Course syllabus

MTF072 Computational fluid dynamics (CFD) Sp2 ht19 (7.5 hp)

The course is offered by the department of Mechanics and Maritime Sciences

Contact details

Course purpose

The course gives a thorough knowledge and understanding of the finite volume method for computational fluid dynamics (CFD).


Schedule page

Course literature

The course material consists of detailed lecture notes and the following textbook:

H.K. Versteeg and W. Malalasekera. An Introduction to Computational Fluid Dynamics – The Finite Volume Method. Second edition. Prentice Hall, US (2007), ISBN: 9780131274983 (e.g. available at Cremona and Internet, but also available for free as on-line e-book through Chalmers' library - search for "versteeg malalasekera" at the top of

No course material can be used at the written examination.

Course design

Lectures are given each week (normally two lectures of two hours each). A reading guide and detailed learning outcomes help the students work through the theory. Three computer exercises form a large part of the course. The computer exercises should be carried out in groups of two students. The computer exercise reports should be handed in through the course homepage and must be passed by the teacher/assistant. If they are failed then need to be improved and handed in again. The reports should also be presented orally. The oral presentations are in form of a very short presentation by the students, followed by questioning by the teacher/assistants. The final assessment and grade is by a written examination. The examination includes both fundamental theoretical understanding, derivations, and implementations (that should be possible to answer by students who have actively worked in the computer exercises).

The fundamental equations for fluid flow are recalled, and written in a general convection-diffusion for that is useful for the understanding of how the equations are solved. The equations must be discretized and reorganized to linear equation systems, that can be solved using boundary conditions and source terms. We start by discretizing steady-state diffusion equations (e.g. steady-state heat conduction), applying boundary conditions and source terms, and solving the equations using linear solvers. We then add the convection term and study how the discretization must be adapted to the behaviour of convection. In fluid flow problems, several equations are coupled. We study the coupling between pressure and velocity, which requires a special treatment to give stable results. We learn how to discretize the time derivative in different ways for unsteady problems. We finally see how turbulence is modelled by turbulence models that fit nicely into the concept of the finite volume method.

Changes made since the last occasion

During the 2019 course:

  • The main course development is to improve the detailed learning outcomes that help the student work through the theory, in order to prepare for the exam. The students need to actively work more with the lectured material, since that forms a large part of the written examination.
  • After the first computer exercise we will add a demonstration of recommended ways of programming. It is done at that time, since then the students have some experience from the first task, and then they can improve their programming skills for the coming two tasks. For this to fit in the schedule, the first presentation is removed, and the students instead have to hand in the first report earlier.
  • We are working on offering Python as an alternative to Matlab. There is a strong wish from industries (e.g. Volvo) that our examined students have knowledge in the use of open source software, and Python in particular. Matlab can still be used during 2019 for those who wish to do so.

After 2017:

  • Only the initial parts of turbulence modelling is kept in this course (Bousinesq hypothesis and the eddy-viscosity concept), to show how turbulence modelling typically enters the CFD codes. The rest of the turbulence modelling has been moved to the course in turbulence modelling, where it belongs.
  • A larger emphasis is put on the important pressure-velocity coupling algorithms, and how to treat collocated grids. The third computer exercise has been changed so that a full CFD solver should be implemented (starting from a template).

Learning objectives

Learning objectives for the entire course:

- Use the finite volume method to discretize, and in the form of a computer code implement, steady diffusion and convection-diffusion equations.
- Apply boundary conditions and source terms for specific problems, and understand different kinds of boundary conditions.
- Implement and use solvers for the linear equation system that results from the discretization and the use of boundary conditions and source terms.
- Evaluate convergence of the solution of the linear equation system, and verify that the equations are fulfilled.
- Understand and evaluate the plausibility of the results, and validate them.
- Derive the order of accuracy of numerical schemes, and understand why, and how, particular treatment is to be used for convection and time schemes.
- Understand, describe and implement what is necessary to get stable results when calculating both pressure and velocity, both using 'staggered grids' and 'collocated grids'.
- Understand, describe and implement an algorithm for the coupling of pressure and velocity (SIMPLE).
- Understand fundamental concepts of turbulence.
- Understand how turbulence models based on the Boussinesq hypothesis align with the finite volume method.

Link to the syllabus on Studieportalen

Detailed learning objectives will be given for each chapter, to be used by the students to actively work through the theory

Examination form

To pass the course it is required that:

  1. All three computer exercises are successfully presented both orally and in the form of written reports (according to the schedule). All exercises must be “passed” by the teacher/assistants, shortly after the submission deadline. The third computer exercise must be passed at the time of the original written examination - otherwise the student has to come back next year.
  2. The written examination is passed. Grade U/3/4/5: 40%: grade 3, 60%: grade 4, 80%: grade 5. No aids can be used at the written exam. One original exam, and two re-exams, are provided each year. No additional opportunities are provided.

The written examination consists of questions related to:

  • Physical understanding (from lecture notes/book and computer exercises)
  • Theoretical knowledge (from lecture notes/book)
  • Derivations (from lecture notes/book)
  • Implementations and common implementation mistakes (computer exercises)


The student should have taken one basic course in fluid mechanics. For students from Chalmers this means one of the following courses:

  • Fluid Mechanics M1 and, preferably, Fluid Mechanics M3
  • Continuum Mechanics and Fluid Dynamics F3
  • Transport Processes K

Course summary:

Date Details Due