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 equation – Reconstruction-evolution – Upwind methods – Boundary conditions – Numerical solution of compressible Navier-Stokes equations – Turbulence Modeling: RANS, LES, DNS – Higher-order methods – Uncertainty in

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

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.

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.

Review of Single-Phase Flows: one dimensional conservation equations – introduction to two-phase flows – flow regimes.

Flow Models for Two-Phase Flows: one-dimensional homogeneous flow model – separated flow model – drift flux model – simplified treatment of bubbly, slug, and annular flows – flow regime maps – transition criterion – pressure drop correlations and void fraction correlation – phenomenological description of flooding – critical two-phase flows – prediction models.

Introduction – materials deformation and fracture phenomena – strength of materials: flaws, defects, and a perfect material, brittle vs ductile material behavior – the need for atomistic simulations – basic atomistic modeling – classical molecular dynamics – interatomic potential, numerical implementation – visualisation – atomistic elasticity – the virial stress and strain – multiscale modeling and simulation methods – deformation and dynamical failure of brittle and ductile materials – applications.

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.

Introduction – linear programming – duality and sensitivity analysis – transportation and assignment problems – goal programming – integer programming – network optimization models – dynamic programming – theory of games – queuing theory – simulation – nontraditional optimization algorithms.

Basics of acoustics – general theory of aerodynamic sound – flow and acoustic interactions – feedback phenomenon – supersonic jet noise – sonic boom – noise radiation from rotors and fans – aeroacoustic measurements.

Introduction to Hypersonic Flows – Inviscid Hypersonic Flow: Newtonian flow, Mach number independence, Hypersonic similarity, Blast wave theory, Hypersonic small disturbance theory, Stagnation region flow – Viscous Hypersonic Flow: Similarity parameters, Self-similar solutions, Hypersonic turbulent boundary layer, Reference temperature method, Stagnation region flow field, Viscous interactions – Real Gas effects: Inviscid equilibrium and non-equilibrium flows, Viscous high temperature flows – Experimental facilities – Hypersonic design considerations.

Introduction Spacecraft Thermal Control: need of spacecraft thermal control – temperature specification – energy balance in a spacecraft – modes of heat transfer – factors that influence energy balance in a spacecraft – principles of spacecraft thermal control.