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## Syllabus for

MTF071 - Computational methods in fluid dynamics

Owner: TMASA
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: A
Department: 42 - APPLIED MECHANICS

Teaching language: English

 Course module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 No Sp 0198 Examination 5,0 c Grading: TH 5,0 c 15 Mar 2007 am V, 28 Aug 2007 am V

#### In programs

TKEFA CHEMICAL ENGINEERING WITH ENGINEERING PHYSICS, Year 4 (elective)
TMASA MECHANICAL ENGINEERING - Energy technology, Year 4 (elective)
TTFYA ENGINEERING PHYSICS, Year 4 (elective)
AUMAS MSc PROGRAMME IN AUTOMOTIVE ENGINEERING, Year 1 (elective)
CEMAS MSc PROGRAMME IN COMPUTATIONAL AND EXPERIMENTAL TURBULENCE, Year 1 (elective)

#### Examiner:

Professor  Sinisa Krajnovic

#### Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

#### Content

We start by carrying out a detailed derivation of the finite volume method. First, the diffusion equation
(heat conduction equation) is treated in one and two dimensions. After that, we carry on to convection-diffusion problems. For the convective part, we discuss different discretization schemes where a delicate balance between numerical accuracy and numerical stability must be considered.

The Navier-Stokes equations are discussed for both compressible and incompressible flow. In incompressible flow special problems arise from the pressure-velocity coupling which leads to pressure oscillations. Two different methods to solve this problems are discussed in some detail.

Many turbulence models are based on the eddy-viscosity concept, where additional transport equation are solved for two scalar quantities. The most well-known models are the k-eps and the k- omega model. Near the walls the grid must be refined in order to resolve the strong gradient prevailing there. A couple of years ago one was forced to, due to limited computer resources, use approximate treatment of the walls in the form of wall functions. In industry these are still often used. However, often more accurate treatments are used, such as low-Reynolds number models.

http://www.tfd.chalmers.se/gr-kurs/MTF071/

#### Organisation

The course includes three exercises (Task 1, 2 and 3). The students writes their own finite volume programs, using MATLAB, solving

* the diffusion equation (heat conduction equation) in two dimensions,

* the convection-diffusion equation in two dimensions,

* turbulent flow, including a turbulence model, in fully developed flow in a channel channel (one dimension).

The exercises should be presented by the students both in written and oral form.

#### Literature

H.K. Versteegh and W. Malalasekera. "An Introduction to Computational Fluid Dynamics - The Finite
Volume Method", Longman Scientific & Technical, Harlow, England, 1995.

L. Davidson, An introduction to turbulence models.
Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology, Gothenburg, 1998.

#### Examination

An optional written examination is given at the end of the course.

As an alternative, an oral examination on the subject of the exercises can be given. The grades given for oral examination are pass (grade 3) or fail.

Written and oral presentations of exercises are also part of the examination.

Page manager Published: Mon 28 Nov 2016.