This unique professional volume is about the recent advances in the lattice Boltzmann method (LBM). It introduces a new methodology, namely the simplified and highly stable lattice Boltzmann method (SHSLBM), for constructing numerical schemes within the lattice Boltzmann framework. Through rigorous mathematical derivations and abundant numerical validations, the SHSLBM is found to outperform the conventional LBM in terms of memory cost, boundary treatment and numerical stability. This must-have title provides every necessary detail of the SHSLBM and sample codes for implementation. It is a useful handbook for scholars, researchers, professionals and students who are keen to learn, employ and further develop this novel numerical method.
Author(s): Zhen Chen, Chang Shu
Series: Advances in Computational Fluid Dynamics, 5
Publisher: World Scientific Publishing
Year: 2020
Language: English
Pages: 274
City: Singapore
Contents
Dedication
Preface
Contents
List of Tables
List of Figures
Chapter 1 Introduction
1.1 Fluid mechanics: physical laws and mathematical models
1.2 The kinetic theory and the Boltzmann equation
1.3 From the Boltzmann equation to the lattice Boltzmann equation
1.4 Lattice Boltzmann models
1.5 From lattice Boltzmann equation to Navier-Stokes equations: Chapman-Enskog expansion analysis
1.6 Boundary treatments in lattice Boltzmann method
1.6.1 Heuristic schemes
1.6.2 Hydrodynamic schemes
1.6.3 Extrapolation schemes
1.7 Computational sequence of lattice Boltzmann method
1.8 Advantages and limitations of lattice Boltzmann method
1.9 Motivations of developing simplified and highly stable lattice Boltzmann method (SHSLBM)
Chapter 2 Simplified and Highly Stable Lattice Boltzmann Method
2.1 Principles of SHSLBM
2.2 Recalling key relationships in Chapman-Enskog analysis
2.3 Reconstruction of the non-equilibrium distribution function
2.4 Derivations of SHSLBM
2.5 Formulations of SHSLBM
2.6 Initial and boundary conditions
2.7 Implementation of SHSLBM on non-uniform meshes
2.8 Summary
Chapter 3 Analysis on Simplified and Highly Stable Lattice Boltzmann Method
3.1 Accuracy
3.2 Stability analysis
3.3 Memory cost
3.4 Efficiency
3.5 Sample application: 2D lid-driven cavity flow
3.5.1 Physical configuration
3.5.2 Program implementation
3.5.3 Numerical results
3.6 Summary
Chapter 4 Simplified Lattice Boltzmann Method for Non-Newtonian and Thermal Flows
4.1 Simplified lattice Boltzmann method for power-law fluid flows
4.1.1 Power-law fluid and lattice Boltzmann models for non-Newtonian fluid flows
4.1.2 Formulations of the simplified lattice Boltzmann method for power-law fluid flows
4.1.3 Truncated power-law model
4.1.4 Sample applications
4.2 Simplified and highly stable thermal lattice Boltzmann method
4.2.1 Double-distribution-function thermal lattice Boltzmann method
4.2.2 Chapman-Enskog expansion analysis of DDF thermal lattice Boltzmann method
4.2.3 Formulations of SHSTLBM
4.2.4 Stability analysis
4.2.5 Sample applications
4.3 Summary
Chapter 5 Immersed Boundary – Simplified Lattice Boltzmann Method for Moving Boundary Problems
5.1 Immersed boundary method
5.2 Predictor step: SHSLBM for intermediate flow variables
5.3 Corrector step: IBM for velocity and temperature corrections
5.3.1 Velocity correction
5.3.2 Temperature correction
5.4 Evaluation of forces and thermal parameters
5.5 Implementation procedures
5.6 Sample applications
5.6.1 Flow past a uniformly accelerated plate
5.6.2 Flow past a flapping foil
5.6.3 Natural convection between an inner sphere and a cubic enclosure
5.7 Summary
Chapter 6 Simplified Axisymmetric Lattice Boltzmann Method
6.1 Kinetic theory based axisymmetric lattice Boltzmann method
6.2 Chapman-Enskog expansion analysis
6.3 Simplified axisymmetric lattice Boltzmann method (SALBM)
6.3.1 Solution reconstruction
6.3.2 Formulations of SALBM
6.3.3 Computational sequence
6.4 Sample applications to axisymmetric swirling and rotating flows
6.4.1 Hagen-Poiseuille flow
6.4.2 Unsteady Womersley flow
6.4.3 Cylindrical cavity flow
6.5 Summary
Chapter 7 Simplified Multiphase Lattice Boltzmann Method
7.1 Multiphase flows and simulation strategies
7.2 Multiphase lattice Boltzmann method as the flow solver
7.3 Cahn-Hilliard equation within the lattice Boltzmann framework
7.4 Chapman-Enskog expansion analysis
7.5 Simplified multiphase lattice Boltzmann method
7.5.1 Reconstruction of flow variables
7.5.2 Reconstruction of the order parameter
7.5.3 Formulations of SMLBM
7.5.4 Implementation of boundary conditions
7.5.5 Computational sequence
7.6 Sample applications to multiphase flows with high density ratios
7.6.1 Laplace law
7.6.2 Bubble rising
7.6.3 Droplet splashing on a thin film
7.7 Summary
Chapter 8 Highly Accurate Simplified Lattice Boltzmann Method for Incompressible Flows
8.1 Amending SHSLBM towards higher order of accuracy
8.2 Highly accurate simplified lattice Boltzmann method
8.2.1 High-order interpolation
8.2.2 Formulations of HSLBM
8.2.3 Implementation of boundary conditions
8.3 Validation and optimization
8.3.1 Validation of spatial accuracy
8.3.2 Parametric optimization: isothermal case
8.3.3 Parametric optimization: thermal case
8.3.4 Validation of temporal accuracy
8.3.5 Stability and mass/energy conservation
8.4 Sample applications
8.4.1 Two-dimensional lid-driven cavity flow
8.4.2 Three-dimensional natural convection in a cubic cavity
8.5 Summary
Appendix A Description of Sample Codes
A.1 Sample Code of the SHSLBM for 2D Lid-driven Cavity Flow
A.2 Sample Code of the SHSTLBM for 2D Natural Convection in A Square Cavity
A.3 Sample Code of the IB-SLBM for Flow Past A Uniformly Accelerated Plate
A.4 Sample Code of the SMLBM for Laplace Law
A.5 Sample Code of the HSLBM for Taylor-Green Vortex Flow
Bibliography
Index
