Lecture Notes

Lecture Notes and References

The following table contains the lecture note files and references for this course. For more information about the topics covered in each lecture, please see the course Calendar.

[Chapra and Canale] = Amazon logo Chapra, S., and R. Canale. Numerical Methods for Engineers. 6th ed. McGraw–Hill Higher Education, 2009. ISBN: 9780073401065.

[Ferziger and Peric] = Amazon logo Ferziger, J., and M. Peric. Computational Methods for Fluid Dynamics. 3rd ed. Springer, 2001. ISBN: 9783540420743.

[Cebeci, et al] = Amazon logo Cebeci, T., J. Shao, et al. Computational Fluid Dynamics for Engineers: From Panel to Navier–Stokes Methods with Computer Programs. Springer, 2005. ISBN: 9783540244516. [Preview with Google Books]

LEC # LECTURE TOPICS SLIDES SUPPORTING MATERIALS
1 Introduction to numerical fluid dynamics (PDF - 1.8MB)

MATLAB® scripts:

  • (ZIP) (This file contains: 3 .m files.)

References:

  • [Chapra and Canale]: sections 1.1–1.3 and 3.1–3.4
  • [Ferziger and Peric]: chapters 1–2
2 Approximation and round–off errors; truncation errors, Taylor series and error analysis (PDF - 1.1MB)

MATLAB scripts:

  • (ZIP) (This file contains: 7 .m files.)

References:

  • [Chapra and Canale]: sections 3.1–3.4 and 4.1–4.4
3 Condition numbers and roots of nonlinear equations: bracketing and open methods (PDF - 1.6MB)

MATLAB scripts:

  • (ZIP) (This file contains: 4 .m files.)

References:

  • [Chapra and Canale]: sections 5.1–5.4 and 6.1–6.5
4 Roots of nonlinear equations (PDF - 1.2MB)

MATLAB scripts:

  • (ZIP) (This file contains: 4 .m files.)

References:

  • [Ferziger and Peric]: chapter 1
  • Amazon logo Kundu, P. K., and I. M. Cohen. Chapter 4 in Fluid Mechanics. 4th ed. Academic Press, 2007. ISBN: 9780123737359. [Preview with Google Books]
  • Amazon logo White, F. M. Chapter 4 in Fluid Mechanics. 7th ed. McGraw–Hill Companies Inc., 2010. ISBN: 9780077422417.
5 The Navier–Stokes equations and their approximations (PDF)

References:

  • [Ferziger and Peric]: chapter 1
  • Amazon logo Kundu, P. K., and I. M. Cohen. Chapter 4 in Fluid Mechanics. 4th ed. Academic Press, 2007. ISBN: 9780123737359. [Preview with Google Books]
  • Amazon logo White, F. M. Chapter 4 in Fluid Mechanics. 7th ed. McGraw–Hill Companies Inc., 2010. ISBN: 9780077422417.
6 Fluid flow modeling: the Navier–Stokes equations and their approximations (cont.) (PDF - 1.1MB)

References:

  • [Chapra and Canale]: sections 9.1–9.8
7 Systems of linear equations (PDF - 1.7MB)

MATLAB scripts:

  • (ZIP) (This file contains: 5 .m files.)

References:

  • [Chapra and Canale]: sections 9.1–9.8 and 10.1–10.3
  • [Ferziger and Peric]: chapter 5
8 Systems of linear equations II (PDF - 1.9MB)

MATLAB scripts:

  • (ZIP) (This file contains: 4 .m files.)

References:

  • [Chapra and Canale]: sections 10.1–10.3 and 11.1
9 Systems of linear equations III (PDF - 4.3MB)

References:

  • [Chapra and Canale]: sections 11.1–11.3
10 Systems of linear equations IV (PDF - 1.5MB)

MATLAB scripts:

  • (ZIP) (This file contains: 1 .m file.)

References:

  • [Chapra and Canale]: chapters 14, 23, and 18, and sections 8.1–8.2
  • [Ferziger and Peric]: chapter 3
11 End of linear algebraic systems and finite differences (PDF - 1.0MB)

MATLAB scripts:

  • (ZIP) (This file contains: 2 .m files.)

References:

  • [Chapra and Canale]: chapters 23 and 18
  • [Ferziger and Peric]: chapter 3
  • Amazon logo Lomax, H., T. Pulliam, and D. Zingg. Chapter 3 in Fundamentals of Computational Fluid Dynamics (Scientific Computation). Springer, 2004. ISBN: 9783540416074.
12 Finite differences (PDF - 1.3MB)

MATLAB scripts:

  • (ZIP) (This file contains: 1 .m file.)

References:

  • [Chapra and Canale]: chapters 23 and 18
  • [Ferziger and Peric]: chapter 3
  • Amazon logo Lomax, H., T. Pulliam, and D. Zingg. Chapter 3 in Fundamentals of Computational Fluid Dynamics (Scientific Computation). Springer, 2004. ISBN: 9783540416074.
13 Finite differences (cont.) (PDF - 1.4MB)

References:

  • Amazon logo Lapidus, L., and G. Pinder. Section 4.5 from Numerical Solution of Partial Differential Equations in Science and Engineering. 1st ed. Wiley–Interscience, 1982. ISBN: 9780471098669. [Preview with Google Books]
  • [Ferziger and Peric]: chapter 3
  • Amazon logo Lomax, H., T. Pulliam, and D. Zingg. Chapter 3 in Fundamentals of Computational Fluid Dynamics (Scientific Computation). Springer, 2004. ISBN: 9783540416074.
14 Finite differences (cont.) (PDF - 1.0MB)

References:

  • [Chapra and Canale]: sections 30.1–30.5
  • Amazon logo Lapidus, L., and G. Pinder. Section 4.5 from Numerical Solution of Partial Differential Equations in Science and Engineering. 1st ed. Wiley–Interscience, 1982. ISBN: 9780471098669. [Preview with Google Books]
15 Finite differences (cont.) (PDF)

MATLAB scripts:

  • (ZIP) (This file contains: 2 .m files.)

References:

  • [Chapra and Canale]: sections 29.1–29.5
16 Finite differences (cont.) (PDF - 2.5MB)

MATLAB scripts:

  • (ZIP) (This file contains: 3 .m files.)

References:

  • [Chapra and Canale]: section 29.4
  • [Ferziger and Peric]: chapter 4
  • Amazon logo Lomax, H., T. Pulliam, and D. Zingg. Chapter 5 in Fundamentals of Computational Fluid Dynamics (Scientific Computation). Springer, 2004. ISBN: 9783540416074.
  • [Cebeci, et al]: section 5.6
17 Finite differences (cont.) (PDF - 1.9MB)

MATLAB scripts:

  • (ZIP) (This file contains: 8 .m files.)

References:

  • [Ferziger and Peric]: chapters 4 and 6
  • Amazon logo Lomax, H., T. Pulliam, and D. Zingg. Chapter 5 and 6 in Fundamentals of Computational Fluid Dynamics (Scientific Computation). Springer, 2004. ISBN: 9783540416074.
  • [Chapra and Canale]: sections 25.1–25.2
18 Finite volume methods (PDF)

References:

  • [Ferziger and Peric]: chapter 6
  • Amazon logo Lomax, H., T. Pulliam, and D. Zingg. Chapter 6 in Fundamentals of Computational Fluid Dynamics (Scientific Computation). Springer, 2004. ISBN: 9783540416074.
  • [Chapra and Canale]: sections 25.3–25.5 and chapter 26
19 Finite volume methods (cont.) (PDF)

References:

  • [Cebeci, et al]: chapter 9
  • [Ferziger and Peric]: chapter 8
20 Time–marching methods and ODEs – initial value problems (PDF - 2.1MB)

MATLAB scripts:

  • (ZIP) (This file contains: 6 .m files.)

References:

  • [Chapra and Canale]: sections 31.1–31.4
  • [Cebeci et al]: chapter 6
21 End of time–marching methods, grid generation and complex geometries (PDF - 1.7MB)

References:

  • [Chapra and Canale]: sections 31.1–31.4
  • [Cebeci, et al]: chapter 6
  • Amazon logo Wendt, J. F., ed. Chapter 10 in Computational Fluid Dynamics: An Introduction. Springer, 1996. ISBN: 9780387594712.
  • Chapters 4 and 8 from Lohner
22 Grid generation and intro to FV complex geometries (PDF - 1.4MB)

References:

  • [Cebeci, et al]: chapters 6 and 11
  • [Ferziger and Peric]: chapter 7
23 Grid generation (end), FV on complex geometries and solution to the Navier–Stokes equations (PDF - 1.5MB)

References:

  • [Ferziger and Peric]: chapter 7
  • [Cebeci, et al]: chapter 11
24 Numerical methods for the Navier–Stokes equations (PDF)

References:

  • [Ferziger and Peric]: chapter 7
  • [Cebeci, et al]: chapter 11
25 Navier–Stokes equations and intro to finite elements (PDF)

References:

  • [Cebeci, et al]: chapter 7
  • [Chapra and Canale]: sections 27.1–27.3
26 Navier–Stokes equations and intro to finite elements (cont.) (PDF)

References:

  • [Ferziger and Peric]: chapter 9
  • [Cebeci, et al]: chapter 3
27 Finite elements and intro to turbulent flows (PDF - 1.4MB)

References:

  • [Chapra and Canale]: chapter 31
  • [Ferziger and Peric]: chapter 9
  • Amazon logo Versteeg, H., and W. Malalasekra. Chapter 3 in An Introduction to Computational Fluid Dynamics: The Finite Volume Method. 2nd ed. Prentice Hall, 2007. ISBN: 9780131274983.
  • Amazon logo Kundu, P. K., and I. M. Cohen. Chapter 4 in Fluid Mechanics. 4th ed. Academic Press, 2007. ISBN: 9780123737359. [Preview with Google Books]
  • [Cebeci, et al]: chapter 3
28 Turbulent flows and their numerical modeling (PDF)

References:

  • [Ferziger and Peric]: chapter 9
  • Amazon logo Versteeg, H., and W. Malalasekra. Chapter 3 in An Introduction to Computational Fluid Dynamics: The Finite Volume Method. 2nd ed. Prentice Hall, 2007. ISBN: 9780131274983.
  • Amazon logo Kundu, P. K., and I. M. Cohen. Chapter 4 in Fluid Mechanics. 4th ed. Academic Press, 2007. ISBN: 9780123737359. [Preview with Google Books]
  • [Cebeci, et al]: chapter 3