Syllabus

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Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1 hour / session

Note: These recitations and review sessions will not be held every week. They will be used in response to student's requests or the needs of the course and teaching staff, including make-up lectures. Students will be informed in advance when these sessions are planned.

Prerequisites

18.075 and one of the following four courses : 2.006, 2.016, 2.20, or 2.25.

Course Description

This course will provide students with an introduction to numerical methods and MATLAB^®. Topics covered throughout the course will include: errors, condition numbers and roots of equations; Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis, and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; Lagrangian Coherent Structures. Subject includes a final research project.

The specific objectives of the course are:

1. To introduce and develop the main approaches and techniques that constitute the basis of numerical fluid mechanics for engineers and applied scientists.
2. To familiarize students with the numerical implementation of these techniques and numerical schemes, so as to provide them with the means to write their own codes and software, and so acquire the knowledge necessary for the skillful utilization of CFD packages or other more complex software.
3. To cover a range of modern approaches for numerical and computational fluid dynamics, without entering all these topics in detail, but aiming to provide students with a general knowledge and understanding of the subject, including recommendations for further studies.

This course continues to be a work in progress. New curricular materials are being developed for this course, and feedback from students is always welcome and appreciated during the term. For example, recitations and reviews on specific topics can be provided based on requests from students.

Evaluation and Grading

The final course grade will be weighted as follows:

MIT defines the grade structure as:

A: Exceptionally good performance, demonstrating a superior understanding of the subject matter, a foundation of extensive knowledge, and a skillful use of concepts and/or materials.

B: Good performance, demonstrating capacity to use the appropriate concepts, a good understanding of the subject matter, and an ability to handle problems and materials encountered in the subject.

C: Adequate performance, demonstrating an adequate understanding of the subject matter, an ability to handle relatively simple problems, and adequate preparation for moving on to more advanced work in the field.

D: Minimally acceptable performance, demonstrating at least partial familiarity with the subject matter and some capacity to deal with relatively simple problems, but also demonstrating deficiencies serious enough to make it inadvisable to proceed further in the field without additional work.

F: Failure. This grade signifies that the student must repeat the subject to receive credit.

Homework Assignments

Eight problem sets will be given. They will be due within one to two weeks later, depending on the class schedule and holidays. To receive credit, you must hand in your solutions on the due date. No late submissions will be accepted without prior permission.

Solutions to the assignments will normally be available on the due date, and will be posted on the course web page. There may be exceptions to this pattern because of tests, institute holidays, and so on. Graded problem sets will be available in class or upon request; at the next class or within one week after the problem set's due date.

We encourage students to work with each other on the homework assignments, but we do not condone copying. Make your own honest collaborative efforts to contribute to the solution and, based on your own understanding, write up the answers in your own words and style. If you worked closely with other students on a given homework assignment and feel that your understanding was substantially influenced by the mutual learning process, you should cite the names of those students with whom you worked.

While some assignments need a considerable amount of coding, we will not always request that you attach or provide your codes. However, you must be ready to present a clear and operational code if asked.

MATLAB is selected as the course basic coding software. You can use other software with prior approval, but you may have a tougher time. While MATLAB might not be the fastest option for "Run Time"; it often helps concentrate on the algorithms themselves rather than on the "coding" of basic and elementary steps.

Quizzes

There will be two (2) quizzes during the term. These will be closed-book. The necessary material and equation sheets will be provided prior to each quiz.

Project

There will be a final project for this class. Students can select the topic of their project in consultation with the instructor. Possible projects include:

1. Comprehensive reviews of material not covered in detail in class, with some numerical examples;
2. Specific fluid-related problems or questions that are numerically studied or solved by the applications of approaches, methods or schemes covered in class;
3. A combination of i and ii.

Projects will be due at the end of term. If possible, we plan to have a final session where all students will make a presentation of their projects to the whole class and staff. We find that such presentations provide an excellent means for additional learning and sharing.

Primary Texts

Chapra, S., and R. Canale. Numerical Methods for Engineers. 6th ed. McGraw-Hill Higher Education, 2009. ISBN: 9780073401065. (or the 5th edition of this book, 2006).

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

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]

Lomax, H., T. Pulliam, and D. Zingg. Fundamentals of Computational Fluid Dynamics (Scientific Computation). Springer, 2004. ISBN: 9783540416074.

Fluid Dynamics References

Kundu, P. K., and I. M. Cohen. Fluid Mechanics. 4th ed. Academic Press, 2007. ISBN: 9780123737359.

White, F. M. Fluid Mechanics. 7th ed. McGraw-Hill Companies Inc., 2010. ISBN: 9780077422417. (or Sixth Edition, 2006).

Useful MATLAB Texts

Recktenwald, Gerald. Numerical Methods with MATLAB: Implementation and Application. Prentice-Hall Inc., 2000. ISBN: 9780201308600.

Driscoll, T. A. Learning MATLAB. SIAM, 2009, p. 97. ISBN: 9780898716832. [Preview with Google Books]

Chapra, S. C. Applied Numerical Methods with MATLAB for Engineers and Scientists. 3rd ed. McGraw-Hill Companies Inc., 2011. ISBN: 9780073401102. (or Second Edition, 2006).

Other Useful CFD References

Wesseling, Pieter. Principles of Computational Fluid Dynamics. Springer, 2000. ISBN: 9783540678533. [Preview with Google Books]

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

Durran D. R. Numerical Methods for Fluid Dynamics: With Applications in Geophysics. Springer, 2010. ISBN: 9781441964113. [Preview with Google Books]

Griebel, M., T. Dornsheifer, and T. Neunhoeffer. Numerical Simulation in Fluid Dynamics: A Practical Introduction. SIAM, 1997. ISBN: 9780898713985. [Preview with Google Books]

Chung, T. J. Computational Fluid Dynamics. 2nd ed. Cambridge University Press, 2010. ISBN: 9780521769693. (or First Edition, 2002). [Preview with Google Books]

Karniadakis, G. E., and S. J. Sherwin. Spectral/hp Element Methods for Computational Fluid Dynamics (Numerical Mathematics and Scientific Computation). 2nd ed. Oxford Science Publications, 2005. ISBN: 9780198528692.

Pozrikidis, C. Introduction to Finite and Spectral Element Methods using MATLAB. Chapman and Hall/CRC, 2005. ISBN: 9781584885290.

Roache, P. J. Fundamentals of Computational Fluid Dynamics. Hermosa, 1998. ISBN: 9780913478097.

Numerical Linear Algebra Reference

Trefethen, L., and D. Bau. Numerical Linear Algebra. SIAM, 1997. ISBN: 9780898713619. [Preview with Google Books]