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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
TME085 - Compressible flow
Kompressibel strömning
Syllabus adopted 2020-02-10 by Head of Programme (or corresponding)
Owner: MPAME
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: Second-cycle
Major subject: Mechanical Engineering

Teaching language: English
Application code: 03125
Open for exchange students: Yes
Block schedule: B

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0107 Examination 7,5 c Grading: TH   7,5 c   18 Mar 2021 am J,  08 Jun 2021 am J,  18 Aug 2021 am J

In programs

MPAME APPLIED MECHANICS, MSC PROGR, Year 1 (compulsory elective)


Niklas Andersson

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General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Basic fluid mechanics, thermodynamics


Compressible flow effects are encountered in numerous engineering applications involving high speed flows, e.g. gas turbines, steam turbines, internal combustion engines, rocket engines, high-speed aerodynamics, high speed propellers, gas pipe flows, etc. In fact, modern society with its dependence on fast ground and air transportation would not function without compressible flow. Special phenomena such as compression shocks, entropy layers, expansion fans, flow induced noise etc are of fundamental scientific importance and directly affect the performance and endurance of these engineering applications.
The main objectives of the course are to convey to the students an overview of the field of compressible flows (including aero-acoustics) and the importance of this topic in the context of common engineering applications. This means that the student should acquire a general knowledge of the basic flow equations and how they are related to fundamental conservation principles and thermodynamic laws and relations. The connections with incompressible flows and aero-acoustics as various limiting cases of compressible flows should also become clear. A general knowledge of the status of commercial CFD codes for compressible flows should also be obtained after this course.

Learning outcomes (after completion of the course the student should be able to)

  • to define the concept of compressibility for flows and to find if a given flow is subject to significant compressibility effects
  • to describe typical engineering flow situations in which compressibility effects are more or less predominant (Mach number regimes)
  • to present different formulations of the governing equations for compressible flows and what basic conservation principles they are based on
  • to explain how thermodynamic relations enter into the flow equations and the special cases of calorically perfect gas, thermally perfect gas and real gas
  • to explain why entropy is important for flow discontinuities
  • to derive (some) and apply (all) of the presented mathematical formulae for classical gas dynamics, that is, 1D isentropic flow, normal shocks, 1D flow with heat addition, 1D flow with friction, oblique and conical shocks, shock reflection at solid walls, Prandtl-Meyer expansion fans in 2D, detached blunt body shocks, nozzle flows, unsteady waves and discontinuities in 1D, basic acoustics, etc
  • to define the general Riemann problem and explain its importance for compressible flow modelling
  • to explain how the incompressible flow equations are derived as a limiting case of the compressible flow equations
  • to explain how the equations for aero-acoustics and classical acoustics are derived as limiting cases of the compressible flow equations
  • to solve engineering problems involving the above mentioned phenomena
  • to apply a given CFD code to a particular compressible flow problem and to understand how to analyze the quality of the numerical solution


The present course follows the book (see below) quite closely and includes the following topics:
  • Introduction, historical review
  • Integral and differential forms of governing equations
  • 1D steady compressible flow
  • Quasi-1D flow (steady)
  • 2D steady compressible flow
  • Unsteady 1D compressible flow
  • Riemann problem
  • Linear and non-linear acoustic waves
  • High temperature effects
  • Numerical techniques (overview)


The course consists of 15 lectures, 9 sessions with exercises and 3 numerical assignments involving problem solution based on classical formulae and/or numerical methods. The numerical tools consist of a Chalmers-developed Finite-Volume-Method-based (FVM) code for simulation of 1D compressible flow and the commercial code FLUENT for 2D compressible flow.

In addition to the numerical assignments there is a more extensive project including numerical analysis elements. The project should be done in groups of up to four students and includes a literature survey, numerical flow simulation (CFD), and presentation in forn of technical reports and an oral presentation.


  • John D. Anderson, Modern Compressible Flow, McGraw-Hill 2004, 3rd revised edition, ISBN 0071241361.
  • Selected lecture notes on numerical methods (fundamental principles) and aeroacoustic.

Examination including compulsory elements

The examination is based on a written test (fail, 3, 4, 5), passed numerical assignments, and passed project. The project work, which is done in groups of up to four students, should be presented in form of a written report and an oral presentation. The project can give bonus points for the written exam.

Page manager Published: Thu 04 Feb 2021.