Large-Eddy Simulation Based on the Lattice Boltzmann Method for Built Environment Problems

Preface
Acknowledgments
Contents
Nomenclature, Symbols, and Abbreviations
	Greek Symbols
	Superscript
	Subscript
	Acronyms, Abbreviations
	Symbols, Operators
Part I Fundamental Theory and Implementation of the Lattice Boltzmann Method
1 Introduction
	1.1 Introduction
	1.2 Review of Navier–Stokes Equations (NSE)-Based Computational Fluid Dynamics (CFD) in the Built Environment
		1.2.1 Continuity Assumption of Fluid
		1.2.2 Governing Equations
		1.2.3 Important Physical Quantities in CFD
		1.2.4 Dimensional Analysis and Dimensionless Form of the NSE
		1.2.5 Similarity
		1.2.6 NSE-Based CFD Simulation Methods
	1.3 Development of the Lattice Boltzmann Method (LBM)
		1.3.1 Lattice Gas Automata (LGA)
		1.3.2 From LGA to LBM
		1.3.3 LBM Development
		1.3.4 LBM Application in the Built Environment
	1.4 Purpose and Outline of This Book
	References
2 Fundamental Theory of the Lattice Boltzmann Method
	2.1 Introduction
	2.2 Fluid From a Mesoscopic Perspective
		2.2.1 Distribution Functions
		2.2.2 Equilibrium Distributions and Maxwell–Boltzmann Distributions
	2.3 Lattice Boltzmann Equation (LBE)
		2.3.1 Stream and Collision
		2.3.2 LBE
	2.4 Discrete Velocity Scheme
		2.4.1 Discrete Velocity and DdQq Schemes
		2.4.2 D2Q9 Scheme for 2D Problems
		2.4.3 D3Q19 and D3Q27 Schemes for 3D Problems
		2.4.4 Equilibrium Distribution Function in the DdQq Scheme
	2.5 Collision Function: Relaxation Time Scheme
		2.5.1 Moment
		2.5.2 Single-Relaxation Time (SRT) Scheme and the BGK Model
		2.5.3 Multi-Relaxation Time (MRT) Scheme
		2.5.4 Two-Relaxation Time (TRT) Scheme
		2.5.5 Other Advanced Collision Function Schemes
	2.6 Summary
	References
3 Implementation of the Boundary Conditions
	3.1 Introduction
	3.2 First-Type BC: The Dirichlet BC
	3.3 Second-Type BC: The Neumann BC
	3.4 Periodic BC
	3.5 Symmetric BC
	3.6 Free-Slip BC
	3.7 Straight Solid-Wall BC: The Bounce-Back Model
		3.7.1 Fullway Bounce-Back
		3.7.2 Halfway Bounce-Back
		3.7.3 Fullway Versus Halfway Bounce-Back
	3.8 Bounce-Back Improvement: The Wall-Function Bounce (WFB) Model
		3.8.1 WFB Framework
		3.8.2 Shear Drag τw Calculation: Spalding’s Law
	3.9 Bounce-Back for Curved-Wall BC: The Bouzidi-Firdaouss-Lallemand (BFL) Scheme
	3.10 Extrapolation Method for Curved-Wall BC: The Guo Scheme
	3.11 Other Solid-Wall BCs
	3.12 Summary
	References
4 From the Lattice Boltzmann Equation to Fluid Governing Equations
	4.1 Introduction
	4.2 Taylor Expansion of the LBE
	4.3 Chapman-Enskog Multi-scale Analysis
	4.4 From Mesoscopic Temporal-Spatial Scale to Macroscopic Scale
	4.5 Definition of Macroscopic Quantities and the Equilibrium Distribution Function
	4.6 Derivation of the Continuity Equation (Mass Conservation)
	4.7 Derivation of the NSE (Momentum Conservation)
	4.8 Detailed Mathematical Operations in the Derivation Process
		4.8.1 Derivation of (4.21)
		4.8.2 Derivation of (4.41)–(4.44)
		4.8.3 Derivation of (4.22)
	4.9 Summary
	References
5 Turbulence Models and LBM-Based Large-Eddy Simulation (LBM-LES)
	5.1 Introduction
	5.2 LES Implementation
		5.2.1 LES for the NSE-Based Method
		5.2.2 LES for LBM
	5.3 Smagorinsky SGS Model and Its Development
		5.3.1 Smagorinsky-Lilly SGS Model
		5.3.2 Dynamic Smagorinsky SGS Model (DSM)
	5.4 Advanced SGS Models in LBM-LES for Built Environment Simulations
		5.4.1 Wall-Adapting Local Eddy-Viscosity (WALE) SGS Model
		5.4.2 Coherent Structure SGS Model (CSM)
	5.5 LBM-LES Workflow
	References
6 From LBE to LBM: Using the LBM to Solve Built Environment Problems
	6.1 Introduction
	6.2 Discretization and Normalization
		6.2.1 Spatial Discretization
		6.2.2 Temporal Discretization
		6.2.3 Normalization of Physical Quantities
	6.3 LBM Simulation Workflow
	6.4 Common User-Induced Simulation Errors in the LBM
		6.4.1 Grid Discretization Errors
		6.4.2 Compressibility Errors
		6.4.3 Over-Relaxation and Numerical Oscillations
	6.5 Summary
	References
Part II Practice of LBM-LES in Built Environment
7 LBM-LES in Ideal 3D Lid-Driven Cavity Flow Problems
	7.1 Introduction
	7.2 Description of the Ideal 3D Lid-Driven Cavity Flow
	7.3 Simulation Methodology and Boundary Conditions
	7.4 Results and Discussion
		7.4.1 Instantaneous and Time-Averaged Velocities
		7.4.2 Comparison Between LBM-LES and FVM-LES
		7.4.3 Comparison Between Vortex Structures
	7.5 Discussion on Computational Time and Parallel Computational Efficiency
	7.6 Summary
	References
8 LBM-LES in an Isothermal Indoor Flow Problem
	8.1 Introduction
	8.2 Isothermal Indoor Flow Problem Description
	8.3 Simulation Methodology and Boundary Conditions
		8.3.1 Simulation Conditions
		8.3.2 Parameters to Discuss
	8.4 Results and Discussion
		8.4.1 Instantaneous and Time-Averaged Scalar Velocities
		8.4.2 Effects According to Grid Resolution
		8.4.3 Effects According to Relaxation Time and Discrete Velocity Scheme
		8.4.4 Effects According to the Discrete Time Interval
		8.4.5 Discussion on Compressibility Errors
		8.4.6 Discussion on Oscillations Caused by Over-Relaxation
	8.5 Comparison Between LBM-LES and FVM-LES
	8.6 Discussion on Computational Performance
		8.6.1 Computational Time
		8.6.2 Parallel Computational Performance
	8.7 Summary
	References
9 LBM-LES in the Outdoor Wind Environment Problem Around a Single Building
	9.1 Introduction to the Outdoor Wind Environment Problem
	9.2 Problem Description of Flow Around a Single Building
		9.2.1 Simulation Target
		9.2.2 Wind Tunnel Experiment
	9.3 Simulation Methodology and Boundary Conditions
		9.3.1 Simulation Conditions and Parameter Settings
		9.3.2 Inlet Boundary Data and Approaching Flow
		9.3.3 Sampling Time Convergence Criteria
		9.3.4 Simulation Accuracy Evaluation Index
	9.4 Results and Discussion
		9.4.1 Instantaneous Velocity
		9.4.2 Time-Averaged Velocity and Flow Structure
		9.4.3 Effect According to Grid Resolution
		9.4.4 Effect According to SGS Model
		9.4.5 Effect According to the Relaxation Time and Discrete Velocity Schemes
		9.4.6 Effect According to the Solid Wall Boundary Condition
	9.5 Comparison Between LBM-LES with FVM-LES in Terms of Predicted Accuracy
	9.6 Discussion on Computational Time and Efficiency
		9.6.1 Computational Time
		9.6.2 Discussion on CTR and PCE
	9.7 Summary
	References
Index