Numerical Fluid Mechanics

Lecture Notes and References

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.	Lecture 1 (PDF - 3.1MB) 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 Non-linear Equations–introduction and Bracketing Methods.	Lecture 2 (PDF) 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.	Lecture 3 (PDF) 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.	Lecture 4 (PDF) 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.	Lecture 5 (PDF) 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.	Lecture 6 (PDF) 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.	Lecture 8 (PDF) 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.	Lecture 10 (PDF - 1.7MB) 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.	Lecture 13 (PDF) MATLAB Scripts (ZIP) (This file contains: 2 .m files.)	[Chapra and Canale] Sections 29.1–29.5.
14	Finite Volume Methods.	Lecture 14 (PDF - 1.3MB) 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.	Lecture 20 (PDF - 1.6MB) 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]