chapter 1 Introduction 1. 1 insight into power of computational fluid dynamics 1. 2 advantages of CFD 1. 3 typical major goals of computational numeric in aerospace 1. 4 error sources in CFD codes and in wind tunnel data 1. 5 requirement of computing power for CFD 1. 6 CFD applications 1. 7 CFD ideas to understand 1. 8 models of flow 1. 9 substantial derivative (time rate of change following a moving fluid element) 1. 10 divergence of velocity (. . V ) 1. 11 compressibility 1. 12 viscosity 1. 13 governing equations of flow 1. 14 All equations are one: some manipulations 1. 15 integral versus differential form of equations 1. 16 comments on the governing equations 1. 17 Physical boundary conditions 1. 18 forms of governing equations particularly suited for CFD work 1. 19 shock fitting and shock capturing Chapter 2 Mathematical behaviour of partial differential equations and its impact on computational fluid dynamics 2. 1 Introduction 2. 2 method to determine classification of partial differential equations 2. 3 classification of PDEs: impact on physical and computational fluid dynamics 2. 4 essence of discrimination 2. 5 difference equation 2. 6 explicit and implicit approach 2. 7 errors and stability analysis 2. 8 stability regions of standard time-stepping techniques 2. 9 system of Second-Order PDEs 2. 10 canonicalization of PDEs Chapter 3 solution methods of finite-difference equations 3. 1 Introduction 3. 2 Time marching 3. 3 space marching 3. 4 relaxation technique 3. 5 Alternating direction implicit (Adi) method 3. 6 successive over-relaxation/under-relaxation 3. 7 lax-Wendorff method 3. 8 upwind schemes 3. 9 midpoint leapfrog 3. 10 shock capturing 3. 11 Numerical viscosity 3. 12 artificial viscosity 3. 13 conservative smoothing 3. 14 unsteady problem-explicit versus implicit Scheme Chapter 4 grid generation 4. 1 Introduction 4. 2 structured grid generation 4. 3 surface grid generation 4. 4 multiblock grid generation 4. 5 unstructured grid generation 4. 6 multigrid methods: cycling strategies Chapter 5 adaptive grid methods and appropriate transformation 5. 1 Introduction 5. 2 adaptive grids 5. 3 structured grid adaptive methods 5. 4 unstructured adaptive grid methods 5. 5 General transformation of the equations 5. 6 matrices and jacobians 5. 7 generic form of the governing flow equations in strong 5. 8 parallel processing Chapter 6 finite volume methods 6. 1 General conservation laws 6. 2 spatial discrimination ? structured finite volume Scheme 6. 3 temporal discrimination ? structured finite volume Scheme 6. 4 boundary conditions 6. 5 case studies 6. 6 high-resolution schemes Chapter 7 computational fluid dynamics: some applications 7. 1 Numerical dissipation and dispersion 7. 2 approximate factorization 7. 3 flux vector splitting 7. 4 computational solution for the laminar boundary layer 7. 5 application to turbulence 7. 6 computational solution for turbulent boundary layer 7. 7 thermal 7. 8 multi-objective shape optimization 7. 9 Inverse design 7. 10 similarity laws 7. 11 method of characteristics 7. 12 fluid structure interaction appendix 7. 1 appendix 7. 2 design exercise: to design three-dimensional aerofoil shapes for maximum endurance for jet-powered plane references index.