Numerical Simulation of Fluids

Numerical Simulation of Fluids is a course that is jointly offered by the groups for

System Simulation	and	Fluid Mechanics

Motivation

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 computer science.

Contents

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

Audience

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.

Prerequisites

A sound background in engineering mathematics and a higher programming language (preferably C/C++).

Format

We will have 2 hours of lecture each week. The exercise classes will meet for two hours each week.

Homework assignments

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.

Schein Policy

• 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.
• Exams:
  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.

Schedule

A detailed schedule can be found here.

Examples

We have already organized this course before. Therefore we have some pictures and 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.

Note:

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