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Course, academic year 2023/2024
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Mathematical Methods in Fluid Mechanics 2 - NMNV538
Title: Matematické metody v mechanice tekutin 2
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: 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 : NMOD201
Interchangeability : NMOD201
Is interchangeable with: NMOD201
Annotation -
Mathematical theory of compressible flow. Equations describing the flow. The Euler equations. Properties of the Euler equations. Cauchy problem. Weak solutions. Finite volume method. Finite volume mesh. Derivation of a general finite volume scheme. Properties of the numerical flux. Construction of some numerical fluxes. The Godunov method.
Last update: T_KNM (14.04.2015)
Course completion requirements -

Written and oral exam

Last update: Felcman Jiří, doc. RNDr., CSc. (07.06.2019)
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. Clarendon Press, Harlow, 2003.

Felcman J.: Numerické metody v mechanice tekutin 2, aktualizovaný internetový učební text

Godlewski E., Raviart P. A.: Numerical Approximation of Hyperbolic Systems of Conservation Laws, Number 118 in Applied Mathematical Sciences, Springer, New York 1996

Smoller J.: Shock Waves and Reaction-Diffusion Equations, Springer, New York, 1983

Last update: Kučera Václav, doc. RNDr., Ph.D. (29.10.2019)
Requirements to the exam -

The exam is written and oral. The examination requirements are given by the topics in the syllabus, in the extent to which they were taught in course.

Last update: Felcman Jiří, doc. RNDr., CSc. (07.06.2019)
Syllabus -

Mathematical theory of compressible flow. Equations describing the flow. The Euler equations. Properties of the Euler equations. Cauchy problem. Weak solutions. Finite volume method. Finite volume mesh. Derivation of a general finite volume scheme. Properties of the numerical flux. Construction of some numerical fluxes. The Godunov method.

Last update: T_KNM (14.04.2015)
Entry requirements -

Basic knowledge of the theory of partial differential equations

Last update: Felcman Jiří, doc. RNDr., CSc. (31.05.2018)
 
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