| Dedication | p. v |
| The Contributions of David Caughey to Computational Fluid Dynamics | p. 1 |
| Introduction | p. 1 |
| Shock Wave Structure and Sonic Boom | p. 2 |
| Potential Flow Simulations | p. 3 |
| Solutions of Euler Equations | p. 4 |
| Solutions of Navier-Stokes Equations | p. 10 |
| Simulation of Turbulent Reactive Flows | p. 13 |
| Special Topics | p. 14 |
| Review Articles | p. 15 |
| Fluid Mechanics: An Interactive Text | p. 16 |
| Concluding Remarks | p. 17 |
| Ph.D. Students Supervised by David A. Caughey | p. 19 |
| Publications of David A. Caughey | p. 21 |
| Design and Optimization | |
| Computational Fluid Dynamics in the Analysis and Design of Engineered Systems | p. 37 |
| Introduction | p. 37 |
| Flow Modeling for Fire Control Strategies and Scenario Planning in an Underground Road Tunnel | p. 38 |
| Flow Modeling in a Hard Disk Drive Enclosure | p. 43 |
| Concluding Remarks | p. 46 |
| Bibliography | p. 46 |
| Advances in Aerodynamic Shape Optimization | p. 49 |
| Introduction | p. 49 |
| Formulation of the Optimization Procedure | p. 52 |
| Design using the Euler Equations | p. 55 |
| The Reduced Gradient Formulation | p. 61 |
| Optimization Procedure | p. 63 |
| Case Studies | p. 67 |
| Super P51 Racer | p. 71 |
| Conclusion | p. 75 |
| Acknowledgment | p. 76 |
| Bibliography | p. 76 |
| Design Optimization of Propeller Blades | p. 81 |
| Introduction | p. 81 |
| Formulation as a Control Problem | p. 82 |
| Implementation | p. 86 |
| Optimization of a Blade Section for Low Cavitation | p. 86 |
| Conclusions | p. 94 |
| Bibliography | p. 95 |
| Flow Boundary Conditions Modeling in 4D for Optimized, Adaptive, and Unsteady Configurations | p. 97 |
| Introduction | p. 97 |
| Geometry Concept for 4-Dimensional Problems | p. 98 |
| Optimization | p. 101 |
| Adaptive Configurations | p. 101 |
| Unsteady Boundary Conditions | p. 102 |
| Bio-fluidmechanic Applications | p. 102 |
| Conclusion | p. 104 |
| Bibliography | p. 104 |
| Algorithms and Accuracy | |
| Stability and Efficiency of Implicit Residual-Based Compact Schemes | p. 107 |
| Introduction | p. 107 |
| Implicit Schemes Description | p. 108 |
| Direct Solver Efficiency | p. 112 |
| Implicit Treatment Description | p. 114 |
| Iterative Solver Efficiency and Stability | p. 120 |
| Concluding Remarks | p. 123 |
| Bibliography | p. 126 |
| Higher-Order Time-Integration Schemes for Dynamic Unstructured Mesh CFD Simulations | p. 129 |
| Abstract | p. 129 |
| Introduction | p. 130 |
| Governing Equations in Arbitrary-Lagrangian-Eulerian (ALE) Form and Base Flow Solver | p. 131 |
| Higher-order Time Integration and the Discrete Geometric Conservation Law | p. 132 |
| Mesh Motion Strategies | p. 134 |
| Acceleration Strategies | p. 137 |
| Mesh Motion Results | p. 137 |
| Unsteady Flow Simulations Using Backwards Difference Schemes | p. 141 |
| Implicit-Runge-Kutta Methods for Dynamic Mesh Problems | p. 147 |
| Conclusions | p. 151 |
| Acknowledgments | p. 152 |
| Bibliography | p. 152 |
| The Geometric Convervation Law for BDF3 | p. 155 |
| Explicit Time Domain Finite Element Methods for Electromagnetics | p. 161 |
| Introduction | p. 161 |
| Electromagnetic Scattering | p. 162 |
| Mesh Generation | p. 164 |
| Numerical Solution Algorithm | p. 164 |
| Numerical Examples | p. 167 |
| Dealing with Electrically Larger Scatterers | p. 169 |
| Conclusions | p. 176 |
| Bibliography | p. 178 |
| Estimating Grid-Induced Errors in CFD Solutions | p. 183 |
| Introduction | p. 183 |
| Classification of Methods | p. 184 |
| Overview of the Discrete Error Transport Equation | p. 186 |
| DETEs for FV Solutions of the Euler Equations | p. 188 |
| Usefulness of the DETEs | p. 192 |
| Final Remarks | p. 195 |
| Bibliography | p. 196 |
| Treatment of Vortical Flow Using Vorticity Confinement | p. 199 |
| Abstract | p. 199 |
| Introduction | p. 200 |
| Illustrative One-dimensional Example | p. 204 |
| Vorticity Confinement | p. 207 |
| Results | p. 217 |
| Other Studies | p. 220 |
| Conclusions | p. 221 |
| Acknowledgments | p. 222 |
| Bibliography | p. 223 |
| Flow Stability and Control | |
| Flow Control Applications with Synthetic and Pulsed Jets | p. 241 |
| Abstract | p. 241 |
| Introduction | p. 242 |
| CFD Flow-Solvers Employed | p. 243 |
| Results and Discussions | p. 244 |
| Conclusions | p. 260 |
| Acknowledgments | p. 260 |
| Bibliography | p. 262 |
| Control of Flow Separation over a Circular Cylinder Using Electro-Magnetic Fields: Numerical Simulation | p. 265 |
| Nomenclature | p. 265 |
| Introduction | p. 266 |
| Second Order Analytical Model of EMHD | p. 268 |
| Least-Squares Finite Element Method | p. 269 |
| Numerical Results | p. 274 |
| Conclusion | p. 277 |
| Acknowledgements | p. 278 |
| Bibliography | p. 278 |
| Bifurcation of Transonic Flow over a Flattened Airfoil | p. 285 |
| Introduction | p. 285 |
| Problem Statement and a Numerical Method | p. 286 |
| Analysis of the Lift Coefficient as a Function of M[infinity] | p. 286 |
| Analysis of Stability with Respect to Variation of [alpha] | p. 289 |
| Summary of the Results | p. 290 |
| Conclusion | p. 290 |
| Bibliography | p. 291 |
| Study of Stability of Vortex Pairs over a Slender Conical Body by Euler Computations | p. 297 |
| Abstract | p. 297 |
| Introduction | p. 298 |
| The Euler Solver and the Flow Model | p. 302 |
| Computational Grid and Boundary Conditions | p. 303 |
| Stationary Symmetric and Asymmetric Solutions and Their Stability | p. 306 |
| Structure of the Vortex Core | p. 315 |
| Summary and Conclusions | p. 322 |
| Bibliography | p. 323 |
| Effect of Upstream Conditions on Velocity Deficit Profiles of the Turbulent Boundary Layer at Global Separation | p. 329 |
| Introduction | p. 329 |
| Singular Inviscid Pressure Gradient | p. 330 |
| Governing Equations | p. 331 |
| Inviscid Sublayer 1 | p. 332 |
| Outer Turbulent Sublayer 2 | p. 333 |
| Outer Turbulent Sublayer 3 | p. 333 |
| Pressure-dominated Flow Pattern | p. 334 |
| Comparison with Experiment | p. 336 |
| Conclusion | p. 336 |
| Bibliography | p. 337 |
| Hypersonic Magneto-Fluid-Dynamic Interactions | p. 341 |
| Abstract | p. 341 |
| Nomenclature | p. 342 |
| Introduction | p. 342 |
| Governing Equations | p. 344 |
| Plasma Models | p. 346 |
| Electro-Fluid-Dynamic Interaction | p. 349 |
| Magneto-Fluid-Dynamic Interaction | p. 354 |
| Concluding Remarks | p. 359 |
| Acknowledgment | p. 361 |
| Bibliography | p. 361 |
| Multiphase and Reacting Flows | |
| Computing Multiphase Flows Using AUSM[superscript +]-up Scheme | p. 367 |
| Abstract | p. 367 |
| Introduction | p. 368 |
| Governing Equations (Models) for Multiphase Flows | p. 369 |
| Calculated Examples and Discussion | p. 383 |
| Concluding Remarks | p. 389 |
| Acknowledgments | p. 391 |
| Bibliography | p. 391 |
| Numerical Flux Formulas | p. 394 |
| A Finite-Volume Front-Tracking Method for Computations of Multiphase Flows in Complex Geometries | p. 395 |
| Introduction | p. 395 |
| Mathematical Formulation | p. 397 |
| Numerical Method | p. 399 |
| Results and Discussion | p. 405 |
| Conclusions | p. 414 |
| Bibliography | p. 415 |
| Optimal Artificial Compressibility in the Stokes Limit | p. 419 |
| Computational Modeling of Turbulent Flames | p. 421 |
| Introduction | p. 421 |
| PDF Calculations of Turbulent Flames | p. 422 |
| Modelling of Turbulent Mixing | p. 425 |
| Acknowledgment | p. 427 |
| Bibliography | p. 427 |
| Education | |
| Educating the Future: Impact of Pedagogical Reform in Aerodynamics | p. 433 |
| Introduction | p. 433 |
| Course Overview | p. 434 |
| Conceptual Understanding and Active Learning | p. 435 |
| Integration of Theory, Computation, and Experiment | p. 438 |
| Project-based Learning | p. 438 |
| Results | p. 440 |
| Outlook | p. 445 |
| Acknowledgements | p. 446 |
| Bibliography | p. 446 |
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