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Chapter One Introduction 1

1.1 Background 1

1.2 Literature Review 3

1.3 Outline of the Thesis 11

Chapter Two Differential Quadrature and Fundamental Equations for Fluid Mechanics 14

2.1 Concepts and Conclusions in DQ 14

2.2 Numerical Methods to Solve DQ Equations 24

2.3 Description ofProblems 30

Chapter Three Traditional and Mixed Differential Quadrature Methods 34

3.1 Mathematical Formulations 36

3.2 Differential Quadrature Formulations 37

3.3 Numerical Results and Discussions 50

Chapter Four Upwind Local Differential Quadrature Method 59

4.1 Upwind Local Differential Quadrature Method 61

4.2 Mathematical Formulations 67

4.3 Numerical Results and Discussions 73

Chapter Five Differential Quadrature Method for Solving Steady Flow Heat Transfer Problem 85

5.1 Mathematical Model for the problem 86

5.2 Perturbation Method 90

5.3 Numerical Formulations 93

5.4 Results and Discussions 99

Chapter Six Application of Differential Quadrature Method 110

6.1 Governing Equations ofthe Problem 111

6.2 Numerical Methods 118

6.3 Numerical Results and Discussions 122

Chapter Seven Conclusions and Expectations 142

7.1 The Main Conclusions of the Dissertation 142

7.2 Expectations 145

References 147

Acknowledgement 159