Mathematical properties of Fluid Dynamics Equations ‐ Elliptic, Parabolic and Hyperbolic equations‐ Initial and Boundary conditions ‐ Well posed‐ ill Posed problems; Discretization of partial differential equations; Grid generation – Introduction, types of grids – structured, unstructured, single and multi‐block grids, hybrid and adaptive grids; Meshless methods; Explicit finite difference methods of subsonic, supersonic and viscous flows‐ Implicit and explicit schemes; Source panel method ‐ Vortex panel method

Boundary layer equations and methods of solution; Implicit time dependent methods for inviscid and viscous compressible flows ‐ Concept of numerical dissipation ‐‐Stability properties of explicit and implicit methods ‐ Conservative upwind discretization for hyperbolic systems ‐ Further advantages of upwind differencing.

Finite Element Techniques in Computational Fluid Dynamics; Introduction ‐ Strong and weak formulations of a boundary value problem ‐ Strong formulation ‐ Weighted residual formulation ‐Galerkin formulation; Weak formulation ‐ Variational formulation ‐ Piecewise defined shape functions; Implementation of the FEM ‐ The solution procedure.

Finite Volume Techniques ‐ Cell centered formulation ‐ Lax – Wendroff time stepping, Runge‐Kutta time Stepping ‐ Multi‐stage time stepping; Accuracy Cell vertex formulation ‐ Multistage Time Stepping ‐ FDM ‐like finite volume techniques ‐ Central and up‐wind type discretization ‐ Treatment of derivatives.

Pressure and Velocity corrections ‐ Pressure correction equation; SIMPLE algorithm and its variants; PISO algorithms; Turbulence models – algebraic mixing length model, one and two equation models ‐ High and low Reynolds number models – Case study of Stage separation Aerodynamics of future space transport systems.