UNIT 1:
Introduction to mathematical properties of fluid dynamics equations
Classification of PDEs: Elliptic equations with examples from subsonic flow
Parabolic and Hyperbolic equations with examples from viscous and supersonic flows
Initial and boundary conditions in CFD problems
Well-posed and ill-posed problems; physical and numerical implications
Discretization of partial differential equations – concepts and approaches
Grid generation: Introduction, structured and unstructured grids
Single/multi-block, hybrid, and adaptive grids; Introduction to meshless methods
Explicit and implicit finite difference schemes; Source and vortex panel methods
UNIT 2:
Boundary layer equations and their characteristics
Analytical and numerical methods of solution for boundary layers
Implicit time-dependent methods for inviscid compressible flows
Implicit methods for viscous compressible flows
Concept of numerical dissipation and its effects
Stability properties of explicit schemes (CFL condition, von Neumann analysis)
Stability properties of explicit schemes (CFL condition, von Neumann analysis)
Conservative upwind discretization for hyperbolic systems
Further advantages of upwind differencing
