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E-grāmata: Lattice Boltzmann And Gas Kinetic Flux Solvers: Theory And Applications

(Nus, S'pore), (Nus, S'pore), (Nus, S'pore), (Nanjing Univ Of Aeronautics And Astronautics, China)
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Lattice Boltzmann And Gas Kinetic Flux Solvers: Theory And ApplicationsPalielināt
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Computational fluid dynamics (CFD) has been widely applied in a wide variety of industrial applications, including aeronautics, astronautics, energy, chemical, pharmaceuticals, power and petroleum. This unique compendium documents the recent developments in CFD based on kinetic theories, introducing flux reconstruction strategies of kinetic methods for the simulation of complex incompressible and compressible flows, namely the lattice Boltzmann and the gas kinetic flux solvers (LBFS or GKFS). LBFS and GKFS combine advantages of both Navier-Stokes (N-S) solvers and kinetic solvers. Detailed derivations, evaluations and applications of LBFS and GKFS, and their advantages over conventional flux reconstruction strategies are analyzed and discussed in the volume. The must-have reference text is useful for scholars, researchers, professionals and students who are keen in CFD methods and numerical simulations.

Dedication v
Preface vii
Contents ix
List of Tables
xiii
List of Figures
xv
Chapter 1 Introduction
1(44)
1.1 Conservation Laws
2(1)
1.2 Governing Equations of Fluid Dynamics
2(4)
1.3 Finite Volume Discretization of Governing Equations
6(5)
1.4 Mathematical Reconstructions of Numerical Fluxes on Cell Interface in Finite Volume Discretization
11(4)
1.4.1 Mathematical reconstruction of inviscid fluxes
11(2)
1.4.2 Mathematical reconstruction of viscous fluxes
13(2)
1.5 Physical Reconstruction of Numerical Fluxes on Cell Interface in Finite Volume Discretization
15(27)
1.5.1 Upwind schemes
15(2)
1.5.2 Flux-vector splitting schemes
17(5)
1.5.3 Riemann solvers
22(20)
1.6 Motivation to Develop Lattice Boltzmann and Gas Kinetic Flux Solvers
42(3)
Chapter 2 Kinetic Equations
45(33)
2.1 Kinetic Theory
45(2)
2.2 BGK-Boltzmann Equation and Maxwellian Distribution Function
47(12)
2.2.1 Continuous Boltzmann equation
47(2)
2.2.2 Maxwellian distribution function and BGK collision model
49(3)
2.2.3 Chapman-Enskog expansion analysis
52(7)
2.3 Discrete Velocity Boltzmann Equation and Its Solution
59(6)
2.3.1 From continuous Boltzmann equation to DVBE
59(3)
2.3.2 Finite volume solution of DVBE
62(2)
2.3.3 Advantages and limitations of DVBE solver
64(1)
2.4 Lattice Boltzmann Equation and Lattice Boltzmann Method
65(11)
2.4.1 From DVBE to lattice Boltzmann equation
65(2)
2.4.2 Lattice Boltzmann models
67(2)
2.4.3 Chapman-Enskog expansion analysis
69(4)
2.4.4 Advantages and limitations of LBM
73(3)
2.5 Summary
76(2)
Chapter 3 Lattice Boltzmann Flux Solver for Isothermal and Thermal Flows
78(38)
3.1 Macroscopic Governing Equations
79(1)
3.2 Lattice Boltzmann Flux Solver for Isothermal Flows
80(12)
3.2.1 Governing equations for isothermal LBFS
82(2)
3.2.2 Numerical algorithms of isothermal LBFS
84(8)
3.3 Lattice Boltzmann Flux Solver for Thermal Flows
92(6)
3.3.1 Governing equation for thermal LBFS
93(2)
3.3.2 Numerical algorithms of thermal LBFS
95(3)
3.4 Sample Applications
98(15)
3.4.1 Accuracy and efficiency test
98(4)
3.4.2 Some two-dimensional applications
102(7)
3.4.3 Some three-dimensional applications
109(4)
3.5 Summary
113(3)
Chapter 4 Multiphase Lattice Boltzmann Flux Solver for Two-Phase Flows
116(37)
4.1 Macroscopic Governing Equations
117(1)
4.2 MLBFS for Flow Field
118(16)
4.2.1 Multiphase lattice Boltzmann model and Chapman-Enskog expansion analysis
118(6)
4.2.2 Original MLBFS
124(4)
4.2.3 Analysis of flux reconstruction by the original MLBFS -
128(4)
4.2.4 Improved MLBFS
132(2)
4.3 Solution of Cahn-Hilliard Equation
134(4)
4.4 Sample Applications
138(14)
4.4.1 Some two-dimensional applications
139(6)
4.4.2 Some three-dimensional applications
145(7)
4.5 Summary
152(1)
Chapter 5 Maxwellian Function-Based Gas Kinetic Flux Solver
153(32)
5.1 BGK-Boltzmann Equation, Navier-Stokes Equations and Their Connection
154(5)
5.2 Maxwellian Function-Based GKS
159(11)
5.2.1 Local integral solution to Boltzmann equation on the cell interface
160(6)
5.2.2 Evaluation of fluxes on the cell interface by M-GKS
166(4)
5.3 Maxwellian Function-Based GKFS
170(9)
5.3.1 Local asymptotic solution to Boltzmann equation on the cell interface
170(6)
5.3.2 Evaluation of fluxes on the cell interface by M-GKFS
176(3)
5.4 Sample Applications
179(5)
5.4.1 Couetteflow
179(1)
5.4.2 Hypersonic flow around a circular cylinder
180(2)
5.4.3 DLR-F6 wing-body configuration
182(2)
5.5 Summary
184(1)
Chapter 6 Simplified Distribution Function-Based Gas Kinetic Flux Solvers
185(61)
6.1 From Maxwellian Function to Circular and Sphere Functions
186(16)
6.1.1 Two-dimensional simplified distribution: circular function
190(3)
6.1.2 Three-dimensional simplified distribution: sphere function
193(3)
6.1.3 Chapman-Enskog expansion analysis to recover Euler/Navier-Stokes equations
196(6)
6.2 Circular Function-Based GKFS for Inviscid Flows
202(10)
6.3 Sphere Function-Based GKFS for Inviscid Flows
212(8)
6.4 D1Q4 Model-Based LBFS for Inviscid Flows
220(5)
6.5 Circular Function-Based GKFS for Viscous Flows
225(13)
6.6 Sample Applications
238(8)
6.6.1 Two-dimensional inviscid flow
241(3)
6.6.2 Three-dimensional inviscid flow
244(1)
6.6.3 Two-dimensional viscous flow
244(2)
677 Summary
246(2)
Chapter 7 Discrete Gas Kinetic Flux Solvers
248(30)
7.1 Moment Relationships and Their Discretization Forms
248(10)
7.1.1 Two-dimensional discrete velocity model
249(5)
7.1.2 Three-dimensional discrete velocity model
254(4)
7.2 Circular Function-Based DGKFS
258(6)
7.3 Sphere Function-Based DGKFS
264(6)
7.4 Sample Applications
270(6)
7.4.1 Two-dimensional viscous incompressible flow
271(1)
7.4.2 Two-dimensional viscous compressible flow
272(3)
7.4.3 Three-dimensional viscous compressible flow
275(1)
7.5 Summary
276(2)
Chapter 8 Gas Kinetic Flux Solvers for Incompressible Flows
278(43)
8.1 Governing Equations and FVM Discretization
279(3)
8.2 Maxwellian Function-Based IGKS
282(9)
8.2.1 Moment relationships of Maxwellian function
282(5)
8.2.2 Evaluation of fluxes on the cell interface by M-IGKS
287(4)
8.3 Circular Function-Based IGKFS
291(8)
8.3.1 Moment relationships of circular function
291(2)
8.3.2 Evaluation of fluxes on the cell interface by C-IGKFS
293(6)
8.4 Sphere Function-Based IGKFS
299(10)
8.4.1 Moment relationships of sphere function
300(1)
8.4.2 Evaluation of fluxes on the cell interface by S-IGKFS
301(8)
8.5 Sample Applications
309(9)
8.5.1 Two-dimensional decaying vortex flow
311(1)
8.5.2 Two-dimensional lid-driven cavity flow
312(2)
8.5.3 Two-dimensional flow over a circular cylinder
314(2)
8.5.4 Three-dimensional flow over a backward-facing step
316(2)
8.6 Summary
318(3)
Appendix A Recurrence Relationships for Moment Integration 321(3)
Appendix B Coefficients for the M-GKS 324(3)
Appendix C Coefficients for the M-IGKS 327(2)
Appendix D Description of Attached Computer Codes 329(6)
Appendix E Supplementary Material 335(2)
Bibliography 337(18)
Index 355
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