This book reviews the relative advantages and drawbacks of Eulerian and Lagrangiancoordinates as well as the Arbitrary Lagrangian-Eulerian （ALE） and various moving meshmethods in Computational Fluid Dynamics （CFD） for one and multidimensional flows.It then systematically introduces the unified coordinate approach to CFD， illustrated withnumerous examples and comparisons to clarify its relation with existing approaches. Thebook is intended for researchers and practitioners in the field of Computational Fluid Dynamics. Emeritus Professor Wai-How Hui and Professor Kun Xu both work at the Department of Mathematics of the Hong Kong University of Science & Technology， China.
Table of Contents
Chapter 1 Introduction
1．1 CFD as Numerical Solution to Nonlinear Hyperbolic PDEs
1．2 Role of Coordinates in CFD
1．3 Outline of the Book
References
Chapter 2 Derivation of Conservation Law Equations
2．1 Fluid as a Continuum
2．2 Derivation of Conservation Law Equations in Fixed Coordinates
2．3 Conservation Law Equations in Moving Coordinates
2．4 Integral Equations versus Partial Differential Equations
2．5 The Entropy Condition for Inviscid Flow Computation
References
Chapter 3 Review of Eulerian Computation for 1-D Inviscid Flow
3．1 Flow Discontinuities and Rankine-Hugoniot Conditions
3．2 Classification of Flow Discontinuities
3．3 Riemann Problem and its Solution
3．4 Preliminary Considerations of Numerical Computation
3．5 Godunov Scheme
3．6 High Resolution Schemes and Limiters
3．7 Defects of Eulerian Computation
References
Chapter 4 I-D Flow Computation Using the Unified Coordinates
4．1 Gas Dynamics Equations Based on the Unified Coordinates
4．2 Shock-Adaptive Godunov Scheme
4．3 The Use of Entropy Conservation Law for Smooth Flow Computation
4．4 The Unified Computer Code
4．5 Cure of Defects of Eulerian and Lagrangian Computation by the UC Method
4．6 Conclusions
References
Chapter 5 Comments on Current Methods for Multi-Dimensional Flow Computation
5．1 Eulerian Computation
5．2 Lagrangian Computation
5．3 The ALE Computation
5．4 Moving Mesh Methods
5．5 Optimal Coordinates
References
Chapter 6 The Unified Coordinates Formulation of CFD
6．1 Hui Transformation
6．2 Geometric Conservation Laws
6．3 Derivation of Governing Equations in Conservation Form
References
Chapter 7 Properties of the Unified Coordinates
7．1 Relation to Eulerian Computation
7．2 Relation to Classical Lagrangian Coordinates
7．3 Relation to Arbitrary-Lagrangian-Eulerian Computation
7．4 Contact Resolution
7．5 Mesh Orthogonality
7．6 Unified Coordinates for Steady Flow
7．7 Effects of Mesh Movement on the Flow
7．8 Relation to Other Moving Mesh Methods
7．9 Relation to Mesh Generation and the Level-Set Function Method
References
Chapter 8 Lagrangian Gas Dynamics
8．1 Lagrangian Gas Dynamics Equations
8．2 Weak Hyperbolicity
8．3 Non-Equivalency of Lagrangian and Eularian Formulation
References
Chapter 9 Steady 2-D and 3-D Supersonic Flow
9．1 The Unified Coordinates for Steady Flow
9．2 Euler Equations in the Unified Coordinates
9．3 The Space-Marching Computation
9．4 Examples
9．5 3-D Flow
References
Chapter 10 Unsteady 2-D and 3-D Flow Computation
10．1 Summary of Solution to the 2-D Euler Equations Using the Unified Coordinates
10．2 Computation Procedure
10．3 Examples
References
Chapter 11 Viscous Flow Computation Using Navier-Stokes Equations
11．1 Navier-Stokes Equations in the Unified Coordinates
11．2 The Angle-preserving Equation
11．3 Advantages of the g-equation Over the h-equation
11．4 Boundary Condition and Movement of Boundary Cells
11．5 Solution Strategies
11．6 Test Examples： Shock/Boundary Flow Interaction and Shock/Shock Interaction
References
Chapter 12 Applications of the Unified Coordinates to Kinetic Theory
12．1 Brief Introduction of Gas-Kinetic Theory
12．2 Gas-Kinetic BGK Model Under the Unified Coordinate Transformation
12．3 Numerical BGK-NS Scheme in a Moving Mesh System
12．4 Numerical Procedure
12．5 Numerical Examples
12．6 Conclusion
References
Chapter 13 Summary
Appendix A Riemann Problem for 1-D Flow in the Unified Coordinate
Appendix B Computer Code for 1-D Flow in the Unified Coordinate
