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Numerical simulation of incompressible fluid flow by the spectral element method
Pokorný, Jan ; Hlavička, Rudolf (referee) ; Čermák, Libor (advisor)
Tato diplomová práce prezentuje metodu spektrálních prvků. Tato metoda je použita k řešení stacionárního 2-D laminárního proudění Newtonovské nestlačitelné tekutiny. Proudění je popsáno stacionarní Navier-Stokesovou rovnicí. Dohromady s okrajovou pod- mínkou tvoří Navier-Stokesův problém. Na slabou formulaci této úlohy je aplikována metoda spektrálních prvků. Touto discretizací se získá soustava nelineárních rovnic. K obrdžení lineární soustavy je použita Newtonova iterační metoda. Podorobný algorit- mus tvoří jádro Navier-Stokeseva solveru, který je naprogramován v Matlabu. Na závěr jsou pomocí tohoto solveru řešeny dva příklady: proudění v kavitě a obtékání válce. Přík- lady jsou řešeny pro různé Reynoldsovy čísla. První od 1 do 1000 a druhý od 1 do 100.
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Physical basis of mathematical operators in continuum mechanics
Konečná, Tereza ; Čermák, Libor (referee) ; Fialová, Simona (advisor)
This bachelor deals with the use of mathematical operators of rotation, divergence and gradient in continuum mechanics. The use of the operators is outlined in examples. Next, two integration theorems are discussed: the Gauss-Ostrogradski theorem with applications to the derivation of relations, equations and theorems from the mechanics of continua. More specifically, the equation for the continuity of flow, first law of thermodynamics, Euler's laws of motion and Bernoulli's priciple for ideal fluid. Another integration theorem is the Stokes' theorem, which is applied in this thesis to deduce the Faraday theorem and formulas for vorticity.
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Barycentric rational interpolation.
Venclovský, Jakub ; Čermák, Libor (referee) ; Hlavička, Rudolf (advisor)
This bachelor thesis deals with deducing of barycentric form of polynomial interpolation and then barycentric form of rational interpolation. It shows disadvantages of classic rational interpolation and deals with elimination of these disadvantages in its barycentric form. It also shows some specific methods of barycentric rational interpolation.
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Meshless modelling of fluid flow
Prochazková, Zdeňka ; Zatočilová, Jitka (referee) ; Čermák, Libor (advisor)
The thesis focuses on the Smoothed Particle Hydrodynamics (SPH) meshfree method. In the thesis, basic equations needed for solving fluid flow problems are derived - continuity equation, momentum equation and energy equation. The text presents the basic principles of the method, selection of a smoothing function, spacial discretization and a suitable time integration method. As an example of usage, the thesis models the shock tube problem. On this problem, we can compare the solution using the SPH method with the accurate solution.
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Algorithm for Calculation of Radiation View Factors
Bílek, Tomáš ; Hlavička, Rudolf (referee) ; Čermák, Libor (advisor)
This thesis deals with a calculation of radiation view factors. The thesis includes mathematical model of the problem and its numerical solution. The main aim of the thesis is the creation of an algorithm for calculation of radiation view factors for given 3D geometries and its application for the heat flux analysis. CAD models of geometries, specified by a NASTRAN file format, are used as an input of the algorithm. Matrix of radiation view factors serves then as an output of the algorithm. The algorithm is programmed in MATLAB, but STAR-CCM+ is used for the NASTRAN specification of separate models. The algorithm is also designed for a computation on a computer cluster for cases of intricate geometries with consideration of shading areas.
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Data Visualization for .NET platform
Šeliga, Ondřej ; Čermák, Libor (referee) ; Hlavička, Rudolf (advisor)
Bachelor thesis deals with methods and procedures of data visualization for .NET platform using ActiViz .NET visualization library. This is an accompanying document to the developed application Vizualizace, which demonstrates how to use controls Control2D and Control3D. It describes ways of working and possibilities of these program components.
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Algorithms of the interpolation by multivariate polynomials
Doktorová, Alice ; Čermák, Libor (referee) ; Kureš, Miroslav (advisor)
This bachelor's work concerns to algorithms of the multivariate interpolation. The problem of the interpolation over the plane is studied in the first part of this work. In the next section, the multivariate Lagrange interpolation is described and the polynomial degree is discussed. A Mathematica program package was developed, by this, the multivariate interpolation over an arbitrary field can be solved.
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Eigenvalue Problem and Applications
Machát, Ondřej ; Čermák, Libor (referee) ; Knotek, Stanislav (advisor)
This thesis contains definition and overview of the properties of eigenvalues´ problems including its generalised alternate and the problem of eigenvalues in differential equations. Several numerical methods of calculations are also listed here. Crux of the thesis are the practical applications of this mathematical domain in use. The reader is progressively going to meet the model of the forging hammer´s procedure, tasks looking for critical load pressure needed to irreversible bending of the imbedded girder. In conclusion the thesis will also deal with the stability of the liquid flowing.
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Computation of compression force on surface
Stejskal, Jiří ; Habán, Vladimír (referee) ; Čermák, Libor (advisor)
In technical computing we often need to find the resulting load on surface caused by the compression force. The aim of this thesis is to suggest one of the possible approaches to do so if the surface is given explicitly or by the coordinates of some of it's points. In the first section, the mathematical definition of the surface with some of it's important properties is mentioned. There is a basic theory of Bézier surfaces, which form the main part of this thesis in the second part. Further on, some results from the theory of surface integrals are mentioned. The last section describes the whole algorithm of computing the resulting load together with the MATLAB program which is added to this thesis. Three examples are given at the end.
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