Wai-How Hui和Kun Xu编写的《统一坐标系下的计算流体力学方法》是运用大规模数值计算来解决流体的运动问题。本书首先回顾了一维和多维计算流体力学中的欧拉、拉格朗日以及ALE(Arbitrary-Lagrangian-Eulerian)方法的优缺点以及各种移动网格方法，然后系统介绍了统一坐标法，用一些具体的算例阐明它和现有方法之间的关系。

　　本书是由Wai-How Hui和Kun Xu编写的《统一坐标系下的计算流体力学方法》。《统一坐标系下的计算流体力学方法》的英文内容简介如下：

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.

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