## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-81-18-M-7

## Module Identification

Module Number Module Name CP (Effort)
MAT-81-18-M-7 Mathematical Theory of Fluid Dynamics 4.5 CP (135 h)

## Basedata

CP, Effort 4.5 CP = 135 h 1 Sem. irreg.  Master (Advanced) [EN] English Pinnau, René, Prof. Dr. (PROF | DEPT: MAT) Klar, Axel, Prof. Dr. (PROF | DEPT: MAT) Pinnau, René, Prof. Dr. (PROF | DEPT: MAT) + further Lecturers of the department Mathematics [MAT-TEMA] Industrial Mathematics [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-81-18-K-7
Mathematical Theory of Fluid Dynamics
P 28 h 107 h - - PL1 4.5 irreg.
• About [MAT-81-18-K-7]: Title: "Mathematical Theory of Fluid Dynamics"; Presence-Time: 28 h; Self-Study: 107 h

## Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: each semester
• Examination number: 86302 ("Mathematical Theory of Fluid Dynamics")

## Contents

The mathematical concepts required to derive the Navier-Stokes equations from conservation principles and the consequent results of fluid dynamics are treated. In particular, the following topics are covered:
• derivation of Stokes and Navier-Stokes equations,
• potential flows, velocity-vorticity form of the Navier-Stokes equations,
• circulation theorems,
• turbulence.

## Competencies / intended learning achievements

Upon successful completion of this module, the students understand advanced mathematical methods required for the study of fluid dynamical equations. They are able to name and to prove the essential propositions of the lecture as well as to classify and to explain the connections. They understand the proofs presented in the lecture and are able to reproduce and explain them. In particular, they can outline the conditions and assumptions that are necessary for the validity of the statements.

By completing concrete exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture.

## Literature

• M. Feistauer: Mathematical Methods in Fluid Dynamics.

None

## References to Module / Module Number [MAT-81-18-M-7]

Module-Pool Name
[MAT-81-MPOOL-7] Specialisation Partial Differential Equations (M.Sc.)
[MAT-8x-MPOOL-7] Specialisation Modelling and Scientific Computing (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)