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. McGrawHill 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. Wileyinterscience, 1999. ISBN: 9780471359449.
[Cebeci et al.] = Cebeci, Tuncer, Jian P. Shao, et al. Computational Fluid Dynamics for Engineers: From Panel to Navierstokes 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 Roundoff Errors. Number Representations. Errors of Numerical Operations. 
MATLAB® Scripts (ZIP) (This file contains: 3 .m files.) 
[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 Nonlinear 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 Nonlinear Equations, Bracketing Methods: Bisection / False Position. Open Methods: Openpoint Iteration / Newtonraphson / 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: Navierstokes 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 Navierstokes 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, Tridiagonal Systems, General Banded Matrices, Symmetric, Positivedefinite 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, Gaussseidel Iteration, Convergence, Successive Overrelaxation 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, Preconditioning. Krylov Methods. Finitedifferences (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, Nonuniform 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  Finitedifferences: 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, Fluxcorrected 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 
Recitationfinite 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. Rungekutta 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. Pressurecorrection, 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. Computational Techniques for Fluid Dynamics, Vol. 1: Fundamental and General Techniques. Springer, 2013. ISBN: 9783540530589. [Preview with Google Books] [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. Fluid Dynamics with a Computational Perspective. Cambridge University Press, 2007. ISBN: 9780521850179. [Preview with Google Books] 