Digital Teaching
For the course "Mathematical Methods in Fluid Mechanics: Perturbation methods", the regular face to face lecture will be offered in the winter semester 2023/24. As an additional service, we will offer electronic material for self-study. The lecture notes and exercises will be available in the Moodle course.
Course Contents
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; turning point problems.
Literature
Lecture notes;
Nayfeh, A.H.: Perturbation Methods, John Wiley & Sons, 1975;
Van Dyke, M.: Pertubation Methods in Fluid Mechanics, Parabolic Press, 1975.
Expected Number of Participants
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.
Additional Information
Exercise and lecture materials will be provided in the course Moodle cours
Online Offerings
moodle
For the course "Mathematical Methods in Fluid Mechanics: Perturbation methods", the regular face to face lecture will be offered in the winter semester 2023/24. As an additional service, we will offer electronic material for self-study. The lecture notes and exercises will be available in the Moodle course.
Course Contents
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; turning point problems.
Literature
Lecture notes;
Nayfeh, A.H.: Perturbation Methods, John Wiley & Sons, 1975;
Van Dyke, M.: Pertubation Methods in Fluid Mechanics, Parabolic Press, 1975.
Expected Number of Participants
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.
Additional Information
Exercise and lecture materials will be provided in the course Moodle cours
Online Offerings
moodle
- Lehrende: Yongqi Wang
Semester: WT 2023/24