## Aerospace Engineering  ## What is Aerospace Engineering?

Aerospace engineering is the primary field of engineering concerned with the design, development, testing, and production of aircraft, spacecraft, and related systems and equipment. The field has traditionally focused on problems related to atmospheric and space flight, with two major and overlapping branches: aeronautical engineering and astronautical engineering.

Aeronautical Engineering focuses on the theory, technology, and practice of flight within the earth’s atmosphere.

Astronautical Engineering focuses on the science and technology of spacecraft and launch vehicles.

### What does an aerospace engineer do?

Aerospace engineers develop leading-edge technologies and integrate them into aerospace vehicle systems used for transportation, communications, exploration, and defense applications. This involves the design and manufacturing of aircraft, spacecraft, propulsion systems, satellites, and missiles, as well as the design and testing of aircraft and aerospace products, components, and subassemblies.

Successful aerospace engineers possess in-depth skills in, and an understanding of, aerodynamics, materials and structures, propulsion, vehicle dynamics and control, and software.

#### Contents covered in the Aerospace Engineering study material

Chapter 1. Introduction 10

1.1. What is Computational Fluid Dynamics? 10

1.2. Modelling the Universe 11

1.3. How do we develop models? 13

1.4. Modelling on the Computer 18

1.5. Important ideas from this chapter 24

Chapter 2. Representations on the Computer 25

2.1. Representing Numbers on the Computer 25

2.2. Representing Matrices and Arrays on the Computer 31

2.3. Representing Intervals and Functions on the Computer 34

2.4. Functions as a Basis: Box Functions 40

2.5. Linear Approximations: Hat Functions 48

2.6. Higher-Order Approximations 59

2.7. Local Error Estimates of Approximations 64

2.8. Representing Derivatives – Finite Differences 67

2.9. Differential Equations 77

2.10. Grid Generation I 78

2.11. Important ideas from this chapter 80

Chapter 3. Simple Problems 81

3.1. Laplace’s Equation 81

3.2. Convergence of Iterative Schemes 92

3.3. Properties Of Solutions To Laplace’s Equation 97

3.4. Accelerating Convergence 98

3.5. Neumann Boundary Conditions 105

3.6. First Order Wave Equation 106

3.7. Numerical Solution to Wave Equation: Stability Analysis 119

3.8. Numerical Solution to Wave Equation: Consistency 125

3.9. Numerical Solution to Wave Equation: Dissipation, Dispersion 128

3.10. Solution to Heat Equation 137

3.11. A Sampling of Techniques 141

3.12. Boundary Conditions 145

3.13. A Generalised First Order Wave Equation 148

3.14. The “Delta” form 152

3.15. The One-Dimensional Second Order Wave Equation 156

3.16. Important ideas from this chapter 158

Chapter 4. One-Dimensional Inviscid Flow 160

4.1. What is one-dimensional flow? 161

4.2. Analysis of the One-dimensional Equations 165

4.3. A Numerical Scheme 174

4.4. Boundary Conditions 176

4.5. The Delta Form 179

4.6. Boundary Conditions Revisited 182

4.7. Running the Code 188

4.8. Preconditioning 188

4.9. Finite Volume Method 193

4.10. Quasi-One-Dimensional Flow 196

4.11. Important ideas from this chapter 197

Chapter 5. Tensors and the Equations of Fluid Motion 198

5.1. Laplace Equation Revisited 198

5.2. Tensor Calculus 203

5.3. Equations of Fluid Motion 216

5.4. Important ideas from this chapter 225

Chapter 6. Multi-dimensional flows and Grid Generation 226

6.1. Finite Volume Method 226

6.2. Finite Difference Methods 233

6.3. Grid Generation 240

6.4. Why Grid Generation? 241

6.5. A Brief Introduction to Geometry 242

6.6. Structured Grids 250

6.7. Generating Two Dimensional Unstructured Grids 255

6.8. Three Dimensional Problems 268

6.9. Hybrid Grids 271

6.10. Overset grids 273

6.11. Important ideas from this chapter 274

7.1. Variational Techniques 275

7.2. Random Walk 288

7.3. Multi-grid techniques 291

7.5. Standard Schemes? 297

7.6. Pseudo Time stepping 298

7.7. Important ideas from this chapter 302

Chapter 8. Closure 303

8.1. Validating Results 303

8.2. Computation, Experiment, Theory 305

Appendix A. Computers 307

A.1. How do we actually write these programs? 309

A.2. Programming 316

A.3. Parallel Programming 317

Appendix B. Some Mathematical Background 320

B.1. Complex Variables 320

B.2. Matrices 323

B.3. Fourier Series 330

Bibliography 333