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Course info
KME / VMT
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Course description
Department/Unit / Abbreviation
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KME
/
VMT
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Computational Methods in Fluid Dynamics
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
5
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
2
[Hours/Week]
Tutorial
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech, English
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Occ/max
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|
|
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Automatic acceptance of credit before examination
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No
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Summer semester
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3 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Summer semester
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Semester taught
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Summer semester
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Minimum (B + C) students
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10
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech, English
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
Yes
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Fundamental course |
No
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Fundamental theoretical course |
Yes
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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KME/MMB, KME/MMM, KME/SZMMM, KME/SZVMM
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Histogram of students' grades over the years:
Graphic PNG
,
XLS
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Course objectives:
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The students are introduced with the numerical solution of problems applied to compressible viscous fluids. The basic numerical methods to solve the laminar flow of incompressible fluids with the application to biomechanics are introduced.
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Requirements on student
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Credit requirements:
Elaboration and delivery of semestral work of adequate level.
Credit obtained in previous years of study is not accepted.
Exam requirements
Active knowledge of lectures and the capability to apply acquired knowledge to the solution of concrete problems
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Content
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1. Mathematical model of compressible fluid flow - conservative systems of Navier-Stokes (NS) and Euler equations. Derivation of balance laws, conversion of the NS equation system to the dimensionless form.
2. Properties of the Euler equations conservative system.
3. Numerical solution of scalar partial differential equation in one dimension, approximation, stability and convergence of differential problems, classical schemes spectral analysis of stability.
4. Numerical solution of spectral hyperbolic partial differential equations in one dimension according to the method of finite deformations. The overview of classical central and upwind schemes. Examination of stability of classical numerical schemes using spectral analysis.
5. Additive viscosity. The construction of modern TVD schemes for the solution of scalar hyperbolic partial differential equations in one dimension.
6. Numerical solution of scalar hyperbolic partial differential equations in two dimensions, overview of numerical schemes. Examination of numerical schemes stability using spectral analysis.
7. Method of finite volumes in two and three dimensions for the conservative system of Euler and NS equations. Semestral work setting. Examples of some compressible and incompressible flow problem solution.
8. Numerical solution of Euler equations solution in two and three dimensions using schemes formulated for the method of finite volumes.
9. Numerical solution of scalar parabolic partial differential equations in one dimension according to the method of finite difference. The overview of principle numerical schemes. Examination of numerical scheme stability according to spectral analysis.
10. Properties of conservative NS equation system, numerical solution of NS equation system in two dimensions. Approximation of viscous fluxes. Application of boundary conditions for the system of NS equations in two dimensions.
11. Mathematical model of incompressible fluid flow and its numerical solution according to the method of artificial viscosity. Practice in computer laboratory - software FLUENT.
12. The basic principles of turbulent flow, the central system of NS equations following Reynolds and Favra. Practice in computer laboratory - software FLUENT.
13. Algebraical models of turbulence. Practice in computer laboratory - software FLUENT.
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Activities
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Fields of study
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https://www.kme.zcu.cz/pro-studenty/modernizace-vyuky-ve-vybranych-predmetech-garantovanych-na-katedre-mechaniky-fav-zcu-v-plzni/modernizace-vyuky-predmetu-vypoctove-metody-dynamiky-tekutin-kme-vmt
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Guarantors and lecturers
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Literature
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Recommended:
Ferziger, Joel H.; Perić, Milovan. Computational methods for fluid dynamics. 3rd ed. Berlin : Springer, 2002. ISBN 3-540-42074-6.
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Recommended:
SPURK, J.H. Fluid mechanics. [1st ed.]. Springer-Verlag, Berlin, 1997. ISBN 3-540-61651-9.
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Recommended:
DVOŘÁK, R. - KOZEL, K. Matematické modelování v aerodynamice. 1. vyd. Vydavatelství ČVUT, Praha, 1996. ISBN 80-01-01541-6.
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Recommended:
HIRSCH, CH. Numerical computation of internal and external flows : vol. 1: fundamentals of numerical discretization. 1st ed. reprint. Chichester : John Wiley & Sons, 1997. ISBN 0-471-92385-0.
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Recommended:
HIRSCH, CH. Numerical computation of internal and external flows : vol. 2: computational methods for inviscid and viscous flows. 1st ed. reprint. Chichester : John Wiley and sons, 1998. ISBN 0-471-92452-0.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Graduate study programme term essay (40-50)
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40
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Contact hours
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52
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Preparation for an examination (30-60)
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45
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Total
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137
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
orientovat se v diferenciálním a integrálním počtu |
orientovat se v mechanice kontinua |
orientovat se v mechnice tekutin |
orientovat se v základech numerické matematiky |
orientovat se v základech tenzorového počtu |
orientovat se ve vektorovém a maticovém počtu |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
popsat a řešit konkrétní úlohy diferenciálního a integrálního počtu s aplikacemi ve fyzice |
popsat a řešit základní problémy lineární mechaniky kontinua s využitím tenzorového počtu |
popsat a řešit základní typy obyčejných a parciálních diferenciálních rovnic s aplikacemi ve fyzice |
popsat a řešit základní úlohy a problémy mechaniky tekutin |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
orientovat se v problematice metody konečných objemů |
orientovat se v oblasti modelování laminárního a turbulentního proudění stlačitelných a nestlačitelných tekutin |
orientovat se v základních diferenčních schématech pro numerické řešení modelové skalární hyperbolické a parabolické PDR |
osvojit si základní znalosti pro využívání výpočtového systému Fluent |
vysvětlit pojmy aproximace, stabilita a konvergence diferenční úlohy |
Skills - skills resulting from the course: |
aplikovat metodu konečných objemů pro numerické řešení proudění stlačitelných a nestlačitelných vazkých tekutin |
numericky řešit jednodušší úlohy laminárního proudění stlačitelných a nestlačitelných tekutin s aplikacemi ve vnitřní aerodynamice a v biomechanice |
numericky řešit pomocí základních diferenčních schémat modelové skalární hyperbolické a parabolické PDR |
sestavit matematické modely proudění stlačitelných a nestlačitelných vazkých tekutin |
vyšetřovat stabilitu základních lineárních diferenčních schémat pomocí spektrální analýzy |
Competences - competences resulting from the course: |
N/A |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Oral exam |
Seminar work |
Skills - skills achieved by taking this course are verified by the following means: |
Skills demonstration during practicum |
Competences - competence achieved by taking this course are verified by the following means: |
Oral exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Interactive lecture |
Self-study of literature |
Task-based study method |
Skills - the following training methods are used to achieve the required skills: |
Individual study |
Practicum |
Competences - the following training methods are used to achieve the required competences: |
Skills demonstration |
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