Fluid Dynamics

1. Computational Fluid Dynamics (CFD)
   1. Introduction to CFD
      1. Definition and Scope
      2. Historical Development of CFD
      3. Importance in Modern Engineering
   2. Numerical Methods
      1. Finite Difference Method
         1. Basic Concept
         2. Discretization of Derivatives
         3. Stability and Convergence
      2. Finite Volume Method
         1. Control Volume Analysis
         2. Flux Calculations
         3. Conservative Properties
      3. Finite Element Method
         1. Mesh Generation
         2. Basis Functions
         3. Application in Complex Geometries
      4. Comparison of Numerical Methods
         1. Strengths and Weaknesses
         2. Selection Criteria
   3. Turbulence Modeling
      1. Direct Numerical Simulation (DNS)
         1. Characteristics and Limitations
         2. Computational Cost
      2. Large Eddy Simulation (LES)
         1. Filtering and Sub-grid Scales
         2. Applications in High Reynolds Number Flows
      3. Reynolds-Averaged Navier-Stokes (RANS)
         1. Turbulence Closure Models
            1. k-epsilon Model
            2. k-omega Model
            3. Spalart-Allmaras Model
         2. Implementation in Industrial Flows
      4. Hybrid Models
         1. Detached Eddy Simulation (DES)
         2. Delayed Detached Eddy Simulation (DDES)
   4. Grid Generation
      1. Structured Grids
         1. Cartesian Grids
         2. Polar and Cylindrical Grids
      2. Unstructured Grids
         1. Triangular and Tetrahedral Elements
         2. Adaptive Mesh Refinement
      3. Grid Quality and Resolution
         1. Mesh Independence Study
         2. Grid Transformation Techniques
   5. Validation and Verification
      1. Code Verification
         1. Method of Manufactured Solutions
         2. Benchmark Problems
      2. Validation Against Experimental Data
         1. Wind Tunnel Results
         2. Field Measurements
      3. Sensitivity Analysis
         1. Parameter Variation
         2. Impact on Results
      4. Error Sources and Estimation
         1. Numerical Error
         2. Modeling Error
         3. Discretization Error
   6. Post-Processing of CFD Results
      1. Visualization Techniques
         1. Streamlines and Pathlines
         2. Contour and Vector Plots
      2. Data Analysis
         1. Flow Quantities Calculation
         2. Force and Pressure Coefficients
      3. Interpretation of Results
         1. Identifying Flow Patterns
         2. Assessing Design Performance
   7. Software and Computational Resources
      1. Commercial Software Packages
         1. ANSYS Fluent
         2. OpenFOAM
         3. COMSOL
      2. Custom CFD Codes
         1. Development and Application
         2. Integration with In-house Tools
      3. High-Performance Computing (HPC)
         1. Parallel Computing
         2. Cloud-Based Simulations
   8. Challenges and Future Directions
      1. Handling Complex Geometries
      2. Multiscale and Multiphysics Coupling
      3. Uncertainty Quantification
      4. Emerging Applications
         1. Renewable Energy Systems
         2. Biomedical Engineering
      5. Future Trends
         1. Machine Learning in CFD
         2. Real-time Simulation Capabilities