computational fluid dynamics

Foundations (Beginner Level)

1. Introduction to CFD
   • What is CFD?
   • Applications in industry and research
   • Advantages and limitations

1. Fluid Mechanics Refresher
   • Continuity equation
   • Navier–Stokes equations
   • Boundary conditions and types of flows

1. Mathematical Foundations
   • Partial differential equations (PDEs)
   • Finite difference method (FDM) basics
   • Taylor series and truncation error

1. Discretization Techniques
   • Finite Difference Method (FDM)
   • Grid generation (structured grids)
   • Time-stepping methods (explicit vs implicit)

1. Simple 1D Problems
   • Heat conduction equation
   • 1D convection-diffusion
   • Upwind vs central differencing schemes
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Core CFD (Intermediate Level)

1. Finite Volume Method (FVM)
   • Control volume approach
   • Conservation laws
   • Flux calculations

1. Numerical Schemes
   • Upwind, QUICK, and TVD schemes
   • Stability analysis (CFL condition)
   • Iterative solvers: Gauss-Seidel, SOR

1. Turbulence Modeling
   • Laminar vs turbulent flow
   • RANS, k-ε, k-ω models
   • Wall functions

1. Boundary Conditions
   • Inflow/outflow, wall, symmetry
   • Pressure-velocity coupling (SIMPLE algorithm)

1. Grid Generation and Quality
   • Structured vs unstructured grids
   • Mesh quality metrics (orthogonality, skewness)

Advanced Topics

1. Compressible Flows
   • Shock waves
   • Mach number and flow regimes
   • Godunov schemes and flux limiters

1. Multiphase Flows
   • Volume of Fluid (VOF)
   • Level-set methods
   • Interface tracking

1. Advanced Turbulence Modeling
   • LES (Large Eddy Simulation)
   • DNS (Direct Numerical Simulation)

1. CFD in Heat Transfer
   • Conjugate heat transfer (CHT)
   • Radiative heat transfer

1. Optimization & Machine Learning in CFD
   • Design optimization via CFD
   • Surrogate models and neural networks
   • Reduced-order modeling