统一坐标系下的计算流体力学 英文版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

统一坐标系下的计算流体力学 英文版PDF格式电子书版下载

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Chapter 1 Introduction1

1.1 CFD as Numerical Solution to Nonlinear Hyperbolic PDEs1

1.2 Role of Coordinates in CFD2

1.3 Outline of the Book5

References6

Chapter 2 Derivation of Conservation Law Equations9

2.1 Fluid as a Continuum9

2.2 Derivation of Conservation Law Equations in Fixed Coordinates10

2.3 Conservation Law Equations in Moving Coordinates14

2.4 Integral Equations versus Partial Differential Equations14

2.5 The Entropy Condition for Inviscid Flow Computation17

References18

Chapter 3 Review of Eulerian Computation for 1-D Inviscid Flow19

3.1 Flow Discontinuities and Rankine-Hugoniot Conditions19

3.2 Classification of Flow Discontinuities21

3.3 Riemann Problem and its Solution26

3.4 Preliminary Considerations of Numerical Computation34

3.5 Godunov Scheme35

3.6 High Resolution Schemes and Limiters38

3.7 Defects of Eulerian Computation39

References40

Chapter 4 1-D Flow Computation Using the Unified Coordinates43

4.1 Gas Dynamics Equations Based on the Unified Coordinates43

4.2 Shock-Adaptive Godunov Scheme45

4.3 The Use of Entropy Conservation Law for Smooth Flow Computation47

4.4 The Unified Computer Code48

4.5 Cure of Defects of Eulerian and Lagrangian Computation by the UC Method52

4.6 Conclusions66

References66

Chapter 5 Comments on Current Methods for Multi-Dimensional Flow Computation69

5.1 Eulerian Computation69

5.2 Lagrangian Computation71

5.3 The ALE Computation73

5.4 Moving Mesh Methods73

5.5 Optimal Coordinates74

References75

Chapter 6 The Unified Coordinates Formulation of CFD79

6.1 Hui Transformation79

6.2 Geometric Conservation Laws80

6.3 Derivation of Governing Equations in Conservation Form80

References85

Chapter 7 Properties of the Unified Coordinates87

7.1 Relation to Eulerian Computation87

7.2 Relation to Classical Lagrangian Coordinates87

7.3 Relation to Arbitrary-Lagrangian-Eulerian Computation88

7.4 Contact Resolution89

7.5 Mesh Orthogonality89

7.6 Unified Coordinates for Steady Flow91

7.7 Effects of Mesh Movement on the Flow92

7.8 Relation to Other Moving Mesh Methods92

7.9 Relation to Mesh Generation and the Level-Set Function Method94

References94

Chapter 8 Lagrangian Gas Dynamics97

8.1 Lagrangian Gas Dynamics Equations97

8.2 Weak Hyperbolicity98

8.3 Non-Equivalency of Lagrangian and Eularian Formulation99

References100

Chapter 9 Steady 2-D and 3-D Supersonic Flow101

9.1 The Unified Coordinates for Steady Flow101

9.2 Euler Equations in the Unified Coordinates102

9.3 The Space-Marching Computation104

9.4 Examples105

9.5 3-D Flow111

References114

Chapter 10 Unsteady 2-D and 3-D Flow Computation117

10.1 Summary of Solution to the 2-D Euler Equations Using the Unified Coordinates117

10.2 Computation Procedure119

10.3 Examples122

References125

Chapter 11 Viscous Flow Computation Using Navier-Stokes Equations127

11.1 Navier-Stokes Equations in the Unified Coordinates127

11.2 The Angle-preserving Equation130

11.3 Advantages of the g-equation Over the h-equation131

11.4 Boundary Condition and Movement of Boundary Cells133

11.5 Solution Strategies134

11.6 Test Examples:Shock/Boundary Flow Interaction and Shock/Shock Interaction138

References145

Chapter 12 Applications of the Unified Coordinates to Kinetic Theory147

12.1 Brief Introduction of Gas-Kinetic Theory147

12.2 Gas-Kinetic BGK Model Under the Unified Coordinate Transformation152

12.3 Numerical BGK-NS Scheme in a Moving Mesh System153

12.4 Numerical Procedure157

12.5 Numerical Examples158

12.6 Conclusion168

References168

Chapter 13 Summary171

Appendix A Riemann Problem for 1-D Flow in the Unified Coordinate173

Appendix B Computer Code for 1-D Flow in the Unified Coordinate177