Next:
List of Figures
Up:
No Title
Previous:
Acknowledgements
Contents
List of Figures
List of Tables
Introduction
The Study of Fluid Motion
Numerical Methods in Fluid Study
Numerical Solutions of the Navier-Stokes Equation
Molecular Dynamics
Lattice Gas Modelling
Lattice Boltzmann Models
Wave Modelling
Aims
Notation
Preview
The Boltzmann Equation
The Classical Boltzmann Equation
The Conservation Equations
The Collision Function
Boltzmann's
H
-Theorem
The Chapman-Enskog Method
The Single Relaxation Model
The Boltzmann Equation for a High Density Fluid
Summary
The Lattice Gas Model
Definition of a Lattice Gas Model
Development of the Lattice Gas Model
The HPP Model
The FHP Models
The FHP-I Model
The FHP-II Model
The FHP-III Model
Other FHP Models
Three-Dimensional Models
The Multi-Speed Model on a Cubic Lattice
Boundaries in the Model
Updating the Lattice
Equations for the Lattice Gas Model
Definitions
Microdynamical Equations
Macrodynamical Equations
Isotropy of the Model
The Navier-Stokes Equation
Units of Measurement in a Lattice Gas Model
Obtaining Macroscopic Quantities
Binary Fluid Models
Introduction to Models with Coloured Particles
Properties of Colour Models
Surface Tension in a Binary Fluid Model
The Reactive Model
The Colour-Field Model
Liquid-Gas Lattice Gas Models
The Interactions
Implementation of the Interactions
Lattice Gas Simulations
Drawbacks of the Lattice Gas Approach
Lack of Galilean Invariance
Noisy Results
Large Collision Matrices
Non-Physical Phase Separation
Summary
Exclusion Principle
Galilean Invariance
Conservables
Isotropy
Results for the FHP Models
The Lattice Boltzmann Model
Development of the Lattice Boltzmann Model
Lattice Boltzmann Model for the Ensemble Averaged Distribution Function
The Linear Collision Operator
The Enhanced Collision Rules
The Single Relaxation Time Lattice Boltzmann Model
An Isotropic, Galilean Invariant BGK Model
The Equilibrium Distribution
The Conservation Equations
Useful Relations
Basic Model
Chapman-Enskog Expansion
Boundaries in a Lattice Boltzmann Model
Bounce Back Boundary Conditions
Higher-Order Boundary Conditions
A Finite Difference Method
Dirichlet Boundary Conditions
Binary-Fluid and Liquid-Gas Lattice Boltzmann Models
Colour Model
Miscible Binary Fluid
The Local Interaction Model
The Free Energy Model
Binary Fluid Model
Liquid-Gas Model
The Distribution Functions and the Equations of Motion for a Binary Fluid
Solving for the Distribution Functions
The Equations of Motion for a Binary Fluid
Model Selection
Implementation of the Free Energy Binary Model
Fluid Separation
Bubble Equilibrium
The Density and Order Parameter at the Interface
Isotropy
Galilean Invariance
Summary
Gravity in a Lattice Boltzmann Model
Introducing Gravity
The Classic Boltzmann Equation
Combining the Gravity Term and the Pressure Tensor
Adding a Force Term to Equation ()
Calculating the Equilibrium Distribution with an Altered Velocity
Adding an Additional Term to the Boltzmann Equation
Review of Methods
Model Implementation
Density Gradient
Model Comparison
Grid Orientation
Results
Gravitational Strength
Single Species Model
Immiscible Binary Fluid
Galilean Invariance
Summary
The Equations of Internal Wave Motion
The Potential Density
Inviscid Wave Equations
The Two-Layer Model
Continuous Density Variation
Waves in a Viscous Fluids
Frequency and Damping Parameter
Wave Velocities
Standing Waves
Summary
Interfacial Standing Wave Simulations
The density Gradient, the Potential Density, the Relative Density and the Gravitational Strength
Standing Wave Initialisation
Standing Wave Simulations
The Wave Period and the Damping Parameter
The Curve Fitting Process
The Contribution to
e
from the Discrete Lattice
Relating the Error Parameter to an Error in the Fitted Parameters
Curve Fitting Results
Comparison with Theory
Continuously Varying Density at the Interface
Velocities
Velocity Variation Across a Vertical Cross-Section
Velocity Variation Across a Horizontal Cross-Section
Boundary Layer at the Solid Boundaries
Peak Horizontal Velocity
Summary
Interfacial Progressive Wave Simulations
Progressive Wave Initialisation
Progressive Interfacial Waves
Experimental Investigations into Progressive Interfacial Waves
Comparison Between Interfacial Wave Simulations and Experimental Results
Wave Parameters
Density Profile
Dimensional Parameters
Dimensionless Parameters
Comparison of Dimensionless Parameters
Numerical Comparisons
Summary
Conclusion
Body Forces
Interfacial Wave Modelling
Comparison of Results with Theory and Experiment
Model Strengths
References
Notation
FHP-III Collisions
Boolean Equations
Lookup Tables
Publications
About this document ...
James Buick
Tue Mar 17 17:29:36 GMT 1998