UNIT 1:
Overview of Computational Fluid Dynamics and its Applications
Importance of Mathematical Models in Fluid Dynamics
Mathematical properties of Fluid Dynamics Equations (Elliptic, Parabolic, Hyperbolic)
Initial and Boundary Conditions: Well-posed and Ill-posed Problems
Introduction to Grid Generation and Types of Grids
Explicit Finite Difference Methods (subsonic/supersonic/viscous flows)
Implicit and Explicit Schemes, Source and Vortex Panel Methods
UNIT 2:
Boundary Layer Theory and Its Importance
Concept of Discretization and Numerical Dissipation
Implicit Time-dependent Methods for Inviscid and Viscous Compressible Flows
Stability Properties of Explicit and Implicit Methods
Conservative Upwind Discretization for Hyperbolic Systems
Advantages of Upwind Differencing
UNIT 3:
Introduction to Finite Element Methods
Strong and Weak Formulations in CFD
Weighted Residual and Galerkin Formulations
Variational Formulation and Shape Functions
Implementation of FEM in CFD
Comparison of FEM with Finite Volume and Finite Difference Methods
UNIT 4:
Introduction to Finite Volume Techniques
Importance of Central and Upwind Discretization
Cell-centered Formulation: Lax-Wendroff and Runge-Kutta Time Stepping
Multi-stage Time Stepping and Its Accuracy
Central and Upwind-type Discretization Techniques
Treatment of Derivatives in FDM-like Finite Volume Techniques
