Fall 2013 Edition
Time & Place: Wednesdays 10:30-12:30 in HH 312 and Fridays 12:30-13:30 in HH/410

Instructor: Dr. Bartosz Protas
Office: HH 326, Ext. 24116
Office hours: Wednesday 9:30-10:30, Friday 10:30-11:30, or by appointment


  • Lecture notes and a number of MATLAB codes concerning computational techniques are already available (see links on the left)

  • A selection of possible problems for the final projects has been posted (see "Term Projects" on the left)

    Outline of the Course:

    In this course we will survey mathematical and computational aspects of incompressible fluid mechanics. The course will focus on the development and properties of mathematical models of fluid flows, such as the Euler and Navier-Stokes equations, and its various simplifications relevant to potential, creeping and boundary-layer flows. In addition to presenting standard theories and known results we will also discuss a number of open problems. In the second part of the course we will review computational approaches relevant to the study of fluid flows emphasizing challenges specific to this field. The specific topics that will be discussed include (optimistic variant):

    1) Conservation of Mass and Momentum
         a) Eulerian and Lagrangian Descriptions
         b) Euler and Navier-Stokes Equations
         c) boundary and initial conditions
    2) Vortex Motion
         a) vorticity and circulation
         b) Helmholtz' Laws
         c) N-vortex problem
    3) Approximations
         a) potential flows
         b) Stokes flows
         c) boundary layers
    4) Computational Fluid Dynamics
         a) discretization techniques for PDEs
         b) enforcing incompressibility
         c) vortex methods

    Primary Reference:

         a) S. Childress, An Introduction to Theoretical Fluid Mechanics, American Mathematical Society (Courant Lecture Notes in Mathematics), 2009 (ISBN 978-0821848883).

    Supplemental References:

         b) D. J. Acheson, Elementary Fluid Dynamics, Oxford University Press, 2009, (ISBN 0198596790).
         c) P. Wesseling, Principles of Computational Fluid Dynamics, Springer, 2001 (ISBN 3540678530).
         d) J. Serrin, Mathematical Principles of Classical Fluid Mechanics, in Encyclopedia of Physics / Handbuch der Physik Volume 3 / 8 / 1, 1959, pp 125-263.

    In addition to the above references, sets of lecture notes and example MATLAB codes will be made available to students on the course webpage.


    Partial Differential Equations, elementary Physics, Numerical Analysis with basic programming skills in MATLAB


    The final grades will be based on
         a) two 20 min quizzes (2 x 10% = 20%),
         a) two homework assignments (2 x 15% = 30%),
         b) a take-home final project (50%).

    The tentative quiz and homework due dates:
         i) Quiz #1 - Friday, October 25
         ii) Quiz #2 - Friday, November 29
         iii) Homework Assignment #1 - Wednesday, October 2 (distributed) / Wednesday, October 9 (due)
         iv) Homework Assignment #2 - Wednesday, October 30 (distributed) / Wednesday, November 6 (due)

    I reserve the right to alter your final grade, in which case, however, the grade may only be increased.

    Academic Integrity:

    You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity.

    Academic dishonesty is to knowingly act or fail to act in a way that results or could result in unearned academic credit or advantage. This behaviour can result in serious consequences, e.g., the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads: "Grade of F assigned for academic dishonesty"), and/or suspension or expulsion from the university.

    It is your responsibility to understand what constitutes academic dishonesty. For information on the various types of academic dishonesty please refer to the Academic Integrity Policy,. The following illustrates only three forms of academic dishonesty:
         1) Plagiarism, e.g., the submission of work that is not one's own or for which other credit has been obtained.
         2) Improper collaboration in group work.
         3) Copying or using unauthorized aids in tests and examinations.

    Important Notice:

    The instructor and university reserve the right to modify elements of the course during the term. The university may change the dates and deadlines for any or all courses in extreme circumstances. If either type of modification becomes necessary, reasonable notice and communication with the students will be given with explanation and the opportunity to comment on changes. It is the responsibility of the student to check their McMaster email and course websites weekly during the term and to note any changes.