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E-raamat: Multiphase Lattice Boltzmann Methods: Theory and Application

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(University of Science and Technology of China), (Florida International University), (University of Science and Technology of China)
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  • Ilmumisaeg: 11-Jun-2015
  • Kirjastus: Wiley-Blackwell
  • Keel: eng
  • ISBN-13: 9781118971345
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Multiphase Lattice Boltzmann Methods: Theory and ApplicationSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 11-Jun-2015
  • Kirjastus: Wiley-Blackwell
  • Keel: eng
  • ISBN-13: 9781118971345
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Multiphase Lattice Boltzmann Methods Theory and Application

Multiphase Lattice Boltzmann Methods: Theory and Application presents a comprehensive review of all popular multiphase Lattice Boltzmann Methods (LBMs) 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 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.
Preface xi
About the companion website xiii
1 Introduction
1(17)
1.1 History of the Lattice Boltzmann method
2(1)
1.2 The Lattice Boltzmann method
3(3)
1.3 Multiphase LBM
6(3)
1.3.1 Color-gradient model
7(1)
1.3.2 Shan--Chen model
7(1)
1.3.3 Free-energy model
8(1)
1.3.4 Interface tracking model
9(1)
1.4 Comparison of models
9(2)
1.5 Units in this book and parameter conversion
11(3)
1.6 Appendix: Einstein summation convention
14(2)
1.6.1 Kronecker δ function
15(1)
1.6.2 Lattice tensors
15(1)
1.7 Use of the Fortran code in the book
16(2)
2 Single-component multiphase Shan--Chen-type model
18(53)
2.1 Introduction
18(3)
2.1.1 "Equilibrium" velocity in the SC model
20(1)
2.1.2 Inter-particle forces in the SC SCMP LBM
20(1)
2.2 Typical equations of state
21(7)
2.2.1 Parameters in EOS
27(1)
2.3 Thermodynamic consistency
28(4)
2.3.1 The SCMP LBM EOS
29(2)
2.3.2 Incorporating other EOS into the SC model
31(1)
2.4 Analytical surface tension
32(2)
2.4.1 Inter-particle Force Model A
32(1)
2.4.2 Inter-particle Force Model B
33(1)
2.5 Contact angle
34(2)
2.6 Capillary rise
36(3)
2.7 Parallel How and relative permeabilities
39(1)
2.8 Forcing term in the SC model
40(15)
2.8.1 Schemes to incorporate the body force
42(2)
2.8.2 Scheme overview
44(1)
2.8.3 Theoretical analysis
44(2)
2.8.4 Numerical results and discussion
46(9)
2.9 Multirange pseudopotential (Inter-particle Force Model B)
55(3)
2.10 Conclusions
58(1)
2.11 Appendix A: Analytical solution for layered multiphase flow in a channel
58(2)
2.12 Appendix B: FORTRAN code to simulate single component multiphase droplet contacting a wall, as shown in Figure 2.7(c)
60(11)
3 Shan and Chen-type multi-component multiphase models
71(23)
3.1 Multi-component multiphase SC LBM
71(2)
3.1.1 Fluid-fluid cohesion and fluid-solid adhesion
73(1)
3.2 Derivation of the pressure
73(3)
3.2.1 Pressure in popular papers (2D)
74(1)
3.2.2 Pressure in popular papers (3D)
75(1)
3.3 Determining Gc and the surface tension
76(2)
3.4 Contact angle
78(5)
3.4.1 Application of Young's equation to MCMP LBM
79(1)
3.4.2 Contact angle measurement
79(1)
3.4.3 Verification of proposed equation
80(3)
3.5 Flow through capillary tubes
83(2)
3.6 Layered two-phase flow in a 2D channel
85(2)
3.7 Pressure or velocity boundary conditions
87(4)
3.7.1 Boundary conditions for 2D simulations
87(2)
3.7.2 Boundary conditions for 3D simulations
89(2)
3.8 Displacement in a 3D porous medium
91(3)
4 Rothman--Keller multiphase Lattice Boltzmann model
94(42)
4.1 Introduction
94(2)
4.2 RK color-gradient model
96(3)
4.3 Theoretical analysis (Chapman--Enskog expansion)
99(4)
4.3.1 Discussion of above formulae
103(1)
4.4 Layered two-phase flow in a 2D channel
103(7)
4.4.1 Cases of two fluids with identical densities
104(2)
4.4.2 Cases of two fluids with different densities
106(4)
4.5 Interfacial tension and isotropy of the RK model
110(1)
4.5.1 Interfacial tension
110(1)
4.5.2 Isotropy
110(1)
4.6 Drainage and capillary filling
111(2)
4.7 MRT RIC model
113(1)
4.8 Contact angle
114(3)
4.8.1 Spurious currents
115(2)
4.9 Tests of inlet/outlet boundary conditions
117(1)
4.10 Immiscible displacements in porous media
118(3)
4.11 Appendix A
121(1)
4.12 Appendix B
122(14)
5 Free-energy-based multiphase Lattice Boltzmann model
136(31)
5.1 Swill free-energy based single-component multiphase LBM
136(7)
5.1.1 Derivation of the coefficients in the equilibrium distribution function
138(5)
5.2 Chapman--Enskog expansion
143(3)
5.3 Issue of Galilean invariance
146(3)
5.4 Phase separation
149(5)
5.5 Contact angle
154(4)
5.5.1 How to specify a desired contact angle
154(1)
5.5.2 Numerical verification
155(3)
5.6 Swift free-energy-based multi-component multiphase LBM
158(1)
5.7 Appendix
158(9)
6 Inamuro's multiphase Lattice Boltzmann model
167(29)
6.1 Introduction
167(8)
6.1.1 Inamuro's method
167(2)
6.1.2 Comment on the presentation
169(1)
6.1.3 Chapman--Enskog expansion analysis
170(3)
6.1.4 Cahn--Hilliard equation (equation for order parameter)
173(1)
6.1.5 Poisson equation
174(1)
6.2 Droplet collision
175(3)
6.3 Appendix
178(18)
7 He--Chen--Zhang multiphase Lattice Boltzmann model
196(57)
7.1 Introduction
196(1)
7.2 HCZ model
196(3)
7.3 Chapman--Enskog analysis
199(3)
7.3.1 N--S equations
199(3)
7.3.2 CH equation
202(1)
7.4 Surface tension and phase separation
202(2)
7.5 Layered two-phase flow in a channel
204(1)
7.6 Rayleigh--Taylor instability
205(5)
7.7 Contact angle
210(3)
7.8 Capillary rise
213(2)
7.9 Geometric scheme to specify the contact angle and its hysteresis
215(4)
7.9.1 Examples of droplet slipping in shear flows
218(1)
7.10 Oscillation of an initially ellipsoidal droplet
219(3)
7.11 Appendix A
222(1)
7.12 Appendix B: 2D code
223(15)
7.13 Appendix C: 3D code
238(15)
8 Axisymmetric multiphase HCZ model
253(39)
8.1 Introduction
253(1)
8.2 Methods
253(5)
8.2.1 Macroscopic governing equations
253(2)
8.2.2 Axisymmetric HCZ LBM (Premnath and Abraham 2005a)
255(1)
8.2.3 MRT version of the axisymmetric LBM (McCracken and Abraham 2005)
256(2)
8.2.4 Axisymmetric boundary conditions
258(1)
8.3 The Laplace law
258(1)
8.4 Oscillation of an initially ellipsoidal droplet
259(4)
8.5 Cylindrical liquid column break
263(2)
8.6 Droplet collision
265(11)
8.6.1 Effect of gradient and Laplacian calculation
267(7)
8.6.2 Effect of BGK and MRT
274(2)
8.7 A revised axisymmetric HCZ model (Huang et al. 2014)
276(3)
8.7.1 MRT collision
276(1)
8.7.2 Calculation of the surface tension
277(1)
8.7.3 Mass correction
278(1)
8.8 Bubble rise
279(7)
8.8.1 Numerical validation
281(2)
8.8.2 Surface-tension calculation effect
283(1)
8.8.3 Terminal bubble shape
284(1)
8.8.4 Wake behind the bubble
284(2)
8.9 Conclusion
286(2)
8.10 Appendix A: Chapman--Enskog analysis
288(4)
8.10.1 Preparation for derivation
288(1)
8.10.2 Mass conservation
289(1)
8.10.3 Momentum conservation
289(2)
8.10.4 CH equation
291(1)
9 Extensions of the HCZ model for high-density ratio two-phase flows
292(42)
9.1 Introduction
292(1)
9.2 Model I (Lee and Lin 2005)
293(8)
9.2.1 Stress and potential form of intermolecular forcing terms
293(1)
9.2.2 Model description
294(3)
9.2.3 Implementation
297(1)
9.2.4 Directional derivative
298(1)
9.2.5 Droplet splashing on a thin liquid film
299(2)
9.3 Model II (Amaya-Bower and Lee 2010)
301(3)
9.3.1 Implementation
302(2)
9.4 Model III (Lee and Liu 2010)
304(1)
9.5 Model IV
305(1)
9.6 Numerical tests for different models
306(10)
9.6.1 A drop inside a box with periodic boundary conditions
306(5)
9.6.2 Layered two-phase flows in a channel
311(2)
9.6.3 Galilean invariance
313(3)
9.7 Conclusions
316(1)
9.8 Appendix A: Analytical solutions for layered two-phase flow in a channel
317(2)
9.9 Appendix B: 2D code based on Amaya-Bower and Lee (2010)
319(15)
10 Axisymmetric high-density ratio two-phase LBMs (extension of the HCZ model)
334(25)
10.1 Introduction
334(1)
10.2 The model based on Lee and Lin (2005)
334(11)
10.2.1 The equilibrium distribution functions I
336(1)
10.2.2 The equilibrium distribution functions II
336(1)
10.2.3 Source terms
337(1)
10.2.4 Stress and potential form of intermolecular forcing terms
337(1)
10.2.5 Chapman--Enskog analysis
338(2)
10.2.6 Implementation
340(2)
10.2.7 Droplet splashing on a thin liquid film
342(1)
10.2.8 Head-on droplet collision
342(3)
10.3 Axisymmetric model based on Lee and Liu (2010)
345(14)
10.3.1 Implementation
347(1)
10.3.2 Head-on droplet collision
348(5)
10.3.3 Bubble rise
353(6)
References 359(12)
Index 371
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.
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