معلومات المقرر

Lehrinhalte
Asymptotic series and expansions; applications of the regular perturbation method in some flow problems; failure of the Poincare expansions; method of strained coordinates; renormalization technique; method of matched asymptotic expansions; flows around a sphere or a cylinder with small Reynolds numbers; method of multiple scales; turning point problems.

Literatur
Lecture notes;
Nayfeh, A.H.: Perturbation Methods, John Wiley & Sons, 1975;
Van Dyke, M.: Pertubation Methods in Fluid Mechanics, Parabolic Press, 1975.

Erwartete Teilnehmerzahl
15

Further Grading Information
[b]Learning Outcomes  [/b]

On successful completion of this module, students should be able to:

1. explain and apply the regular perturbation method for solving differential equations, specially flow problems, by means of parameter or coordinate perturbation;

2. recognize the limitations of the regular perturbation method;

3. choose and apply alternative suitable singular perturbation methods if the regular perturbation method fails for given differential equations;

4. recognize relations and distinctions of different singular perturbation methods, e.g. methods of strained coordinates, renormalization, multiple scales.

[b]Prerequisites for participation[/b]

Basic knowledge of ordinary and partial differential equations and the corresponding solution methods; basic knowledge of fluid mechanics. Knowledge of Part I of this lecture is not required.

[b]Assessment methods[/b]

Oral exam 30 min.

Zusätzliche Informationen
Übungs- und Vorlesungsunterlagen werden im moodle-Kurs der Verantaltung bereitsgestellt:

[url]https://moodle.tu-darmstadt.de/course/view.php?id=11972[/url]

Online-Angebote
moodle