Theory and Application of Multiphase Lattice Boltzmann Methods presents a comprehensive review of all popular multiphase Lattice Boltzmann Methods developed thus far and is aimed at researchers and practitioners within relevant Earth Science disciplines as well as Petroleum, Chemical, Mechanical and Geological Engineering. Clearly structured throughout, this book will be an invaluable reference on the current state of all popular multiphase Lattice Boltzmann Methods (LBMs). The advantages and disadvantages of each model are presented in an accessible manner to enable the reader to choose the model most suitable for the problems they are interested in. The book is targeted at graduate students and researchers who plan to investigate multiphase flows using LBMs. Throughout the text most of the popular multiphase LBMs are analyzed both theoretically and through numerical simulation. The authors present many of the mathematical derivations of the models in greater detail than is currently found in the existing literature. The approach to understanding and classifying the various models is principally based on simulation compared against analytical and observational results and discovery of undesirable terms in the derived macroscopic equations and sometimes their correction. A repository of FORTRAN codes for multiphase LBM models is also provided.
Autorentext
Haibo Huang is an Associate Professor in the University of Science and Technology of China. He was a Courtesy Associate Professor during his stays at Florida International University.
Michael C. Sukop is Professor of Hydrogeology at Florida International University in Miami and author of "Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers". His research emphasis is on flow and transport in porous media.
Xiyun Lu is a Professor of Fluid Mechanics in the University of Science and Technology of China. His research interests mainly include computational fluid dynamics, turbulence simulation and biomechanics.
Zusammenfassung
Theory and Application of Multiphase Lattice Boltzmann Methods presents a comprehensive review of all popular multiphase Lattice Boltzmann Methods developed thus far and is aimed at researchers and practitioners within relevant Earth Science disciplines as well as Petroleum, Chemical, Mechanical and Geological Engineering. Clearly structured throughout, this book will be an invaluable reference on the current state of all popular multiphase Lattice Boltzmann Methods (LBMs). The advantages and disadvantages of each model are presented in an accessible manner to enable the reader to choose the model most suitable for the problems they are interested in. The book is targeted at graduate students and researchers who plan to investigate multiphase flows using LBMs.
Throughout the text most of the popular multiphase LBMs are analyzed both theoretically and through numerical simulation. The authors present many of the mathematical derivations of the models in greater detail than is currently found in the existing literature. The approach to understanding and classifying the various models is principally based on simulation compared against analytical and observational results and discovery of undesirable terms in the derived macroscopic equations and sometimes their correction. A repository of FORTRAN codes for multiphase LBM models is also provided.
Inhalt
Preface xi
About the companion website xiii
1 Introduction 1
1.1 History of the Lattice Boltzmann method 2
1.2 The Lattice Boltzmann method 3
1.3 Multiphase LBM 6
1.3.1 Color-gradient model 7
1.3.2 Shan-Chen model 7
1.3.3 Free-energy model 8
1.3.4 Interface tracking model 9
1.4 Comparison of models 9
1.5 Units in this book and parameter conversion 11
1.6 Appendix: Einstein summation convention 14
1.6.1 Kronecker d function 15
1.6.2 Lattice tensors 15
1.7 Use of the Fortran code in the book 16
2 Single-component multiphase Shan-Chen-type model 18
2.1 Introduction 18
2.1.1 "Equilibrium" velocity in the SC model 20
2.1.2 Inter-particle forces in the SC SCMP LBM 20
2.2 Typical equations of state 21
2.2.1 Parameters in EOS 27
2.3 Thermodynamic consistency 28
2.3.1 The SCMP LBM EOS 29
2.3.2 Incorporating other EOS into the SC model 31
2.4 Analytical surface tension 32
2.4.1 Inter-particle Force Model A 32
2.4.2 Inter-particle Force Model B 33
2.5 Contact angle 34
2.6 Capillary rise 36
2.7 Parallel flow and relative permeabilities 39
2.8 Forcing term in the SC model 40
2.8.1 Schemes to incorporate the body force 42
2.8.2 Scheme overview 44
2.8.3 Theoretical analysis 44
2.8.4 Numerical results and discussion 46
2.9 Multirange pseudopotential (Inter-particle Force Model B) 55
2.10 Conclusions 58
2.11 Appendix A: Analytical solution for layered multiphase flow in a channel 58
2.12 Appendix B: FORTRAN code to simulate single component multiphase droplet contacting a wall as shown in Figure 2.7(c) 60
3 Shan and Chen-type multi-component multiphase models 71
3.1 Multi-component multiphase SC LBM 71
3.1.1 Fluid-fluid cohesion and fluid-solid adhesion 73
3.2 Derivation of the pressure 73
3.2.1 Pressure in popular papers (2D) 74
3.2.2 Pressure in popular papers (3D) 75
3.3 Determining Gc and the surface tension 76
3.4 Contact angle 78
3.4.1 Application of Young's equation to MCMP LBM 79
3.4.2 Contact angle measurement 79
3.4.3 Verification of proposed equation 80
3.5 Flow through capillary tubes 83
3.6 Layered two-phase flow in a 2D channel 85
3.7 Pressure or velocity boundary conditions 87
3.7.1 Boundary conditions for 2D simulations 87
3.7.2 Boundary conditions for 3D simulations 89
3.8 Displacement in a 3D porous medium 91
4 Rothman-Keller multiphase Lattice Boltzmann model 94
4.1 Introduction 94
4.2 RK color-gradient model 96
4.3 Theoretical analysis (Chapman-Enskog expansion) 99
4.3.1 Discussion of above formulae 103
4.4 Layered two-phase flow in a 2D channel 103
4.4.1 Cases of two fluids with identical densities 104
4.4.2 Cases of two fluids with different densities 106
4.5 Interfacial tension and isotropy of the RK model 110
4.5.1 Interfacial tension 110
4.5.2 Isotropy 110
4.6 Drainage and capillary filling 111
4.7 MRT RK model 113
4.8 Contact angle 114
4.8.1 Spurious currents 115
4.9 Tests of inlet/outlet boundary conditions 117
4.10 Immiscible displacements in porous media 118
4.11 Appendix A 121
4.12 Appendix B 122
5 Free-energy-based multiphase Lattice Boltzmann model 136
5.1 Swift free-energy based single-component multiphase LBM 136
5.1.1 Derivation of the coefficients in the equilibrium distribution function 138
5.2 Chapman-Enskog expansion 143
5.3 Issue of Galilean invariance 146
5.4 Phase separation 149
5.5 Contact angle 154
5.5.1 How to specify a desired contact angle 154
5.5.2 Numerical verification 155
5.6 Swift free-energy-based multi-component multiphase LBM 158
5.7 Appendix 158
6 Inamuro's multiphase Lattice Boltzmann model 167
6.1 Introduction 167
6.1.1 Inamuro's method 167
6.1.2 Comment on the presentation 169
6.1.3 Chapman-Enskog expansion analysis 170
6.1.4 Cahn-Hilliard equation (equation for order parameter) 173
6.1.5 Poisson equation 174
6.2 Droplet collision 175
6.3 Appendix 178
7 He-Chen-Zhang multiphase Lattice Boltz…