Course syllabus

MTF073 Computational Fluid Dynamics, Sp2, 7.5 hp

Offered by the Department of Mechanics and Maritime Sciences

Staff

• Examiner/lecturer:
  Håkan Nilsson 
• Teaching assistants:
  Konstantinos Konstantinidis
  Debarshee Ghosh  

Course purpose and contents

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

The governing equations of fluid flow are recalled, and written in a general convection-diffusion form that is useful for the understanding of how the equations are solved in a CFD code. 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 behavior 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.

Course schedule and organization

The schedule is found at the schedule page.

• Lectures and theory:
  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.
  Discussion treads are available for questions and discussions on the learning outcomes and the course contents in general. The exam questions will be inspired by those discussions! Active students may thus have an explicit benefit, in addition to learning more just by being active.
• Computer tasks and practical application of the theory:
  Three computer tasks form a large part of the course. The computer tasks should be carried out in groups of two students. The computer task reports should be handed in through the course homepage and must be passed by the teacher/assistants. If they are failed they need to be improved and handed in again. The knowledge gained in the computer tasks will be assessed in the written exam, by special task-related questions. Completely correct reports give up to 2 bonus points per computer task in the original written exam (not re-exams or future exams). This is provided that the report is not handed in late and that no resubmission is requested.
• Examination, to assess the theoretical knowledge and practical application of the theory:
  The final assessment and grade is by a written examination. The examination includes both fundamental theoretical understanding, derivations, and CFD code implementations (that should be possible to answer by students who have actively worked in the computer tasks). The exam questions will be inspired by the discussions in the discussion threads!
• Ladok:
  Each passed task is reported with 1.5 hp, and the written exam is reported with 3 hp. All 7.5 hp must be passed to pass the course. The grade is given by the written exam only (counting possible bonus points only at the original exam).

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 http://www.bokus.com/, but also available for free as on-line e-book through Chalmers' library - search for "versteeg malalasekera" at the top of lib.chalmers.se).

No course material can be used at the written examination (under pandemics, special rules may apply).

Learning outcomes

Learning outcomes 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 outcomes are given for each chapter, to be used by the students to actively work through the theory. The students are encouraged to discuss and ask questions about the learning outcomes and the course in general, through discussion threads. Those discussions will be an inspiration for the questions in the written exam. Active students may thus have an explicit benefit, in addition to learning more just by being active.

Examination form

To pass the course it is required that:

1. All three computer tasks are successfully presented in the form of written reports. All tasks must be “passed” by the teacher/assistants, shortly after the submission deadline of each task (and at the time of the original written examination for the third task) - otherwise the student has to come back and pass the un-passed task(s) next year.
2. The written examination is passed. Bonus points for the computer tasks may be given, as stated above (only for original exam). 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.  (under pandemics, special rules may apply)

The written examination consists of questions related to:

• Physical understanding (from lecture notes/book and computer tasks)
• Theoretical knowledge (from lecture notes/book)
• Derivations (from lecture notes/book)
• Implementations, common implementation mistakes and interpretation of results (computer tasks)

Only one old exam is handed out, to show what an exam may look like. It is highly encouraged that the students use the course material to learn instead of just looking at old exams. We promise to do our best to design completely new questions for each exam, to test knowledge and understanding rather than memorization.

Prerequisites

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