Mathematical Methods in Fluid Mechanics 1 - NMNV537
Title: Matematické metody v mechanice tekutin 1
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English
Teaching methods: full-time
Guarantor: doc. RNDr. Jiří Felcman, CSc.
Teacher(s): doc. RNDr. Jiří Felcman, CSc.
Class: M Mgr. MOD
M Mgr. MOD > Povinně volitelné
M Mgr. NVM
M Mgr. NVM > Povinně volitelné
Classification: Mathematics > Numerical Analysis
Incompatibility : NMOD101
Interchangeability : NMOD101
Is interchangeable with: NMOD101
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Annotation -
Brief survey of equations describing fluid flow, main theoretical results for the Stokes, Oseen and Navier-Stokes problems, finite element solution of viscous incompressible flow
Last update: T_KNM (07.04.2015)
Course completion requirements -

The subject will be finished by an exam.

Last update: Feistauer Miloslav, prof. RNDr., DrSc., dr. h. c. (29.10.2019)
Literature -

Feistauer M.: Mathematical Methods in Fluid Dynamics. Longman Scientific-Technical, Harlow, l993

Feistauer M.,Felcman J., Straškraba I.: Mathematical and Computational Methods for Compressible Flow. Oxford University Press, Oxford, 2003

V. Girault, P.-A. Raviart: Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms. Springer, Berlin, 1986.

Last update: Feistauer Miloslav, prof. RNDr., DrSc., dr. h. c. (29.10.2019)
Requirements to the exam -

The exam has two parts: writing part and oral part. If the writing part failed, then the oral part does not continue. If the oral part is not successful, it is necessary to repeat the whole exam.

The requirements to the both parts of the exam correspond to the sylabus corresponding to the contents presented in the course.

Last update: Feistauer Miloslav, prof. RNDr., DrSc., dr. h. c. (29.10.2019)
Syllabus -

A brief survey of equations describing flow: Navier-Stokes equations for viscous incompressible flow.

Main theoretical results for the Stokes, Oseen and Navier-Stokes problems.

Finite element method for the solution of viscous incompressible flow: Babuska-Brezzi condition, conformal and nonconformal finite elements, existence and uniqueness of the solution to the Stokes problem, discretization of the stationary and nonstationary Navier-Stokes problem, stabilization of numerical methods.

The course is suitable for students of Numerical and Computational Mathematics and Mathematical Modelling in Physics and Technology.

Last update: Feistauer Miloslav, prof. RNDr., DrSc., dr. h. c. (07.04.2015)
Entry requirements -

Basic concepts and results from the functional analysis and partial differential equations.

Last update: Feistauer Miloslav, prof. RNDr., DrSc., dr. h. c. (13.05.2019)