Computational Fluid Dynamics : Finite Difference Method and Lattice Boltzmann Method

• Autore: Hou Guoxiang
• Pubblicazione: Singapore : , : Springer Singapore Pte. Limited, , 2024; ©2024
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (265 pages)
• Altri autori: ChenCaikan QinShenglei GaoYuan WangKai
• Nota di contenuto: Intro -- Preface -- Contents -- About the Authors -- Part I Finite Difference Method -- 1 Difference Scheme -- 1.1 Taylor Series Expansion -- 1.2 Method of Polynomial Interpolation -- 1.3 Being-Determined Coefficient Method -- 1.4 Integral Methods -- 1.5 Method of Characteristics -- 1.6 Control Volume Method -- 1.7 Difference Operators -- 2 The Compatibility, Convergence, and Stability of Difference Schemes -- 2.1 Theoretical Basis of Finite Difference Methods -- 2.2 Compatibility and Truncation Error of Difference Scheme -- 2.3 Convergence and Discretization Errors -- 2.4 Stability and Round-Off Error -- 2.5 Von-neumann Method -- 2.6 A New Method to Get a Transition Matrix from Difference Operator Transformation -- 2.7 Further Discussion of Lax Equivalence Theorem, Convergence, and Stability -- 2.8 Other Methods for Stability Analysis -- References -- 3 Common Difference Schemes for Several Model Equations -- 3.1 Convection Equation -- 3.2 Diffusion Equation -- 3.3 Convection Diffusion Equation -- 4 Difference Schemes for Multi-dimensional Problems -- 4.1 Explicit and Implicit Schemes for Multi-dimensional Problems -- 4.2 Alternating Direction Method -- 4.3 Operator-Splitting Method -- 4.4 Predictor-Corrector Scheme -- 5 Variable Coefficients and Nonlinear Problems -- 5.1 Linear Partial Differential Equation with Variable Coefficients -- 5.2 Nonlinear Partial Differential Equations -- 5.3 Conservative Difference Scheme -- 6 Initial Boundary Value Problems -- 6.1 Initial Boundary Problem of Advection Equation -- 6.2 Initial Boundary Problem of Diffusion Equation -- 6.3 Illustrations of Boundary Conditions in Hydrodynamics Problems -- 6.4 Time-Independent Boundary Value Problem and Time-Dependent Method -- 7 Numerical Effect -- 7.1 Approximate Property of Difference Quotient Approaching to Differential Quotient. ; 7.2 Physical Dissipation and Dispersion -- 7.3 Numerical Dissipation and Dispersion -- 7.4 Numerical Oscillation Effect -- 8 Applications of Finite Difference Methods in Fluid Mechanics -- 8.1 Stream Function-Vorticity Method -- 8.2 Velocity-Pressure Method -- 8.3 Difference Method of Boundary Layer Problem -- References -- Part II Numerical Methods and Applications in LB Community -- 9 Fundamentals of Lattice Boltzmann Method -- 9.1 Hydrodynamics with Motion Description Approaches -- 9.1.1 Macroscopic Description: Hydrodynamic Equations -- 9.1.2 Microscopic Description: Molecular Dynamics -- 9.1.3 Mesoscopic Description: Kinetic Theory -- 9.2 History of LBE -- 9.2.1 Two-Dimensional Lattice Gas Model (LGM) of Fluid Flows -- 9.2.2 From LGA to LBE -- 9.2.3 From Continuous Boltzmann Equation to LBE -- 9.3 Basic Models of LBE -- 9.3.1 BGK Models -- 9.4 Initial and Boundary Conditions for Lattice Boltzmann Method -- 9.4.1 Initial Conditions -- 9.4.2 Boundary Conditions -- References -- 10 Studying Drag Reduction of Square Cylinder Based on the LBM -- 10.1 Introduction -- 10.2 Numerical Method -- 10.3 Results and Discussion -- 10.3.1 Flow Past a Single Square Cylinder with Slip Boundary -- 10.3.2 Flow Past a Single Oblique Cylinder with Slip Boundary -- 10.3.3 Flow Past Side-By-Side Cylinders with Slip Boundary -- 10.4 Summary -- References -- 11 Coupled Simplified Lattice Boltzmann Method Study on Thermal Flows -- 11.1 Introduction of Mixed Convection and the Simplified Lattice Boltzmann Method -- 11.2 Basic Equations of the Numerical Methods -- 11.2.1 Physical Configuration and the Governing Equations -- 11.2.2 Standard Lattice Boltzmann Method -- 11.2.3 Coupled Simplified Lattice Boltzmann Method -- 11.2.4 Algorithm Validation -- 11.3 Convergence Analysis and Grid Independence Test. ; 11.4 Mixing Influence of Vertical Temperature Gradients with Different Heated Lengths -- 11.5 Conclusion -- References -- 12 One-Step Simplified Lattice Boltzmann Method and Its Application to Multiphase Flow -- 12.1 Introduction of the One-Step Simplified Lattice Boltzmann Method -- 12.2 Basic Mathematical Equations of the NOSLBM in Simulating Multiphase Flows -- 12.2.1 The Original LB Model -- 12.2.2 The One-Step Simplified Lattice Boltzmann Method -- 12.3 Numerical Examples -- 12.3.1 Spinodal Decomposition -- 12.3.2 Bubble Rising -- 12.3.3 Droplet Splashing on a Thin Film -- 12.4 Summary -- References -- 13 A Simplified Lattice Boltzmann Flux Solver of Multiphase Flows -- 13.1 Introduction of the Simplified Lattice Boltzmann Flux Solver of Multiphase Flows -- 13.2 Numerical Method -- 13.2.1 The Model of the Lattice Boltzmann Flux Solver of the Multiphase Flows -- 13.2.2 The Simplified Lattice Boltzmann Flux Solver of the Multiphase Flows -- 13.3 Numerical Examples -- 13.3.1 Laplace Law -- 13.3.2 Rayleigh-Taylor Instability -- 13.4 Summary -- References -- 14 Assessment and Validation of No-slip Boundary Conditions for the Discrete Unified Gas Kinetic Scheme -- 14.1 Introduction of No-slip Boundary Conditions for the DUGKS -- 14.2 Mathematical Equations of DUGKS -- 14.2.1 DUGKS with a Force Term -- 14.2.2 Original Schemes of No-slip Boundary Conditions -- 14.2.3 New Schemes of No-slip Boundary Conditions -- 14.2.4 Analysis of Numerical Errors of New Schemes -- 14.3 Numerical Examples -- 14.3.1 The Couette Flow -- 14.3.2 The Lid-Driven Cavity Flow -- 14.3.3 The Poiseuille Flow -- 14.3.4 Normal Dipole-Wall Collision -- 14.4 Summary -- References.
• Titolo autorizzato: Computational Fluid Dynamics
• ISBN: 981-9703-49-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910855397403321
• Lo trovi qui: Univ. Federico II
• Serie: Engineering Applications of Computational Methods Series