Welcome to MATH 749 - MATHEMATICAL AND COMPUTATIONAL FLUID DYNAMICS
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
1) Conservation of Mass and Momentum
Eulerian and Lagrangian Descriptions
Euler and Navier-Stokes Equations
boundary and initial conditions
2) Vortex Motion
vorticity and circulation
4) Computational Fluid Dynamics
discretization techniques for PDEs
S. Childress, An Introduction to Theoretical Fluid
Mechanics, American Mathematical Society (Courant Lecture Notes in
Mathematics), 2009 (ISBN 978-0821848883).
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
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.
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
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
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.
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.