## References Key

[Chapra and Canale] = Chapra, Steven, and Raymond Canale. *Numerical Methods for Engineers*. 7th ed. McGraw–Hill Higher Education, 2014. ISBN: 9780073397924.

[Ferziger and Peric] = Ferziger, Joel H., and Milovan Peric. *Computational Methods for Fluid Dynamics*. 3rd ed. Springer, 2013. ISBN: 9783540420743.

[Kundu et al.] = Kundu, Pijush K., Ira M. Cohen, and David R. Dowling. *Fluid Mechanics*. 6th ed. Academic Press, 2015. ISBN: 9780124059351. [Preview with Google Books]

[White] = White, Frank. *Fluid Mechanics*. 7th ed. McGraw-Hill Education, 2010. ISBN: 9780077422417.

[Lomax et al.] = Lomax, Harvard, Thomas H. Pulliam, and David W. Zingg. *Fundmentals of Computational Fluid Dynamics*. Springer, 2004. ISBN: 9783540416074.

[Lapidus and Pinder] = Lapidus, Leon, and George F. Pinder. *Numerical Solution of Partial Differential Equations in Science and Engineering*. Wiley-interscience, 1999. ISBN: 9780471359449.

[Cebeci et al.] = Cebeci, Tuncer, Jian P. Shao, et al. *Computational Fluid Dynamics for Engineers: From Panel to Navier-stokes Methods with Computer Programs*. Springer, 2005. ISBN: 9783540244516.

[Wendt] = Wendt, John. *Computational Fluid Dynamics: An Introduction*. Springer, 2008. ISBN: 9783540850557. [Preview with Google Books]

[Löhner] = Löhner, Rainald. *Applied Computational Fluid Dynamics Techniques: An Introduction Based on Finite Element Methods*. Wiley, 2008. ISBN: 9780470519073.

[Versteeg and Malalasekera] = Versteeg, H., and W. Malalasekera. *An Introduction to Computational Fluid Dynamics: The Finite Volume Method*. 2nd ed. Prentice Hall, 2007. ISBN: 9780131274983.

Lec # | TOPICS | LECTURE SLIDES and MATLAB SCRIPTS | READINGS and REFERENCES |
---|---|---|---|

1 | Introduction to Numerical Fluid Mechanics: Models to Simulations, Error Types. Approximation and Round-off Errors. Number Representations. Errors of Numerical Operations. | MATLAB | [Chapra and Canale] Sections 1.1–1.3 and 3.1–3.4. [Ferziger and Peric] Chapters 1 and 2. |

2 | Recursion. Truncation Errors, Taylor Series and Error Analysis. Error Propagation and Estimation. Condition Numbers. Roots of Non-linear Equations–introduction and Bracketing Methods. | MATLAB Scripts (ZIP) (This file contains: 6 .m files.) | [Chapra and Canale] Sections 3.1–3.4 and 4.1–4.4. |

3 | Roots of Non-linear Equations, Bracketing Methods: Bisection / False Position. Open Methods: Open-point Iteration / Newton-raphson / Secant Methods, Extension to Systems of Equations. | MATLAB Scripts (ZIP) (This file contains: 4 .m files.) | [Chapra and Canale] Sections 5.1–5.4 and 6.1–6.5. |

R2 | Review: Navier-stokes Equations and their Approximations. Conservation Laws, Material Derivative, Reynolds Transport Theorem, Constitutive Equations. | [Ferziger and Peric] Chapter 1. [Kundu et al.] Chapter 4. [White] Chapter 4. | |

4 | Systems of Linear Equations: Motivations and Plans, Direct Methods, Gauss Elimination. | MATLAB Scripts (ZIP) (This file contains: 4 .m files.) | [Chapra and Canale] Sections 9.1–9.8. |

5 | Systems of Linear Equations. Gaussian Elimination (Special Cases, Multiple Right Hand Sides). LU Decomposition and Factorization, Pivoting. Error Analysis for Linear Systems. Operations Counts. | MATLAB Scripts (ZIP) (This file contains: 5 .m files.) | [Chapra and Canale] Sections 9.1–9.8 and 10.1–10.3. [Ferziger and Peric] Chapter 5. |

R3 | End of Navier-stokes Review (if needed). Compressible and Incompressible Flows, Vorticity, Euler's Equations, Potential Flows and (boundary) Integral Equations. | [Ferziger and Peric] Chapter 1. [Kundu et al.] Chapter 4. [White] Chapter 4. | |

6 | Systems of Linear Equations. Special Matrices: LU Decompositions, Tri-diagonal Systems, General Banded Matrices, Symmetric, Positive-definite Matrices. Introduction to Iterative Methods. | MATLAB Scripts (ZIP) (This file contains: 4 .m files.) | [Chapra and Canale] Sections 10.1–10.3 and 11.1. |

7 | Systems of Linear Equations. Iterative Methods: Jacobi's Method, Gauss-seidel Iteration, Convergence, Successive Over-relaxation Methods, Gradient Methods, Stop Criteria, Examples. | Lecture 7 (PDF) | [Chapra and Canale] Sections 11.1–11.3. |

8 | End of Systems of Linear Equations: Gradient Methods, Pre-conditioning. Krylov Methods. Finite-differences (FD): Classification of PDEs and Examples, Error Types and Discretization Properties. | MATLAB Scripts (ZIP) (This file contains: 2 .m files.) | [Chapra and Canale] Chapters 14, 18, and 23, and Sections 8.1–8.2. [Ferziger and Peric] Chapter 3. |

9 | FD Schemes: Finite Difference Based on Taylor Series for Higher Order Accuracy Differences. Examples. Taylor Tables or Method of Undetermined Coefficients. | Lecture 9 (PDF) | [Chapra and Canale] Chapters 18 and 23. [Ferziger and Peric] Chapter 3. |

10 | FD Schemes: Polynomial Approximations (Newton, Lagrange, Hermite and Pade Schemes), Iterative Improvements and Extrapolations, Boundary Conditions, Non-uniform Grids, Grid Refinement. | MATLAB Scripts (ZIP) (This file contains: 1 .m files.) | [Chapra and Canale] Chapters 18 and 23. [Ferziger and Peric] Chapter 3. [Lomax et al.] Chapter 3. |

11 | Finite-differences: Fourier Error Analysis, Introduction to Stability: Heuristic, Energy and Von Neumann Methods, Hyperbolic PDEs, Characteristics. | Lecture 11 (PDF) | [Lapidus and Pinder] Section 4.5. [Ferziger and Peric] Chapter 3. [Lomax et al.] Chapter 3. |

12 | Stability, Hyperbolic Eqns. Revisited, CFL Condition and Von Neumann Stability, Elliptic Equations Revisited and FD Schemes. | Lecture 12 (PDF) | [Chapra and Canale] Sections 30.1–30.5. [Lapidus and Pinder] Section 4.5. |

13 | End of Elliptic / Hyperbolic Equations, Special Advection Schemes (Donor Cell, Flux-corrected Transport, WENO), Parabolic Equations Revisited and Numerical FD Schemes. | MATLAB Scripts (ZIP) (This file contains: 2 .m files.) | [Chapra and Canale] Sections 29.1–29.5. |

14 | Finite Volume Methods. | MATLAB Scripts (ZIP) (This file contains: 9 .m files.) | [Chapra and Canale] Section 29.4. [Ferziger and Peric] Chapter 4. [Lomax et al.] Chapter 5. [Cebeci et al.] Chapter 5.6. |

R8 | Recitation-finite Volume Methods (cont.) | [Ferziger and Peric] Chapter 4. [Lomax et al.] Chapter 5. | |

15 | Methods for Unsteady Problems. Time Marching Methods. Ordinary Differential Equations (ODEs). Initial Value Problems (IVPs). Euler's Method. Runge-kutta Methods. | Lecture 15 (PDF - 1.2MB) | [Ferziger and Peric] Chapter 6. [Lomax et al.] Chapter 6. [Chapra and Canale] Sections 25.1–25.5. |

16 | Time Marching (cont.): Higher Order ODEs, Stiffness and Multistep Methods. Solutions of the Navier Stokes Equation, Incompressible and Compressible. | Lecture 16 (PDF) | [Chapra and Canale] Chapter 26. [Ferziger and Peric] Chapter 7. [Cebeci et al.] Chapter 11. |

17 | Solutions of the Navier Stokes Equation: Incompressible and Compressible. Pressure-correction, Fractional Step. | Lecture 17 (PDF- 1.2MB) | [Ferziger and Peric] Chapter 7. [Cebeci et al.] Chapter 11. |

18 | Solutions of the Navier Stokes Equation: Incompressible and Compressible. Vorticity, Artificial Compressibility and Other Methods. | Lecture 18 (PDF - 1.1MB) | [Ferziger and Peric] Chapter 7. [Cebeci et al.] Chapter 11. |

19 | Grid Generation and complex Geometries. | Lecture 19 (PDF - 1.1MB) | [Ferziger and Peric] Chapter 8. [Cebeci et al.] Chapter 9. |

20 | Finite Volume on Complex Geometries. Finite Element Methods: Introduction. Fluid Applications. | MATLAB Scripts (ZIP) (This file contains: 6 .m files.) | [Chapra and Canale] Sections 31.1–31.4. Fletcher, C. A. J. [Wendt] Chapter 10. [Löhner] Chapters 4 and 8. |

21 | Finite Element Methods (cont.): Continuous Galerkin and Discontinuous Galerkin Methods. Spectral Methods. | Lecture 21 (PDF - 2.2MB) | [Cebeci et al.] Chapter 6. [Wendt] Chapter 10. [Löhner] Chapters 4 and 8. |

22 | Lecture / Recitation. Inviscid Flow Equations: Boundary Element Methods. Panel Methods. | Lecture 22 (PDF - 1.8MB) | [Cebeci et al.] Chapters 6 and 11. [Ferziger and Peric] Chapter 7. |

R13 | Recitation–Special Topics, Boundary Layer Equations, ODEs–Boundary Value Problems. | [Cebeci et al.] Chapter 7. [Chapra and Canale] Sections 27.1–27.3. | |

23 | Turbulent Flows: Models and Numerical Simulations. | Lecture 23 (PDF - 2.2MB) | [Ferziger and Peric] Chapter 9. [Cebeci et al.] Chapter 3. |

24 | Finite Volume on Complex Geometries: Turbulent Flows and Their Numerical Modeling. | Lecture 24 (PDF - 1.3MB) | [Ferziger and Peric] Chapters 8 and 9. [Versteeg and Malalasekera] Chapter 3. [Kundu et al.] Chapter 4. [Cebeci et al.] Chapter 3. |

25 | Turbulence | Lecture 25 (PDF) | [Ferziger and Peric] Chapter 9. [Versteeg and Malalasekera] Chapter 3. [Kundu et al.] Chapter 4. [Cebeci et al.] Chapter 3. Durbin, Paul A., and Gorazd Medic. |