UNIT 1:
Mathematical properties of Fluid Dynamics Equations ‐ Elliptic, Parabolic and Hyperbolic
Explicit finite difference
Grid generation – Introduction, types of grids
Source panel method ‐ Vortex panel method
UNIT 2:
Stability properties of explicit and implicit methods
‐ Concept of numerical dissipation
Boundary layer equations and methods of solution
Further advantages of upwind differencing.
UNIT 3:
Finite Element Techniques in Computational Fluid Dynamics
Implementation of the FEM ‐ The solution procedure.
Piecewise defined shape functions;
‐ Weighted residual formulation ‐Galerkin formulation
UNIT 4:
Lax – Wendroff time stepping, Runge‐Kutta time Stepping ‐ Multi‐stage time stepping
Lax – Wendroff time stepping, Runge‐Kutta time Stepping ‐ Multi‐stage time stepping
Finite Volume Techniques ‐ Cell centered formulation
Accuracy Cell vertex formulation
FDM ‐like finite volume techniques
Central and up‐wind type discretization
UNIT 5:
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
Case study of Stage separation Aerodynamics of future space transport systems
CFD models utilizing algebraic mixing length models
