Course Details

Compressible Flow TME085
Credits 5.0 credit points (7.5 ects)
Grading scale fail, 3, 4, 5
Educational level Master course
Main field Mechanical Engineering
Master's program Applied Mechanics
Department Department of Mechanics and Maritime Sciences
Division Division of Fluid Dynamics
Language English


The main objectives of the course are to convey to the students an overview of and familiarity with the field of compressible flows 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 and some experience with typical CFD codes for compressible flows should also be obtained after this course.

Intended Learning Outcomes

After the completing the course, each student should be able to:

  1. Define the concept of compressibility for flows
  2. Explain how to find out if a given flow is subject to significant compressibility effects
  3. Describe typical engineering flow situations in which compressibility effects are more or less predominant (e.g. Mach number regimes for steady-state flows)
  4. Present at least two different formulations of the governing equations for compressible flows and explain what basic conservation principles they are based on
  5. Explain how thermodynamic relations enter into the flow equations
  6. Define the special cases of calorically perfect gas, thermally perfect gas and real gas and explain the implication of each of these special cases
  7. Explain why entropy is important for flow discontinuities
  8. Derive ( marked) and apply (all) the presented mathematical formulae for classical gas dynamics
    1. 1D isentropic flow
    2. Normal shocks
    3. 1D flow with heat addition
    4. 1D flow with friction
    5. Oblique shocks in 2D
    6. Shock reflection at solid walls
    7. Contact discontinuities
    8. Prandtl-Meyer expansion fans in 2D
    9. Detached blunt body shocks, nozzle flows
    10. Unsteady waves and discontinuities in 1D
    11. Basic acoustics
  9. Solve engineering problems involving the above-mentioned phenomena (8.a - 8.k)
  10. Explain how the incompressible flow equations are derived as a limiting case of the compressible flow equations
  11. Explain how the equations for aero-acoustics and classical acoustics are derived as limiting cases of the compressible flow equations
  12. Explain the main principles behind a modern Finite Volume CFD code and such concepts as explicit/implicit time stepping, CFL number, conservation, handling of compression shocks, and boundary conditions
  13. Apply a given CFD code to a particular compressible flow problem
  14. Analyse and verify the quality of the numerical solution
  15. Explain the limitations in fluid flow simulation software
  16. Report numerical analysis work in form of a technical report
    1. Describe a numerical analysis with details such that it is possible to redo the work based on the provided information
    2. Write a technical report (structure, language)
  17. Search for literature relevant for a specific physical problem and summarize the main ideas and concepts found
  18. Present engineering work in the form of oral presentations

Course Literature

Modern Compressible Flow with Historical Perspective
John D. Andersson
4th revised edition
McGraw-Hill 2021
ISBN: 987-1-260-57082-3

Chapter 1 Compressible Flow
Chapter 2 Integral Forms of the Conservation Equations for Inviscid Flows
Chapter 3 One-Dimensional Flow
Chapter 4 Oblique Shocks and Expansion Waves
Chapter 5 Quasi-One-Dimensional Flow
Chapter 6 Differential Conservation Equations for Inviscid Flows
Chapter 7 Unsteady Wave Motion
Chapter 12 The Time-Marching Technique
Chapter 16 Properties of High-Temperature Gases
Chapter 17 High-Temperature Flows

Course Outline

In the course there are in total 15 lectures and seven sessions with exercises. There are also four compulsory numerical assignments involving problem solution based on classical formulae and/or numerical methods. One of these assignments, referred to as The Compressible Flow Project, spans over all eight course weeks and includes a literature survey part and a hands-on numerical assignment. The project is done in groups of up to four students and should be presented in form of a technical report (mandatory) at the end of the course. There is also a mandatory oral-presentation session in the end of the course where each of the groups presents their approach to solve their specific problem and their major findings. The numerical tools used in the course consist of a Chalmers-developed in-house code for simulation of 1D compressible flow called CFLOW and the commercial code STAR-CCM+ is used for simulation of 2D compressible flow.


The examination is based on a written test (fail, 3, 4, 5), passed assignments; three numerical assignments and one larger project. The project may give up to seven bonus points for the written exam if all the assessment criteria are fulfilled. The written exam is divided into one part (part I) with theory questions (20 p.) and one part (part II) with problems to solve (40 p.).

grade 3 4 5
number of points on the exam 24-35 36-47 48-60

In addition to the tabulated grade limits, it is required that at least 6 of the total number of points are in the theory question part of the exam (Part I) and at least 10 points in the problem part (Part II)