An Introduction to the Lattice Boltzmann Method: A Numerical Method for Complex Boundary and Moving Boundary Flows

✍ Scribed by Takaji Inamuro, Masato Yoshino, Kosuke Suzuki

• Publisher: World Scientific Publishing
• Year: 2021
• Tongue: English
• Leaves: 166
• Category: Library

✦ Synopsis

The book introduces the fundamentals and applications of the lattice Boltzmann method (LBM) for incompressible viscous flows. It is written clearly and easy to understand for graduate students and researchers. The book is organized as follows. In Chapter 1, the SRT- and MRT-LBM schemes are derived from the discrete Boltzmann equation for lattice gases and the relation between the LBM and the Navier-Stokes equation is explained by using the asymptotic expansion (not the Chapman-Enskog expansion). Chapter 2 presents the lattice kinetic scheme (LKS) which is an extension method of the LBM and can save memory because of needlessness for storing the velocity distribution functions. In addition, an improved LKS which can stably simulate high Reynolds number flows is presented. In Chapter 3, the LBM combined with the immersed boundary method (IB-LBM) is presented. The IB-LBM is well suitable for moving boundary flows. In Chapter 4, the two-phase LBM is explained from the point of view of the difficulty in computing two-phase flows with large density ratio. Then, a two-phase LBM for large density ratios is presented. In Appendix, sample codes (available for download) are given for users.

✦ Table of Contents

Contents
Preface
1. Lattice Boltzmann Method (LBM)
1.1 Lattice Gas Model
1.2 Basic Equation
1.3 Formulation of the Collision Term
1.4 Local Equilibrium Distribution Function
1.5 Derivation of the Fluid Dynamic Equations
1.6 LBM with an External Force Term
1.7 Incompressible Local Equilibrium Distribution Function
1.8 Flow with Heat Transfer
1.9 Equation of an Acoustic Field
1.10 LBM-derived Method
1.11 Boundary Condition
1.12 Computational Algorithm of LBM
1.13 Numerical Examples
1.13.1 Flows in a porous structure
1.13.2 Rayleigh–Bénard convection
2. Lattice Kinetic Scheme
2.1 LKS
2.2 LWACM
2.3 Improved LKS
2.4 Bulk Viscosity Coefficient
2.5 Boundary Condition
2.6 Computational Algorithm of Improved LKS
2.7 Numerical Examples
2.7.1 Natural convection ows in a square cavity
2.7.2 Taylor–Green vortex
2.8 Comparison between Improved LKS and MRT-LBM
3. Immersed Boundary–Lattice Boltzmann Method (IB-LBM)
3.1 LBM-based Methods for Moving Boundary Flows
3.2 Idea of IBM
3.3 LBM with an External Forcing Term (Fractional-Step Method)
3.4 Formulation of the IBM
3.5 Force and Torque Acting on a Moving Object
3.6 Motion of the Boundary Lagrangian Points
3.7 Computational Algorithm of IB-LBM
3.8 Thermal Immersed Boundary–Lattice Boltzmann Method (Thermal IB-LBM)
3.9 Multi-block Grid Method
3.10 Numerical Examples
3.10.1 Sedimentation of an elliptical cylinder
3.10.2 Sedimentation of a cold circular cylinder in a hot channel with natural convection
3.10.3 Forward ight of a buttery
3.10.4 Sharp-turn ight of a dragony
4. Two-Phase Lattice Boltzmann Method (Two-Phase LBM)
4.1 Classication of Two-Phase LBM
4.2 Free-Energy Model
4.3 Computation of ϕ by LKS
4.4 Wettability on the Body Surface (Boundary Condition for ϕ)
4.5 Two-Phase LBM for Equal Density
4.6 Pressure Computation at Large Density Ratio
4.7 Two-Phase LBM for Large Density Ratios
4.8 Computational Algorithm of Two-Phase LBM for Large Density Ratios
4.9 Two-Phase LBM for Large Density Ratios (Method in 2004)
4.10 Numerical Examples
4.10.1 Droplet deformation and breakup in shear flows
4.10.2 Layered Poiseuille ow
4.10.3 Droplet collision
4.10.4 Milk crown
Appendix A Definitions of Dimensionless Variables
Appendix B D3Q19 and D3Q27 Models
Appendix C LBM with the MRT Model (MRT-LBM)
C.1 Formulation
C.2 Asymptotic Analysis (S-Expansion)
Appendix D Summation Formulae of Particle Velocities ci
Appendix E Lattice Units
Appendix F Program Examples
F.1 Flow Past a Circular Cylinder
F.2 Stationary Droplet
Afterword
Bibliography
Index