1. Introduction to Computational Fluid Dynamics. 2. Classification of Fluid Flow Problems and Boundary Conditions. 3. Finite Difference Method. 4. Time-Stepping Techniques.

5. Preserving Oscillatory Accuracy in Numerical Time-Stepping. 6. Boundary Value Problems. 7. Advection Equation. 8. Diffusion Problem.

9. Stabilizing Explicit Schemes with Hyperviscosity and Filtering. 10. 2D Unsteady Parabolic Problems. 11. Linear Advection-Diffusion Equation. 12. The Viscous Burgers Equation.

13. Elliptic Partial Differential Equations and Grid Arrangement Strategies. 14. Iterative Methods for Elliptic PDEs: Laplace and Poisson Solvers. 15. Pressure-Velocity Coupling in Incompressible Flows: Finite Difference Method. 16. Classical Finite Difference Methods for Hyperbolic PDEs and Discontinuities.

17. Finite Volume Method I: Introduction. 18. Finite Volume Method II: Pressure-Velocity Coupling in Incompressible Flows. 19. Finite Volume Methods III: Flow and Discontinuities. 20. Turbulence Models.

21. Direct and Large Eddy Simulations. Appendix I. Grid Sensitivity Analysis and Grid Convergence Index (GCI). Appendix II. Grid Independence Analysis in LES Investigation.