Preface |
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xv | |
Acknowledgments |
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xix | |
List of Abbreviations |
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xxiii | |
Nomenclature |
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xxvii | |
1 Introduction to Computational Aerodynamics |
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1 | (44) |
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2 | (4) |
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1.2 The Goals of Computational Aerodynamics |
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6 | (1) |
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7 | (3) |
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1.4 A Bit of Computational Aerodynamics History |
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10 | (9) |
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1.5 What Can Computational Aerodynamics Do Today and Tomorrow? |
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19 | (6) |
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1.5.1 Commercial Aircraft Applications |
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19 | (3) |
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1.5.2 Military Aircraft Applications |
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22 | (3) |
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1.6 Integration of CA and Experiments |
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25 | (2) |
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1.7 Design, Analysis, and Multidisciplinary Optimization |
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27 | (2) |
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1.8 The Computational Aerodynamics Process |
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29 | (8) |
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31 | (1) |
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32 | (1) |
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33 | (1) |
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34 | (1) |
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35 | (2) |
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1.9 Computational Aerodynamics Users and Errors |
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37 | (1) |
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1.10 Scope, Purpose, and Outline of the Book |
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38 | (2) |
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40 | (1) |
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40 | (5) |
2 Computers, Codes, and Engineering |
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45 | (48) |
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46 | (1) |
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2.2 From Engineering Methods to High-Performance Computing |
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47 | (12) |
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2.2.1 Semi-Empirical Methods |
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48 | (7) |
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2.2.2 Linear Potential Flow Methods |
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55 | (1) |
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55 | (1) |
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2.2.4 When Should You Use a Given Method? |
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55 | (4) |
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59 | (19) |
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2.3.1 Why CA Requires Large Computers |
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61 | (2) |
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2.3.2 CA Historical Development |
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63 | (3) |
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2.3.3 Computer Measures of Merit |
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66 | (5) |
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2.3.4 Parallel Computer Scalability |
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71 | (7) |
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2.4 Computer Codes: Verification, Validation, and Certification |
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78 | (4) |
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2.5 Some Comments on Programming |
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82 | (4) |
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2.6 Elements of a Solution |
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86 | (3) |
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89 | (1) |
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90 | (3) |
3 Getting Ready for Computational Aerodynamics: Fluid Mechanics Foundations |
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93 | (68) |
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94 | (1) |
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3.2 Governing Equations of Fluid Mechanics |
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94 | (4) |
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3.3 Derivation of Governing Equations |
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98 | (18) |
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3.3.1 Conservation of Mass: The Continuity Equation |
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100 | (4) |
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3.3.2 Conservation of Momentum and the Substantial Derivative |
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104 | (9) |
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3.3.2.1 Substantial Derivative |
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104 | (3) |
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107 | (6) |
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3.3.3 The Energy Equation |
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113 | (3) |
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3.4 Solution of the Set of Governing Equations |
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116 | (1) |
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3.5 Standard Forms and Terminology of Governing Equations |
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117 | (7) |
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3.5.1 Nondimensionalization |
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118 | (1) |
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3.5.2 Use of Divergence Form |
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118 | (2) |
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3.5.3 The "Standard" or "Vector" Form of the Equations |
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120 | (4) |
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3.6 Boundary Conditions, Initial Conditions, and the Mathematics Classification of Partial Differential Equations (PDEs) |
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124 | (6) |
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126 | (1) |
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126 | (1) |
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127 | (1) |
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3.6.4 Equations of Mixed Type |
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127 | (1) |
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3.6.5 Elaboration on Characteristics |
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128 | (2) |
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130 | (1) |
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131 | (1) |
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132 | (1) |
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133 | (5) |
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3.11 Using and Simplifying These Equations: High- to Low-Fidelity Flowfield Models |
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138 | (1) |
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3.12 Inviscid Flow Models |
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138 | (9) |
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139 | (2) |
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3.12.2 Small Disturbance Expansion of the Full Potential and Energy Equation |
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141 | (3) |
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3.12.3 Transonic Small Disturbance Equation |
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144 | (1) |
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3.12.4 Prandtl-Glauert Equation |
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145 | (1) |
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3.12.5 Incompressible Irrotational Flow: Laplace's Equation |
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146 | (1) |
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147 | (8) |
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3.13.1 Thin-Layer Navier-Stokes Equations |
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149 | (3) |
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3.13.2 Parabolized Navier-Stokes Equations |
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152 | (1) |
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3.13.3 Boundary-Layer Equations |
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153 | (2) |
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3.14 Examples of Zones of Application |
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155 | (1) |
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3.15 Requirements for a Complete Problem Formulation |
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156 | (1) |
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157 | (1) |
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158 | (3) |
4 Getting Ready for Computational Aerodynamics: Aerodynamic Concepts |
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161 | (103) |
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162 | (1) |
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4.2 Review of Potential Flow Theory |
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163 | (5) |
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164 | (3) |
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4.2.2 Simplified Equations of Motion |
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167 | (1) |
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4.3 Potential Flow Applications |
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168 | (9) |
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4.3.1 Flow Over a Circular Cylinder |
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169 | (4) |
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4.3.2 Flow Over a Circular Cylinder with Circulation |
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173 | (4) |
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4.4 Applications to Airfoils |
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177 | (2) |
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177 | (1) |
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4.4.2 Singularity Distribution Approaches |
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178 | (1) |
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178 | (1) |
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4.5 Boundary Layers and Viscous Effects |
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179 | (9) |
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4.5.1 Boundary Layer Concepts |
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179 | (5) |
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4.5.1.1 Laminar Boundary Layers |
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180 | (1) |
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4.5.1.2 Turbulent Boundary Layers |
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181 | (1) |
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4.5.1.3 Relative Features of Boundary Layers |
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182 | (2) |
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4.5.2 Skin Friction Estimation |
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184 | (4) |
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188 | (20) |
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4.6.1 Airfoil Terminology |
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189 | (1) |
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4.6.2 Forces and Moments on an Airfoil |
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189 | (3) |
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4.6.3 Airfoil Aerodynamic Coefficients |
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192 | (1) |
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4.6.4 Airfoil Lift and Drag Variations |
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192 | (3) |
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4.6.5 NACA Airfoil Families |
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195 | (1) |
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4.6.6 How to Use NACA Airfoil Data |
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196 | (2) |
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4.6.7 Factors That Affect Airfoil Aerodynamics |
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198 | (1) |
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198 | (1) |
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198 | (1) |
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199 | (1) |
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199 | (5) |
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4.6.9 Thin Airfoil Theory |
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204 | (4) |
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208 | (14) |
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209 | (1) |
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4.7.2 Wing Aerodynamic Coefficients |
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210 | (1) |
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4.7.3 The Vortex Filament |
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211 | (2) |
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4.7.4 Prandtl's Lifting Line Theory |
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213 | (5) |
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4.7.5 Subsonic Compressibility Effects |
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218 | (4) |
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4.8 Transonic Aerodynamics |
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222 | (15) |
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227 | (1) |
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4.8.2 Supercritical Airfoils |
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227 | (2) |
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4.8.3 Korn Airfoil Equation |
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229 | (1) |
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230 | (5) |
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235 | (2) |
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4.9 Supersonic Aerodynamics |
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237 | (12) |
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4.9.1 Supersonic Linear Theory and Airfoil Aerodynamics |
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240 | (5) |
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4.9.2 Volumetric Wave Drag |
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245 | (2) |
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247 | (2) |
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4.10 Hypersonic Aerodynamics |
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249 | (9) |
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4.10.1 Importance of Temperature in Hypersonic Flow |
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250 | (2) |
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4.10.2 Newtonian and Modified Newtonian Flow Theory |
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252 | (1) |
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4.10.3 Aerodynamic Heating |
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253 | (2) |
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4.10.4 Engine/Airframe Integration |
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255 | (3) |
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258 | (6) |
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259 | (1) |
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260 | (4) |
5 Classical Linear Theory Computational Aerodynamics |
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264 | (86) |
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265 | (2) |
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267 | (38) |
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5.2.1 The Integral Equation for the Potential |
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269 | (8) |
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5.2.2 An Example of a Panel Code: The Classic Hess and Smith Method |
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277 | (4) |
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281 | (9) |
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5.2.4 Geometry and Design |
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290 | (2) |
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5.2.4.1 Effects of Shape Changes on Pressure Distributions |
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291 | (1) |
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5.2.4.2 Shape for a Specified Pressure Distribution |
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291 | (1) |
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5.2.5 Issues in the Problem Formulation for 3D Potential Flow Over Aircraft |
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292 | (2) |
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5.2.6 Example Applications of Panel Methods |
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294 | (5) |
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5.2.7 Using Panel Methods |
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299 | (2) |
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5.2.7.1 Commonsense Rules for Panels |
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301 | (1) |
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5.2.7.2 What a Panel Method Can and Cannot Do |
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301 | (1) |
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5.2.8 Advanced Panel Methods: What Is a "Higher Order" Panel Method? |
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301 | (1) |
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5.2.9 Current Standard Panel Method Programs: A Brief Survey |
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302 | (2) |
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302 | (1) |
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302 | (2) |
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304 | (1) |
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304 | (1) |
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5.3 Vortex Lattice Methods |
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305 | (34) |
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5.3.1 Boundary Conditions on the Mean Surface and the Pressure Relation |
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307 | (10) |
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5.3.1.1 Linearized Form of the Boundary Condition |
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309 | (1) |
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5.3.1.2 Transfer of the Boundary Conditions |
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310 | (1) |
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5.3.1.3 Decomposition of Boundary Conditions into Camber/Thickness/Alpha |
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311 | (1) |
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5.3.1.4 Thin Airfoil Theory Pressure Relation |
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312 | (1) |
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5.3.1.5 Ac due to Camber/Alpha (Thickness Effects Cancel!) |
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313 | (4) |
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5.3.2 The Classical Vortex Lattice Method |
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317 | (6) |
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5.3.3 Examples of the Use and Accuracy of the Vortex Lattice Method |
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323 | (11) |
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5.3.3.1 The Warren 12 Test Case |
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323 | (2) |
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5.3.3.2 Isolated Swept Wing |
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325 | (1) |
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326 | (2) |
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5.3.3.4 Control Surface Deflection |
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328 | (1) |
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5.3.3.5 Pitch and Roll Damping Estimation |
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328 | (1) |
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5.3.3.6 Slender Lifting Body Results |
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329 | (2) |
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5.3.3.7 Non-Planar Results |
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331 | (1) |
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5.3.3.8 Ground Effects and Dihedral Effects |
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332 | (2) |
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5.3.4 Inverse Design Methods and Program DesCam |
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334 | (2) |
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5.3.5 Alternate and Advanced VLM Methods |
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336 | (1) |
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5.3.6 Unsteady Flow Extension |
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337 | (1) |
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5.3.7 Vortex Lattice Method Summary |
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338 | (1) |
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339 | (5) |
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344 | (6) |
6 Introduction to Computational Fluid Dynamics |
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350 | (98) |
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351 | (2) |
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6.2 Options for Numerically Solving the Navier-Stokes Equations |
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353 | (5) |
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6.2.1 Finite Difference Methods |
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354 | (1) |
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6.2.2 Finite Volume Methods |
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355 | (1) |
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6.2.3 Finite Element/Pseudo Spectral Methods |
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356 | (2) |
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6.3 Approximations to Derivatives |
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358 | (1) |
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6.4 Finite Difference Methods |
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359 | (8) |
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6.5 Representing Partial Differential Equations |
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367 | (4) |
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369 | (1) |
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370 | (1) |
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370 | (1) |
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370 | (1) |
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371 | (6) |
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6.6.1 Fourier or Von Neumann Stability Analysis |
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372 | (2) |
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6.6.2 Examples of Stability and Instability |
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374 | (3) |
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377 | (6) |
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6.7.1 Forward Difference in x |
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379 | (1) |
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6.7.2 Central Difference in x |
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379 | (1) |
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6.7.3 Backward Difference in x |
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379 | (1) |
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380 | (1) |
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6.7.5 Lax-Wendroff Method |
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381 | (1) |
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381 | (2) |
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6.8 Truncation Error Analysis of the Wave Equation: The Modified Equation |
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383 | (2) |
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385 | (4) |
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386 | (1) |
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387 | (2) |
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389 | (2) |
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6.11 The Finite Volume Method |
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391 | (5) |
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6.12 Time Integration and Differences |
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396 | (7) |
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6.12.1 Explicit Time Integration |
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397 | (3) |
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6.12.1.1 First-Order Time Accuracy |
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397 | (1) |
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6.12.1.2 Second-Order Time Accuracy |
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398 | (1) |
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6.12.1.3 General Form of Backward Time Difference |
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398 | (1) |
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6.12.1.4 Runge-Kutta Time Integration |
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399 | (1) |
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6.12.2 Implicit Time Integration |
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400 | (1) |
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401 | (1) |
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6.12.4 Solution Method for Time Integration |
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402 | (1) |
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403 | (7) |
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6.13.1 Farfield Boundary Conditions |
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403 | (2) |
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6.13.2 Solid Wall Boundary Conditions |
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405 | (4) |
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6.13.3 Numerical Representation of Boundary Conditions |
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409 | (1) |
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6.14 Solution of Algebraic Equations |
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410 | (11) |
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411 | (1) |
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6.14.2 Sparse and Banded Matrix |
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411 | (1) |
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6.14.3 General Sparse Matrix |
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412 | (1) |
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6.14.4 Point Jacobi and Point Gauss-Seidel |
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413 | (1) |
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6.14.5 Gauss-Seidel and Successive Over-Relaxation |
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413 | (2) |
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6.14.6 Successive Line Over-Relaxation |
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415 | (1) |
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6.14.7 Approximate Factorization |
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416 | (4) |
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420 | (1) |
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421 | (1) |
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421 | (4) |
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425 | (14) |
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6.16.1 Finite Difference Methods |
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425 | (3) |
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6.16.2 Higher-Order Methods |
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428 | (2) |
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6.16.3 Finite Volume Methods |
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430 | (9) |
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439 | (4) |
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443 | (5) |
7 Geometry and Grids: Key Considerations in Computational Aerodynamics |
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448 | (91) |
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449 | (1) |
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7.2 Surface Shape Development: Lofting Techniques |
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449 | (5) |
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7.3 Computational Grid Overview |
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454 | (1) |
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455 | (8) |
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463 | (5) |
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463 | (5) |
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7.6 Methods for Creating Structured Grids |
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468 | (13) |
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7.6.1 Algebraic Grid Generation and Stretching/Clustering |
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472 | (3) |
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7.6.2 Conformal Transformation |
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475 | (2) |
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7.6.3 Elliptic Grid Generation |
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477 | (3) |
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7.6.4 Hyperbolic Grid Generation |
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480 | (1) |
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481 | (3) |
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482 | (2) |
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7.8 Methods for Creating Unstructured Meshes |
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484 | (5) |
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7.8.1 Delaunay Triangulation |
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484 | (2) |
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7.8.2 Advancing Front/Advancing Layer |
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486 | (2) |
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488 | (1) |
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489 | (4) |
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493 | (4) |
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7.11 Grid Properties that Affect Solution Accuracy |
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497 | (16) |
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7.11.1 Outer Boundary Size |
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497 | (2) |
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7.11.2 Structured Cell Geometry |
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499 | (6) |
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499 | (1) |
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500 | (1) |
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7.11.2.3 Cell Orthogonality at a Surface Boundary |
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501 | (1) |
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502 | (3) |
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7.11.3 Unstructured Cell Geometry |
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505 | (6) |
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7.11.3.1 Flow Alignment and Boundary Layer Gradients |
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505 | (1) |
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506 | (2) |
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7.11.3.3 Cell Skew and Smoothness |
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508 | (2) |
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7.11.3.4 Cell Isotropy and Spacing |
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510 | (1) |
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7.11.4 Viscous Grid Requirements |
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511 | (2) |
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7.12 Grid Sensitivity Studies |
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513 | (3) |
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7.13 Examples of Grids for Complex Geometries |
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516 | (9) |
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7.13.1 Ranger Jet Aircraft Inviscid Block-structured Grid |
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516 | (2) |
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7.13.2 X-31 Viscous Block Structured Grid |
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518 | (2) |
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7.13.3 Block Structured Grid for Helicopter with Sliding Interface Rotor |
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520 | (1) |
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7.13.4 Unstructured High Lift Commercial Transport |
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520 | (2) |
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7.13.5 Unstructured Mesh for Aircraft with Stores |
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522 | (1) |
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7.13.6 C-130 Unstructured Chimera Mesh with Ring-Slot Parachute |
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522 | (2) |
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7.13.7 V-22 Rotorcraft with Cartesian Overset Grids |
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524 | (1) |
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7.14 Current Grid Generation Software and Data Structures |
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525 | (3) |
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528 | (2) |
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530 | (9) |
8 Viscosity and Turbulence Modeling |
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539 | (78) |
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540 | (1) |
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8.2 Types of Viscous Effects |
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540 | (3) |
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543 | (2) |
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545 | (9) |
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554 | (1) |
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8.6 Characteristics of Turbulence |
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555 | (5) |
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8.7 Turbulence Modeling Approaches |
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560 | (3) |
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8.8 Reynolds-Averaged Navier-Stokes (RANS) |
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563 | (27) |
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8.8.1 Mass-Weighted Averaging |
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566 | (1) |
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8.8.2 Taxonomy of Turbulence Models |
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567 | (2) |
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8.8.3 Prandtl's Mixing-Length Theory - An Example of a Zero-Equation Model |
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569 | (3) |
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8.8.4 Examples of the Use of Various RANS Models |
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572 | (11) |
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8.8.5 FLOMANIA Project Results |
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583 | (1) |
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8.8.6 AIAA Drag Prediction Workshop results |
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584 | (6) |
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8.9 Large-Eddy Simulation |
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590 | (5) |
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591 | (1) |
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8.9.2 Subgrid Scale Models |
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592 | (1) |
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8.9.3 Example LES Applications |
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593 | (2) |
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8.10 Hybrid Approach (RANS/LES) |
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595 | (12) |
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8.10.1 Detached-Eddy Simulation |
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596 | (3) |
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8.10.2 Delayed Detached-Eddy Simulation |
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599 | (3) |
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8.10.3 Improved Delayed Detached-Eddy Simulation |
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602 | (1) |
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603 | (4) |
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8.11 Direct Numerical Simulation |
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607 | (3) |
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610 | (7) |
9 Flow Visualization: The Art of Computational Aerodynamics |
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617 | (45) |
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618 | (2) |
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9.2 Flow Visualization Background |
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620 | (7) |
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9.3 How Flow Visualization Works |
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627 | (7) |
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9.3.1 Smooth Contour Lines |
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628 | (2) |
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9.3.2 Three-Dimensional Vector Plots |
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630 | (1) |
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631 | (1) |
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9.3.4 Flow Function Computation |
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632 | (2) |
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9.4 How to View Scalar Properties |
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634 | (3) |
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9.5 How to View Vector Properties |
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|
637 | (13) |
|
9.5.1 Commonly Used Vectors in Fluid Dynamics and Flow Visualization |
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|
637 | (3) |
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|
638 | (1) |
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9.5.1.2 Helicity Density and Relative Helicity |
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|
638 | (1) |
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|
639 | (1) |
|
9.5.1.4 Shear Stress Vector |
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|
639 | (1) |
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9.5.2 Examples of vector flow visualization |
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|
640 | (7) |
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|
640 | (1) |
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9.5.2.2 Streamline/Stream Ribbons |
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|
641 | (2) |
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9.5.2.3 Vortex Visualization Using Vector Magnitudes |
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|
643 | (3) |
|
9.5.2.4 Vortex Visualization Using the Q-Criterion |
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|
646 | (1) |
|
9.5.2.5 Vortex Visualization Using Vortex Tracking |
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|
647 | (1) |
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9.5.3 Skin Friction Lines |
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|
647 | (3) |
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9.6 Newer Flow Visualization Approaches |
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|
650 | (9) |
|
9.6.1 Line Integral Convolution |
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|
650 | (1) |
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9.6.2 Numerical Schlieren |
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|
651 | (2) |
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|
653 | (4) |
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9.6.4 Unsteady Flow and Movies |
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|
657 | (2) |
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|
659 | (1) |
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|
659 | (3) |
10 Applications of Computational Aerodynamics |
|
662 | (69) |
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|
663 | (1) |
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10.2 Getting to Know Flowfields |
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|
663 | (6) |
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10.3 Transonic Aerodynamics Prediction |
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|
669 | (11) |
|
10.3.1 Brief Review of Methodology Development for Transonic Flow Calculations |
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|
669 | (1) |
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|
670 | (2) |
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|
672 | (1) |
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|
673 | (3) |
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10.3.5 Fighter Aircraft Design |
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|
676 | (4) |
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10.4 Supersonic Aerodynamics Prediction |
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|
680 | (10) |
|
10.4.1 Initial Application of CFD at Supersonic Speeds |
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|
680 | (3) |
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10.4.2 Application of CFD to a Supersonic Configuration |
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|
683 | (2) |
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10.4.3 Application to Low Sonic Boom Aircraft Design |
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|
685 | (5) |
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10.5 Hypersonic Aerodynamics Prediction |
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|
690 | (6) |
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10.6 Aerodynamic Design and MDO |
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|
696 | (8) |
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10.6.1 High Speed Civil Transport Example |
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|
699 | (2) |
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10.6.2 Truss-Braced Wing Example |
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|
701 | (3) |
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10.7 Integration of Computational and Experimental Work |
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|
704 | (14) |
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10.7.1 Pros and Cons of Experiments |
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|
704 | (1) |
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10.7.2 Pros and Cons of Computations |
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|
705 | (1) |
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10.7.3 Delta Wing with Periodic Suction and Blowing for Flow Control |
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|
706 | (2) |
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10.7.4 Pitching UCAV Configuration |
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|
708 | (3) |
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10.7.5 C-130 Airdrop Configuration |
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|
711 | (1) |
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10.7.6 Closed-Loop Flow Control |
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|
712 | (4) |
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|
716 | (2) |
|
10.8 Current Applications of Potential Flow Codes |
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|
718 | (3) |
|
10.8.1 Compressible Vortex Lattice Method |
|
|
719 | (1) |
|
10.8.2 Transonic Lifting-Line Method |
|
|
719 | (1) |
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10.8.3 Unsteady Vortex-Lattice Method for Aeroelasticity |
|
|
720 | (1) |
|
10.8.4 Meshless Full Potential Solver |
|
|
721 | (1) |
|
10.9 The Future of Computational Aerodynamics |
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|
721 | (3) |
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|
724 | (1) |
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|
724 | (7) |
Appendix A Geometry for Aerodynamicists |
|
731 | (35) |
Appendix B Sources of Experimental Data for Code Validation |
|
766 | (10) |
Appendix C Potential Flow Review |
|
776 | (14) |
Appendix D Computational Aerodynamics Programs |
|
790 | (12) |
Appendix E Structured Grid Transformations |
|
802 | (6) |
Appendix F Commonly Used Turbulence Models |
|
808 | (15) |
Glossary |
|
823 | (10) |
Index |
|
833 | |