Macroscopic Variables
3.3.3.4 Equilibrium
3.3.3.5 Collision
3.4 Discretisation in Velocity Space
3.4.1 Non-dimensionalisation
3.4.2 Conservation Laws
3.4.3 Hermite Polynomials
3.4.3.1 Definition and Construction of Hermite Polynomials
3.4.3.2 Orthogonality and Series Expansion
3.4.4 Hermite Series Expansion of the Equilibrium Distribution
3.4.5 Discretisation of the EquilibriumDistribution Function
3.4.6 Discretisation of the Particle Distribution Function
3.4.7 Velocity Sets
3.4.7.1 General Comments and Definitions
3.4.7.2 Construction and Requirements of Velocity Sets
3.4.7.3 Common Velocity Sets for Hydrodynamics
3.4.7.4 Velocity Set Relations
3.4.7.5 Equilibrium Distributions
3.4.7.6 Macroscopic Moments
3.5 Discretisation in Space and Time
3.5.1 Method of Characteristics
3.5.2 First- and Second-Order Discretisation
3.5.2.1 First-Order Discretisation
3.5.2.2 Second-Order Discretisation
3.5.3 BGK Collision Operator
3.5.3.1 Under-, Full and Over-Relaxation
3.5.4 Streaming and Collision
References
4 Analysis of the Lattice Boltzmann Equation
4.1 The Chapman-Enskog Analysis
4.1.1 The Perturbation Expansion
4.1.2 Taylor Expansion, Perturbation, and Separation
4.1.3 Moments and Recombination
4.1.4 Macroscopic Equations
4.2 Discussion of the Chapman-Enskog Analysis
4.2.1 Dependence of Velocity Moments
4.2.2 The Time Scale Interpretation
4.2.3 Chapman-Enskog Analysis for Steady Flow
4.2.4 The Explicit Distribution Perturbation
4.2.5 Alternative Multi-scale Methods
4.3 Alternative Equilibrium Models
4.3.1 Linear Fluid Flow
4.3.2 Incompressible Flow
4.3.3 Alternative Equations of State
4.3.4 Other Models
4.4 Stability
4.4.1 Stability Analysis
4.4.2 BGK Stability
4.4.3 Stability for Advanced Collision Operators
4.4.4 Stability Guidelines
4.5 Accuracy
4.5.1 Formal Order of Accuracy
4.5.2 Accuracy Measure
4.5.3 Numerical Errors
4.5.3.1 Round-Off Error
4.5.3.2 Iterative (Steady-State) Error
4.5.3.3 Discretisation Error
4.5.4 Modelling Errors
4.5.5 Lattice Boltzmann Accuracy
4.5.6 Accuracy Guidelines
4.6 Summary
References
5 Boundary and Initial Conditions
5.1 Boundary and Initial Conditions in LBM in a Nutshell
5.1.1 Boundary Conditions
5.1.2 Initial Conditions
5.2 Fundamentals
5.2.1 Concepts in Continuum Fluid Dynamics
5.2.2 Initial Conditions in Discrete Numerical Methods
5.2.3 Boundary Conditions in Discrete Numerical Methods
5.2.4 Boundary Conditions for LBM: IntroductoryConcepts
5.2.4.1 Which Lattice Sites Should Be Subjected to Boundary Conditions?
5.2.4.2 What Differentiates Boundary Conditions in LBM from Other more Traditional Numerical Methods in Fluid Dynamics?
5.2.4.3 How Can Boundary Conditions Be Formulated for LBM?
5.2.4.4 What Determines the Numerical Accuracy of LB Boundary Conditions?
5.3 Boundary Condition Methods
5.3.1 Periodic Boundary Conditions
5.3.2 Periodic Boundary Conditions with PressureVariations
5.3.3 Solid Boundaries: Bounce-Back Approach
5.3.3.1 Principle of the Bounce-Back Method
5.3.3.2 Fullway Versus Halfway Bounce-Back Method
5.3.3.3 Resting Walls
5.3.3.4 Moving Walls
5.3.3.5 Advantages and Disadvantages
5.3.3.6 Numerical Evaluation of the Accuracy of the Bounce-Back Method
First-order analysis
Second-order analysis
5.3.4 Solid Boundaries: Wet-Node Approach
5.3.4.1 Finding the Density on Boundaries
5.3.4.2 Equilibrium Scheme
Accuracy benchmark of the equilibrium scheme
5.3.4.3 Non-equilibrium Extrapolation Method
Accuracy benchmark of the non-equilibrium extrapolation method
5.3.4.4 Non-equilibrium Bounce-Back Method
5.3.5 Open Boundaries
5.3.5.1 Velocity Boundary Conditions: Bounce-Back Approach
5.3.5.2 Pressure Boundary Conditions: Anti-bounce-Back Approach
5.3.5.3 Velocity Boundary Conditions: Wet-Node Approach
5.3.5.4 Pressure Boundary Conditions: Wet-Node Approach
5.3.6 Corners
5.3.6.1 Corners and the Bounce-Back Rule
5.3.6.2 Corners and the NEBB Method
5.3.7 Symmetry and Free-Slip Boundaries
5.4 Further Topics on Boundary Conditions
5.4.1 The Chapman-Enskog Analysis for Boundary Conditions
5.4.1.1 Bounce-Back Method
5.4.1.2 Non-equilibrium Bounce-Back Method
5.4.2 Mass Conservation at Solid Boundaries
5.4.2.1 Link-Wise Approach: Bounce-Back
5.4.2.2 Wet-Node Approach: Non-equilibrium Bounce-Back
5.4.3 Momentum Exchange at Solid Boundaries
5.4.3.1 Momentum Exchange in the Bounce-Back Method
5.4.3.2 Accuracy of the Momentum Exchange Method
5.4.4 Boundary Conditions in 3D
5.5 Initial Conditions
5.5.1 Steady and Unsteady Situations
5.5.2 Initial Conditions in LB Simulations
5.5.2.1 Role of Populations and Macroscopic Fields
5.5.2.2 Chicken or Egg? Order of Collision and Propagation
5.5.2.3 Consistent Initialisation via a Modified LB Scheme
5.5.3 Example: Decaying Taylor-Green Vortex Flow
References
6 Forces
6.1 Motivation and Background
6.2 LBM with Forces in a Nutshell
6.3 Discretisation
6.3.1 Discretisation in Velocity Space
6.3.2 Discretisation in Space and Time
6.3.2.1 First-Order Integration
6.3.2.2 Second-Order Integration
6.4 Alternative Forcing Schemes
6.4.1 General Observations
6.4.2 Forcing Schemes
6.4.2.1 Guo et al. (2002)
6.4.2.2 Shan and Chen (1993, 1994)
6.4.2.3 He et al. (1998)
6.4.2.4 Kupershtokh (2004)
6.4.2.5 Other, Less Accurate Approaches
6.5 Chapman-Enskog and Error Analysis in the Presenceof Forces
6.5.1 Chapman-Enskog Analysis with Forces
6.5.2 Errors Caused by an Incorrect Force Model
6.5.2.1 Discretisation of Velocity Space: The Issue of Unsteady and Steady Cases
6.5.2.2 Discretisation of Space and Time: The Issue of Discrete Lattice Effects
6.6 Boundary and Initial Conditions with Forces
6.6.1 Initial Conditions
6.6.2 Boundary Conditions
6.6.2.1 Bounce-Back
6.6.2.2 Non-equilibrium Bounce-Back
6.7 Benchmark Problems
6.7.1 Problem Description
6.7.2 Numerical Procedure
6.7.3 Constant Force
6.7.3.1 Bounce-Back
6.7.3.2 Non-equilibrium Bounce-Back
6.7.4 Constant Force and Pressure Gradient
6.7.4.1 Bounce-Back
6.7.4.2 Non-equilibrium Bounce-Back
6.7.5 Linear Force and Pressure Gradient
6.7.5.1 Bounce-Back
6.7.5.2 Non-equilibrium Bounce-Back
6.7.6 Role of Compressibility
6.7.6.1 Constant Force
6.7.6.2 Constant Force and Pressure Gradient
6.7.6.3 Linear Force and Pressure Gradient
References
7 Non-dimensionalisation and Choice of Simulation Parameters
7.1 Non-dimensionalisation
7.1.1 Unit Scales and Conversion Factors
7.1.2 Law of Similarity and Derived Conversion Factors
7.2 Parameter Selection
7.2.1 Parameters in the Lattice Boltzmann Method
7.2.1.1 Viscosity
7.2.1.2 Pressure, Stress and Force
7.2.2 Accuracy, Stability and Efficiency
7.2.2.1 Accuracy and Parameter Scaling
7.2.2.2 Stability
7.2.2.3 Efficiency
7.2.3 Strategies for Parameter Selection
7.2.3.1 Mapping of Dimensionless Physical Parameters
7.2.3.2 Parameter Selection Strategies
7.2.3.3 Small Reynolds Numbers
7.3 Examples
7.3.1 Poiseuille Flow I
7.3.2 Poiseuille Flow II
7.3.3 Poiseuille Flow III
7.3.4 Womersley Flow
7.3.5 Surface Tension and Gravity
7.4 Summary
References
Part III Lattice Boltzmann Extensions, Improvements, and Details
8 Lattice Boltzmann for Advection-Diffusion Problems
8.1 Lattice Boltzmann Advection-Diffusion in a Nutshell
8.2 Advection-Diffusion Problems
8.3 Lattice Boltzmann for Advection-Diffusion
8.3.1 Similarities of Advection-Diffusionand Navier-Stokes
8.3.2 Equilibrium Distribution
8.3.3 Lattice Vectors
8.3.4 Chapman-Enskog Analysis
8.3.4.1 Analysis Procedure
8.3.4.2 Error Term
8.3.5 Model Extensions
8.3.5.1 Source Term
8.3.5.2 Advanced Physical Models
8.3.5.3 Stability Improvements and Advanced Collision Operators
8.4 Thermal Flows
8.4.1 Boussinesq Approximation and Rayleigh-Bénard Convection
8.4.2 Non-dimensionalisation of the Temperature Field
8.4.3 LBM for Thermal Flows with Energy Conservation
8.4.3.1 Single-Population Model
8.4.3.2 Two-Population Model
8.4.4 LBM for Thermal Flows Without EnergyConservation
8.5 Boundary Conditions
8.5.1 Normal and Tangential Conditions
8.5.2 Dirichlet Boundary Conditions
8.5.2.1 Anti-Bounce-Back Scheme
8.5.2.2 Inamuro's Boundary Condition
8.5.3 Neumann Boundary Conditions
8.5.3.1 Inamuro's Flux Boundary Condition
8.5.3.2 Transformation of Neumann into Dirichlet Boundary Condition
8.6 Benchmark Problems
8.6.1 Advection-Diffusion of a Gaussian Hill
8.6.2 Diffusion from Cylinder Without Flow
8.6.3 Diffusion from Plate in Uniform Flow
8.6.4 Diffusion in Poiseuille Flow
References
9 Multiphase and Multicomponent Flows
9.1 Introduction
9.1.1 Liquid-Gas Coexistence and Maxwell Area Construction Rule
9.1.2 Surface Tension and Contact Angle
9.1.3 Sharp and Diffuse Interface Models
9.1.4 Surface Tension and Young-Laplace Test
9.2 Free-Energy Lattice Boltzmann Model
9.2.1 Liquid-Gas Model
9.2.1.1 Bulk Thermodynamics
9.2.1.2 Equations of Motion
9.2.1.3 The Lattice Boltzmann Algorithm
9.2.1.4 Galilean Invariance
9.2.1.5 A Practical Guide to Simulation Parameters
9.2.1.6 Surface Thermodynamics
9.2.1.7 Wetting Boundary Condition
9.2.2 Binary Fluid Model
9.2.2.1 Bulk Thermodynamics
9.2.2.2 Surface Thermodynamics
9.2.2.3 Equations of Motion
9.2.2.4 The Lattice Boltzmann Algorithm
9.2.2.5 A Practical Guide to Simulation Parameters
9.3 Shan-Chen Pseudopotential Method
9.3.1 General Considerations
9.3.2 Multiphase Model for Single Component
9.3.2.1 Physical Interpretation and Equation of State
9.3.2.2 Planar Interface and Thermodynamic Consistency
9.3.2.3 Boundary Conditions and Contact Angle
9.3.2.4 Algorithm and Forcing Schemes
9.3.2.5 Example: Young-Laplace Test
9.3.3 Multicomponent Method Without Phase Change
9.3.3.1 Shan-Chen Force and Algorithmic Implications
9.3.3.2 Fluid Velocity in the Multicomponent Model
9.3.3.3 Component Forces
9.3.3.4 Immiscible and (Partially) Miscible Fluids, Surface Tension
9.3.3.5 Boundary Conditions and Contact Angle
9.4 Limitations and Extensions
9.4.1 Spurious Currents and Multirange Forces
9.4.1.1 Shan-Chen Model
9.4.1.2 Free-Energy Model
9.4.2 Equation of State and Liquid-Gas Density Ratio
9.4.3 Restrictions on the Surface Tension
9.4.4 Viscosity Ratio and Collision Operator
9.4.5 What Else Can Be Done with These Models?
9.5 Showcases
9.5.1 Droplet Collisions
9.5.2 Wetting on Structured Surfaces
9.5.2.1 Chemical Patterning
9.5.2.2 Topographical Patterning: Superhydrophobic Surfaces
References
10 MRT and TRT Collision Operators
10.1 Introduction
10.2 Moment Space and Transformations
10.3 General MRT Algorithm
10.4 MRT for the D2Q9 Velocity Set
10.4.1 Hermite Polynomials
10.4.2 Gram-Schmidt Procedure
10.4.3 Discussion of MRT Approaches
10.5 Inclusion of Forces
10.6 TRT Collision Operator
10.6.1 Introduction
10.6.2 Implementation
10.7 Overview: Choice of Collision Models and Relaxation Rates
10.7.1 BGK Model
10.7.2 TRT Model
10.7.3 MRT Model
References
11 Boundary Conditions for Fluid-Structure Interaction
11.1 Motivation
11.2 Bounce-Back Methods
11.2.1 Simple Bounce-Back and Staircase Approximation
11.2.1.1 Revision of the Halfway Bounce-Back Method
11.2.1.2 Stationary Boundaries
11.2.1.3 Rigid Moving Particles
11.2.2 Interpolated Bounce-Back
11.2.2.1 Basic Algorithm
11.2.2.2 Moving Boundaries
11.2.2.3 Extended and Alternative Methods
11.2.3 Partially Saturated Bounce-Back
11.2.3.1 Basic Algorithm
11.2.3.2 Advantages and Limitations
11.2.4 Destruction and Creation of Fluid Nodes
11.2.5 Wall Shear Stress
11.3 Ghost Methods
11.3.1 Definitions
11.3.2 Filippova-Hänel (FH) and Mei-Luo-Shyy (MLS) Methods
11.3.2.1 Original Method by Filippova and Hänel (FH)
11.3.2.2 Improvements by Mei, Luo and Shyy (MLS)
11.3.3 Guo-Zheng-Shi (GZS) Method
11.3.4 Image-Based Ghost Methods
11.4 Immersed Boundary Methods
11.4.1 Introduction
11.4.2 Mathematical Basis
11.4.2.1 Eulerian and Lagrangian Systems
11.4.2.2 Continuous Governing Equations
11.4.2.3 Discretised Governing Equations
11.4.2.4 Kernel Functions
11.4.2.5 General IB-LBM Algorithm
11.4.2.6 Implications of the Combination of IBM and LBM
11.4.2.7 Distribution of Markers in Space
11.4.2.8 Accuracy and Convergence
11.4.3 Explicit Feedback IBM for Rigid Boundaries
11.4.3.1 Algorithm
11.4.3.2 Stationary Boundary: Poiseuille Flow
11.4.4 Direct-Forcing IB-LBM for Rigid Boundaries
11.4.4.1 Background
11.4.4.2 Implicit IB-LBM
11.4.4.3 Multi Direct-Forcing IB-LBM
11.4.4.4 Explicit, Non-iterative Direct-Forcing IB-LBM
11.4.5 Explicit IBM for Deformable Boundaries
11.4.5.1 Constitutive Models
11.4.6 Additional Variants and Similar BoundaryTreatments
11.5 Concluding Remarks
References
12 Sound Waves
12.1 Background: Sound in Viscous Fluids
12.1.1 The Viscous Wave Equation
12.1.2 The Complex-Valued Representation of Waves
12.1.3 Simple One-Dimensional Solutions: Free and Forced Waves
12.1.4 Time-Harmonic Waves: The Helmholtz Equation
12.1.5 Other Attenuation and Absorption Mechanisms
12.1.6 Simple Multidimensional Waves: The Green'sFunction
12.2 Sound Propagation in LB Simulations
12.2.1 Linearisation Method
12.2.2 Linearisation Results
12.2.2.1 Forced Waves
12.2.2.2 Free Waves
12.2.2.3 Discussion
12.3 Sources of Sound
12.3.1 Example: The Pulsating Sphere
12.3.2 The Inhomogeneous Wave Equation
12.3.3 Point Source Monopoles in LB Simulations
12.4 Non-reflecting Boundary Conditions
12.4.1 Reflecting Boundary Conditions
12.4.2 Characteristic Boundary Conditions
12.4.3 Absorbing Layers
12.5 Summary
References
Part IV Numerical Implementation of the Lattice Boltzmann Method
13 Implementation of LB Simulations
13.1 Introduction
13.1.1 Programming Languages and Development Tools
13.1.2 Floating Point Arithmetic
13.1.3 Taylor-Green Vortex Decay
13.2 Optimisation
13.2.1 Basic Optimisation
13.2.2 Automatic Optimisation During Compilation
13.2.3 Memory Caches
13.2.4 Measuring Performance
13.3 Sequential Code
13.3.1 Introductory Code
13.3.2 Optimising the Introductory Code
13.3.3 Data Output and Post-Processing
13.3.4 LBM Algorithm Optimisations
13.4 Parallel Computing
13.4.1 Multithreading and OpenMP
13.4.1.1 OpenMP Directives
13.4.1.2 Data Sharing
13.4.1.3 Compiling and Running OpenMP Code
13.4.1.4 Multithreaded LBM Implementation
13.4.1.5 Performance Results
13.4.2 Computing Clusters and MPI
13.4.2.1 MPI Concepts
13.4.2.2 MPI LBM Implementation
13.4.2.3 Blocking and Non-blocking Communications
13.4.2.4 Collective Communications
13.4.2.5 I/O
13.4.2.6 Compilation and Execution
13.4.2.7 Performance Results
13.4.3 General Purpose Graphics Processing Units
13.4.3.1 NVIDIA GPU Architecture
13.4.3.2 Programming Model
13.4.3.3 Code Compilation and Execution
13.4.3.4 GPU LBM Implementation
13.4.3.5 GPU Performance Optimisation and Results
13.4.3.6 Further Reading
13.5 Convergence Study
13.6 Summary
References
Appendix
A.1 Index Notation
A.2 Details in the Chapman-Enskog Analysis
A.2.1 Higher-Order Terms in the Taylor-Expanded LBE
A.2.2 The Moment Perturbation
A.2.3 Chapman-Enskog Analysis for the MRT Collision Operator
A.3 Taylor-Green Vortex Flow
A.4 Gauss-Hermite Quadrature
A.5 Integration Along Characteristics for the BGK Operator
A.6 MRT for D3Q15, D3Q19, and D3Q27 Velocity Sets
A.6.1 D3Q15
A.6.2 D3Q19
A.6.3 D3Q27
A.7 Planar Interface for the Free Energy Gas-Liquid Model
A.8 Planar Interface for the Shan-Chen Liquid-Vapour Model
A.9 Programming Reference
A.9.1 Comments
A.9.2 Expressions and Operators
A.9.3 Data Types
A.9.4 Composite Data Types
A.9.5 Variable Scope
A.9.6 Pointers
A.9.7 Dynamic Memory Allocation
A.9.8 Arrays
A.9.9 If Statement
A.9.10 While Loop
A.9.11 For Loop
A.9.12 Functions
A.9.13 Screen and File Output
A.9.14 Header Files
A.9.15 Compilation and Linking
References
Index
Graduate Texts in Physics
Timm Krüger
Halim Kusumaatmaja
Alexandr Kuzmin
Orest Shardt
Goncalo Silva
Erlend Magnus Viggen
The Lattice
Boltzmann
Method
Principles and Practice
Graduate Texts in Physics
Series editors
Kurt H. Becker, Polytechnic School of Engineering, Brooklyn, USA
Jean-Marc Di Meglio, Université Paris Diderot, Paris, France
Sadri Hassani, Illinois State University, Normal, USA
Bill Munro, NTT Basic Research Laboratories, Atsugi, Japan
Richard Needs, University of Cambridge, Cambridge, UK
William T. Rhodes, Florida Atlantic University, Boca Raton, USA
Susan Scott, Australian National University, Acton, Australia
H. Eugene Stanley, Boston University, Boston, USA
Martin Stutzmann, TU München, Garching, Germany
Andreas Wipf, Friedrich-Schiller-Univ Jena, Jena, Germany
Graduate Texts in Physics
Graduate Texts in Physics publishes core learning/teaching material for graduate-
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More information about this series at http://www.springer.com/series/8431
Timm KrRuger Halim Kusumaatmaja
Alexandr Kuzmin Orest Shardt Goncalo Silva
Erlend Magnus Viggen
The Lattice Boltzmann
Method
Principles and Practice
123
Timm KrRuger
School of Engineering
University of Edinburgh
Edinburgh, United Kingdom
Alexandr Kuzmin
Maya Heat Transfer Technologies
Westmount, Québec, Canada
Halim Kusumaatmaja
Department of Physics
Durham University
Durham, United Kingdom
Orest Shardt
Department of Mechanical and Aerospace
Engineering
Princeton University
Princeton, NJ, USA
Goncalo Silva
IDMEC/IST
University of Lisbon
Lisbon, Portugal
Erlend Magnus Viggen
Acoustics Research Centre
SINTEF ICT
Trondheim, Norway
ISSN 1868-4513
Graduate Texts in Physics
ISBN 978-3-319-44647-9
DOI 10.1007/978-3-319-44649-3
ISSN 1868-4521 (electronic)
ISBN 978-3-319-44649-3 (eBook)
Library of Congress Control Number: 2016956708
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Preface
Interest in the lattice Boltzmann method has been steadily increasing since it
grew out of lattice gas models in the late 1980s. While both of these methods
simulate the flow of liquids and gases by imitating the basic behaviour of a gas—
molecules move forwards and are scattered as they collide with each other—the
lattice Boltzmann method shed the major disadvantages of its predecessor while
retaining its strengths. Furthermore, it gained a stronger theoretical grounding in the
physical theory of gases. These days, researchers throughout the world are attracted
to the lattice Boltzmann method for reasons such as its simplicity, its scalability on
parallel computers, its extensibility, and the ease with which it can handle complex
geometries.
We, the authors, are all young researchers who did our doctoral studies on the
lattice Boltzmann method recently enough that we remember well how it was to
learn about the method. We remember particularly well the aspects that were a
little difficult to learn; some were not explained in the literature in as clear and
straightforward a manner as they could have been, and some were not explained
in sufficient detail. Some topics were not possible to find in a single place: as the
lattice Boltzmann method is a young but rapidly growing field of research, most of
the information on the method is spread across many, many articles that may follow
different approaches and different conventions. Therefore, we have sought to write
the book that the younger versions of ourselves would have loved to have had during
our doctoral studies: an easily readable, practically oriented, theoretically solid, and
thorough introduction to the lattice Boltzmann method.
As the title of this book says, we have attempted here to cover both the lattice
Boltzmann method’s principles, namely, its fundamental theory, and its practice,
namely, how to apply it in practical simulations. We have made an effort to make
the book as readable to beginners as possible: it does not expect much previous
knowledge except university calculus, linear algebra, and basic physics, ensuring
that it can be used by graduate students, PhD students, and researchers from a wide
variety of scientific backgrounds. Of course, one textbook cannot cover everything,
and for the lattice Boltzmann topics beyond the scope of this book, we refer to the
literature.
v
vi
Preface
The lattice Boltzmann method has become a vast research field in the past 25
years. We cannot possibly cover all important applications in this book. Examples
of systems that are often simulated with the method but are not covered here
in detail are turbulent flows, phase separation, flows in porous media, transonic
and supersonic flows, non-Newtonian rheology, rarefied gas flows, micro- and
nanofluidics, relativistic flows, magnetohydrodynamics, and electromagnetic wave
propagation.
We believe that our book can teach you, the reader, the basics necessary to read
and understand scientific articles on the lattice Boltzmann method, the ability to run
practical and efficient lattice Boltzmann simulations, and the insights necessary to
start contributing to research on the method.
How to Read This Book
Every textbook has its own style and idiosyncrasies, and we would like to make you
aware of ours ahead of time.
The main text of this book is divided into four parts. First, Chaps. 1 and 2 provide
background for the rest of the book. Second, Chaps. 3–7 cover the fundamentals of
the lattice Boltzmann method for fluid flow simulations. Third, Chaps. 8–12 cover
lattice Boltzmann extensions, improvements, and details. Fourth, Chap. 13 focuses
on how the lattice Boltzmann method can be optimised and implemented efficiently
on a variety of hardware platforms. Complete code examples accompany this book
and can be found at https://github.com/lbm-principles-practice.
For those chapters where it is possible, we have concentrated the basic practical
results of the chapter into an “in a nutshell” summary early in the chapter instead
of giving a summary at the end. Together, the “in a nutshell” sections can be
used as a crash course in the lattice Boltzmann method, allowing you to learn the
basics necessary to get up and running with a basic LB code in very little time.
Additionally, a special section before the first chapter answers questions frequently
asked by beginners learning the lattice Boltzmann method.
Our book extensively uses index notation for vectors (e.g. u˛) and tensors (e.g.
˛ˇ), where a Greek index represents any Cartesian coordinate (x, y, or z) and
repetition of a Greek index in a term implies summation of that term for all possible
values of that index. For readers with little background in fluid or solid mechanics,
this notation is fully explained, with examples, in Appendix A.1.
The most important paragraphs in each chapter are highlighted, with a few
keywords in bold. The purpose of this is twofold. First, it makes it easier to know
which results are the most important. Second, it allows readers to quickly and easily
pick out the most central concepts and results when skimming through a chapter by
reading the highlighted paragraphs in more detail.
Instead of gathering exercises at the end of each chapter, we have integrated them
throughout the text. This allows you to occasionally test your understanding as you
Preface
vii
read through the book and allows us to quite literally leave certain proofs as “an
exercise to the reader”.
Acknowledgements
We are grateful to a number of people for their help, big and small, throughout the
process of writing this book.
We are indebted to a number of colleagues who have helped us to improve this
book by reading and commenting on early versions of some of our chapters. These
are Emmanouil Falagkaris, Jonas Latt, Eric Lorenz, Daniel Lycett-Brown, Arunn
Sathasivam, Ulf Schiller, Andrey Ricardo da Silva, and Charles Zhou.
For various forms of help, including advice, support, discussions, and encour-
agement, we are grateful to Santosh Ansumali, Miguel Bernabeu, Matthew Blow,
Paul Dellar, Alex Dupuis, Alejandro Garcia, Irina Ginzburg, Jens Harting, Oliver
Henrich, Ilya Karlin, Ulf Kristiansen, Tony Ladd, Taehun Lee, Li-Shi Luo, Miller
Mendoza, Rupert Nash, Chris Pooley, Tim Reis, Mauro Sbragaglia, Ciro Sempre-
bon, Sauro Succi, Muhammad Subkhi Sadullah, and Alexander Wagner.
On a personal level, Alex wants to thank his family which allowed him to spend
some family time on writing this book. Erlend wants to thank Joris Verschaeve
for helping him get started with the LBM and his friends and family who worried
about how much time he was spending on this book; it all worked out in the end.
Halim wants to thank his family for the continuous and unwavering support and
Julia Yeomans for introducing him to the wonder of the LBM. Goncalo thanks his
family for their unlimited support, Alberto Gambaruto for introducing him to the
LBM, and Viriato Semiao for the chance to start working in the field; special thanks
to Irina Ginzburg for the opportunity to work with her and the countless discussions
and teachings. Orest thanks his family, friends, and colleagues for their valuable
support during his doctoral and postdoctoral studies. Timm thanks Aline for her
understanding and support and Fathollah Varnik for introducing him to the LBM.
Finally, we would like to thank our editor Angela Lahee for her support and
patience.
Edinburgh, UK
Durham, UK
Brossard, QC, Canada
Princeton, NJ, USA
Lisbon, Portugal
Trondheim, Norway
The authors can be contacted at authors@lbmbook.com.
Timm Krüger
Halim Kusumaatmaja
Alexandr Kuzmin
Orest Shardt
Goncalo Silva
Erlend Magnus Viggen
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