UNIT 1:
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
Explicit finite difference methods of subsonic, supersonic and viscous flows
Implicit and explicit schemes; Source panel method ‐ Vortex panel method
UNIT 2:
Boundary layer equations and methods of solution
Implicit time dependent methods for inviscid compressible flows
Implicit time dependent methods for viscous compressible flows
Concept of numerical dissipation
Stability properties of explicit and implicit methods
Stability properties of explicit and implicit methods
Conservative upwind discretization for hyperbolic systems
UNIT 3:
Finite Element Techniques in Computational Fluid Dynamics
Introduction ‐ Strong and weak formulations of a boundary value problem
Weighted residual formulation - Galerkin formulation
Weighted residual formulation - Galerkin formulation
Piecewise defined shape functions
Implementation of the FEM
UNIT 4:
Finite Volume Techniques ‐ Cell centered formulation
Lax – Wendroff time stepping
Runge‐Kutta time Stepping
Multi‐stage time stepping
Multi‐stage time stepping
Accuracy Cell vertex formulation
FDM ‐like finite volume techniques
UNIT 5:
Pressure and Velocity corrections
Pressure correction equation
SIMPLE algorithm and its variants
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.
