Spring 2021 - APMA 930 G100

Computational Fluid Dynamics (4)

Class Number: 3623

Delivery Method: Remote


  • Course Times + Location:

    Jan 11 – Apr 16, 2021: Tue, Thu, 2:30–4:20 p.m.



Basic equations governing compressible and incompressible fluid mechanics. Finite difference and finite volume schemes for hyperbolic, elliptic, and parabolic partial differential equations. Practical applications in low Reynolds number flow, high-speed gas dynamics, and porous media flow. Software design and use of public-domain codes. Students with credit for MATH 930 may not complete this course for further credit


This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.

You will need a camera to take photographs of your work. A phone is acceptable.

Computational Fluid Dynamics

This course will introduce students to a variety of computational approaches for solving the partial differential equations governing fluid dynamics, focusing on finite difference and finite volume techniques. Theoretical background material will be introduced as necessary, but the emphasis of the course will be on the numerical methods, their accuracy and stability, and applying them in practical calculations of real fluid flows. Students will gain experience writing their own codes, as well as employing existing open-source software packages. Applications will be drawn from a wide variety of problems arising in wave propagation, incompressible fluids, compressible gas dynamics, and porous media flow. In contrast with the common engineering approaches to teaching CFD, I will not emphasize the study of complex flows in sophisticated geometries using commercial codes, but will focus instead on the design of the underlying algorithms, and carefully assessing their correctness, accuracy, efficiency and robustness.

Prerequisites: Previous courses in ordinary and partial differential equations (such as MATH 310 or MATH 314) are required.  A previous course in fluid dynamics (such as MATH 462) would be an advantage, but is not required.  Some computing experience is highly recommended (with any programming language). The majority of algorithms presented in class will be implemented in MATLAB, although some compiled codes written in C or FORTRAN may also be used.


  • Homework 60%
  • Project 40%





There is no textbook for this course. Material will be drawn from a number of texts, some of which are held on reserve in the library.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:


SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html


Teaching at SFU in spring 2021 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.

Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112).