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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
TME085 - Compressible flow
Syllabus adopted 2014-02-21 by Head of Programme (or corresponding)
Owner: MPAME
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Mechanical Engineering
Department: 42 - APPLIED MECHANICS

Teaching language: English
Open for exchange students
Block schedule: B

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0107 Examination 7,5 c Grading: TH   7,5 c   19 Mar 2015 am M,  13 Apr 2015 am M,  19 Aug 2015 am M

In programs

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


Professor  Lars-Erik Eriksson


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

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 understand how thermodynamic relations enter into the flow equations and the special cases of calorically perfect gas, thermally perfect gas and real gas
to understand 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 modeling
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
Potential flow theory
Numerical techniques (overview)
High temperature compressible flow


The course consists of 10 lectures, 8 sessions with exercises and 3 numerical assignments involving problem solution based on classical formulae and/or numerical methods. The numerical tools consist of a Matlab code for 1D compressible flow and the commercial code FLUENT for 2D compressible flow.


John D. Anderson, Modern Compressible Flow, McGraw-Hill 2004, 3rd revised edition, ISBN 0071241361.
Selected lecture notes on aero-acoustics.


The examination is based on a written test (fail, 3, 4, 5) and on passed numerical assignments.

Page manager Published: Thu 04 Feb 2021.