Numerical Simulation of Fluids
Numerical Simulation of Fluids is a course that is jointly offered by
the groups for
The numerical simulation of physical and technical phenomena is a
field of steadily growing importance in the natural and engineering
sciences as well as in industry. The process of numerical simulation
can roughly be divided into several stages
- establishment of a physical / mathematical model
- discretization of that model
- construction of a solution algorithm
- efficient implementation of that algorithm
- visualization and interpretation of the results
The process therefore demands knowledge from several distinct fields and
interdisciplinarity is necessary. The aim of the course is to
familiarize the participants with the different stages of the simulation
process. This will be accomplished by means of the problem of
computational fluid dynamics (CFD).
CFD allows to simulate and predict the aerodynamic or hydrodynamic
properties in many technical applications where the transport in or
of fluids such as air and water is of importance. Notable examples are
the aerodynamics of aircraft, passenger cars or turbomachinery. Other
important fields of interest are related to applications in
thermodynamics, combustion and chemistry. Thus, CFD contains major
contributions from physics, chemistry, mathematics, engineering and
The course will be split up into two parallel sections. The first one
consists of a series of lectures that should provide the participants
with the neccessary theoretical background for the second part, the
practical one. Topics planed for the lectures are:
- Derivation of the Navier-Stokes equations
- Discretization of the equations by means of finite-differences
- Solution techniques for the arising linear systems
- Basic ideas of turbulence modelling
The aim of the course's practical part is to have each participant
write his/her own basic solver for the Navier-Stokes equations. Thus
they can personally experience the difficulties that lie in the
creation of complex (numerical) software packages.
In order to familiarize the students with the techniques for creation
of large software projects and to allow inter-changeability the
structuring of the program into modules, the corresponding interfaces
and data structures will be pre-specified.
After the participants have succeeded in this task, they will be divided
into groups, that delve into a special subtopic to extend the
capabilities of the code. Such topics can be e.g.:
- Turbulence Modeling
- Treatment of free surfaces and visualization
- Heat transport
- Extension to 3D and use of multigrid solver
- Porous media flow and adsorption
This lecture is intended for Bachelor and Master students of
Computational Engineering and students in Informatik
(Diplom). Of course also interested students of other technical
subjects are welcomed.
A sound background in engineering mathematics and a
higher programming language (preferably C/C++).
We will have 2 hours of lecture each week. The exercise classes will
meet for two hours each week.
There will be seven assignments and the presentation of your project at
the end of the semester. Please notice that depending on your
programming experience you have to spent a lot of time for the programming
of the assignments.
- Ungraded Scheins:
Students who wish to receive an ungraded Schein are required to participate
successfully in the first part of the course (Programming of Solver),
take part in the project phase (Group Work) and give a suitable presentation
of the results.
- Graded Scheins:
Students who wish to receive a graded Schein have to fulfill the requirements
for an ungraded Schein and take part in an exam to determine the grade.
For students who wish to take this class for a "studienbegleitende Prüfung"
there will be an exam. Do not be mistaken, this course has an important
practical part. If you do not participate regularly and fullfil the
requirements for an ungraded Schein, you are very unlikely to pass the exam.
A detailed schedule can be found here.
We have already organized this course before. Therefore we have some
movies with results
for example applications. They show the versatility of the approach,
and each participant will/should be able to produce similar pictures
of his own at the end of the course.
This course benefits from a quite similar project that was
performed at the
Chair V of the Department of Informatics at the
TU München and
led to the book Numerical Simulation in Fluid Dynamics - A Practical
Introduction by Michael Griebel, Thomas Dornseifer and Tilman
Neunhoeffer, SIAM 1998, ISBN 0-89871-398-6