统一坐标系下的计算流体力学 英文版PDF电子书下载

Chapter 1 Introduction 1

1.1 CFD as Numerical Solution to Nonlinear Hyperbolic PDEs 1

1.2 Role of Coordinates in CFD 2

1.3 Outline of the Book 5

References 6

Chapter 2 Derivation of Conservation Law Equations 9

2.1 Fluid as a Continuum 9

2.2 Derivation of Conservation Law Equations in Fixed Coordinates 10

2.3 Conservation Law Equations in Moving Coordinates 14

2.4 Integral Equations versus Partial Differential Equations 14

2.5 The Entropy Condition for Inviscid Flow Computation 17

References 18

Chapter 3 Review of Eulerian Computation for 1-D Inviscid Flow 19

3.1 Flow Discontinuities and Rankine-Hugoniot Conditions 19

3.2 Classification of Flow Discontinuities 21

3.3 Riemann Problem and its Solution 26

3.4 Preliminary Considerations of Numerical Computation 34

3.5 Godunov Scheme 35

3.6 High Resolution Schemes and Limiters 38

3.7 Defects of Eulerian Computation 39

References 40

Chapter 4 1-D Flow Computation Using the Unified Coordinates 43

4.1 Gas Dynamics Equations Based on the Unified Coordinates 43

4.2 Shock-Adaptive Godunov Scheme 45

4.3 The Use of Entropy Conservation Law for Smooth Flow Computation 47

4.4 The Unified Computer Code 48

4.5 Cure of Defects of Eulerian and Lagrangian Computation by the UC Method 52

4.6 Conclusions 66

References 66

Chapter 5 Comments on Current Methods for Multi-Dimensional Flow Computation 69

5.1 Eulerian Computation 69

5.2 Lagrangian Computation 71

5.3 The ALE Computation 73

5.4 Moving Mesh Methods 73

5.5 Optimal Coordinates 74

References 75

Chapter 6 The Unified Coordinates Formulation of CFD 79

6.1 Hui Transformation 79

6.2 Geometric Conservation Laws 80

6.3 Derivation of Governing Equations in Conservation Form 80

References 85

Chapter 7 Properties of the Unified Coordinates 87

7.1 Relation to Eulerian Computation 87

7.2 Relation to Classical Lagrangian Coordinates 87

7.3 Relation to Arbitrary-Lagrangian-Eulerian Computation 88

7.4 Contact Resolution 89

7.5 Mesh Orthogonality 89

7.6 Unified Coordinates for Steady Flow 91

7.7 Effects of Mesh Movement on the Flow 92

7.8 Relation to Other Moving Mesh Methods 92

7.9 Relation to Mesh Generation and the Level-Set Function Method 94

References 94

Chapter 8 Lagrangian Gas Dynamics 97

8.1 Lagrangian Gas Dynamics Equations 97

8.2 Weak Hyperbolicity 98

8.3 Non-Equivalency of Lagrangian and Eularian Formulation 99

References 100

Chapter 9 Steady 2-D and 3-D Supersonic Flow 101

9.1 The Unified Coordinates for Steady Flow 101

9.2 Euler Equations in the Unified Coordinates 102

9.3 The Space-Marching Computation 104

9.4 Examples 105

9.5 3-D Flow 111

References 114

Chapter 10 Unsteady 2-D and 3-D Flow Computation 117

10.1 Summary of Solution to the 2-D Euler Equations Using the Unified Coordinates 117

10.2 Computation Procedure 119

10.3 Examples 122

References 125

Chapter 11 Viscous Flow Computation Using Navier-Stokes Equations 127

11.1 Navier-Stokes Equations in the Unified Coordinates 127

11.2 The Angle-preserving Equation 130

11.3 Advantages of the g-equation Over the h-equation 131

11.4 Boundary Condition and Movement of Boundary Cells 133

11.5 Solution Strategies 134

11.6 Test Examples:Shock/Boundary Flow Interaction and Shock/Shock Interaction 138

References 145

Chapter 12 Applications of the Unified Coordinates to Kinetic Theory 147

12.1 Brief Introduction of Gas-Kinetic Theory 147

12.2 Gas-Kinetic BGK Model Under the Unified Coordinate Transformation 152

12.3 Numerical BGK-NS Scheme in a Moving Mesh System 153

12.4 Numerical Procedure 157

12.5 Numerical Examples 158

12.6 Conclusion 168

References 168

Chapter 13 Summary 171

Appendix A Riemann Problem for 1-D Flow in the Unified Coordinate 173

Appendix B Computer Code for 1-D Flow in the Unified Coordinate 177