Panel methods – Unsteady potential flows – Compressible flow over wings – Axisymmetric flows and slender body theories – Boundary layer analysis – Viscous-inviscid coupling – Flight vehicle aerody- namics – Rotor aerodynamics – Low Reynolds number aerodynamics – Flapping wings – Two- and three-dimensional flow separation.

Introduction to stability – Review of dynamical systems concepts – Instabilities of fluids at rest – Stability of open shear flows: Inviscid and viscous theory, spatio-temporal stability analysis (absolute and convective instabilities) – Parabolized stability equation – Transient growth – Introduction to global instabilities.

Governing equations for viscous fluid flow – Heat conduction and compressibility – Exact solutions – Laminar boundary layer approximations – Similar and nonsimilar boundary layers – Momentum integral methods – Separation of boundary layer – Compressible boundary layer equations – Recov- ery factor – Reynolds analogy – Similar solutions – Stability of boundary layer flows: Transition prediction and bypass transition – Turbulent Flows: Phenomenological theories – Reynolds stress – Turbulent boundary layer – Momentum integral methods – Turbulent free shear layer – Flow separation.

Multidisciplinary Design Optimization (MDO): Need and importance – Coupled systems – Analyser vs. evaluator – Single vs. bi-level optimisation – Nested vs.

General features and applications of high temperature flows – Equilibrium Kinetic Theory: Maxwellian distribution, collision rates and mean free path – Chemical thermodynamics – Mixture of perfect gases, law of mass action – Statistical Mechanics: Enumeration of micro-states, energy distribution, contribution of internal structure – Equilibrium Flow: Ideal dissociating gas, equilibrium shock wave relations, nozzle flows – Vibrational and chemical rate processes – Flows with vibrational and chemical non-equilibrium.

Launch vehicle ascent trajectory design – Reentry trajectory design – Low thrust trajectory design – Satellite constellation design – Rendezvous mission design – Ballistic lunar and interplanetary trajectory design – Basics of optimal control theory – Mission design elements for various missions – Space flight trajectory optimization – Direct and indirect optimization techniques – Restricted 3-body problem – Lagrangian points – Mission design to Lagrangian point.

Problem formulation – Performance measures – Selection of performance measures – Dynamics programming – Optimal control law – Application to a routing problem – Recurrence relations – Computational procedures – Alternative approach through Hamiltonial-Jacobi-Bellman equation – Review of Calculus of Variations: Functionals involving several independent functions – Constrained minimization of functional – Optimal control: Variational approach – Necessary condition for opti- mal control – Pontryagin’s minimum principle – Additional necessary conditions – Minimum time problems – Optimal control

Principles of Inertial Navigation: Components, two-dimensional navigation – Coordinate systems – 3D strapdown navigation system – Strapdown system mechanizations – Attitude representation – Navigation equations expressed in component form – Effects of elliptic earth – Inertial Sensors: Gy- roscope principles, single-axis rate gyroscope, accelerometers, rate integrating gyroscope – Elements of guidance system – Guidance phases – Guidance trajectories – Guidance sensors – Classification of Guidance and Navigation Systems: Basic navigation systems, combined navigation systems – Clas- sificatio

Basic equations – Hierarchy of mathematical models – Mathematical nature of flow equations and boundary conditions – Finite difference and finite volume methods – Analysis of Schemes: Numerical errors, stability, numerical dissipation – Grid generation – Wave equation – Numerical Solution of Compressible Euler Equation: Discontinuities and entropy, mathematical properties of Euler equa- tion – Reconstruction-evolution – Upwind methods – Boundary conditions – Numerical solution of compressible Navier-Stokes equations – Turbulence Modeling: RANS, LES, DNS – Higher-order methods – Uncertainty

Introduction to turbulence – Equations of fluid motion – Statistical description of turbulent flows – Mean-flow equations – Space and time scales of turbulent motion – Jets, wakes and boundary layers – Coherent structures – Spectral dynamics – Homogeneous and isotropic turbulence – Two-dimensional turbulence – Coherent structures – Vorticity dynamics – Intermittency – Modeling of turbulent flows.