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Thermophoretic and Hydrodynamic Interactions in Artificial Active Matter
Kolář, Martin ; Holubec, Viktor (advisor) ; Tůma, Karel (referee)
The study of artificial active matter has significantly intensified in recent years due to its potential practical applications and promises to understand living organisms' in- teractions and collective behaviour. The research is done on all levels - experimental, theoretical, and numerical. This thesis presents a numerical simulation approach based on solving partial differential equations from the continuum mechanics framework. The results obtained can be used to predict the dynamics and thermodynamics of the system or serve as input data for stochastic simulations. Using this approach, it is also possible to simulate actual laboratory experiments numerically. 1
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Viscoelastic rate-type fluids: a study of the effect of stress diffusion by means of numerical simulations
Cach, Jakub ; Tůma, Karel (advisor) ; Průša, Vít (referee)
Describing viscoelastic fluids is a difficult task, as the viscoelastic phenomena are not fully understood. This work follows a method for deriving viscoelastic models that accu- rately capture the behavior of fluids with polymeric substances, which macroscopically manifest as the stress diffusion, within a consistent thermodynamic framework. We im- plemented these models using the open-source computing platform FEniCS as a finite element library for Python, and we provide a numerical study of the stress diffusion as a stabilization. By extending our implementation using the arbitrary Lagrangian-Eulerian method, we are able to simulate well-known non-Newtonian phenomena, in particular the Weissenberg effect, demonstrating the effectiveness of our approach in enabling a better understanding of these complex fluids. 1
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Numerical simulations of interaction between fluid flow and rigid particles
Hrůza, Jan ; Tůma, Karel (advisor) ; Souček, Ondřej (referee)
The thesis describes the implementation of a numerical model that simulates the interaction between rigid particles and a fluid. The numerical model is based on the arbitrary Lagrangian-Eulerian (ALE) method, which uses the movement of the mesh to realize the movement of particles. The ALE method is initially presented on a simple problem of calculating the drag force acting on a single sphere moving through a viscous fluid. A general version of the model capable of simulating tens of particles is then described and tested on various benchmarks to prove the reliability of used method. Finally, a problem inspired by the flow of red blood cells in the blood is studied to show the effect of shear thinning emerging in a mixture of Newtonian fluid and rigid particles. 1
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Unidirectional flows for binary fluid mixtures
Púček, Jiří ; Málek, Josef (advisor) ; Tůma, Karel (referee)
In a recent work Málek a Souček (2021), the authors propose several classes of simple models suitable to describe flows of binary mixtures, such as bubbly liquids, emulsions, etc. The objective of the bachaler thesis is to investigate the potential of these model by their investigation in simple geometrical settings linked with the assumption that the admissible flows are isothermal and unidirectional. In addition we will compare our results with other models. 1
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Modelling of viscoelastic materials with temperature dependence
Miloš, Vojtěch ; Hron, Jaroslav (advisor) ; Tůma, Karel (referee)
Materials such as asphalt, polymers or the Earth's crust tend to behave in a way that can be described neither with a model of viscous fluid, nor a model from solid mechanics. There are indeed models capable of capturing these so called viscoelastic phenomena far better, but they are based on the presumption of constant temperature. In many cases, e.g. in the glass industry or in geophysics, the properties of a viscoelastic material strongly depend on temperature. That is why it is precisely these changes that need to be described. There are viscoelastic models used in practice that take into account the material parameters' dependence on temperature, however, they do not consider the viscoelastic nature of the material when describing the temperature evolution. The objective of this thesis is to derive thermodynamically consistent viscoelastic models with temperature dependent parameters and the appropriate evolution equation for temperature, implementation of the models and computing simple test simulations. Powered by TCPDF (www.tcpdf.org)
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Fourier method for solving partial differential equations
Tůma, Karel ; Pokorný, Milan (advisor) ; Knobloch, Petr (referee)
Na./cv prace: Fouricrova metoda pro feseni parc.ialnich dirornncialnich rovnic Autor: Karri Tuma Katedra (ust.av): Matematicky ust.av UK Vedouci bakalafske praoo: Mgr. Milan Pokorny, Ph.D. e-mail vodouciho: pokorny@karlin.mff.cuni.cz Abstra.kt: V pfedlo/ene praci odvodime rovnici vedeni tepla a.rovnici slruny. Ty pak nasledno. fesime v jodno prost.orove dimenxi ponioci Fonricrovy me- tody apocivajfci v separaci promennych a nale/eni feseni vc l.varn ncko- nccnc' fady. Zaljyvainc so t.fonii ru/nymi okrajovynii podininkanii. Dah^ vy- sotrujomo vlastnosii foscni tcchlo dvou problcmu. Provadinio analyzu kon- vorgtuicc fx'soni vu tvaru fad v -/avislosti na pocat.ocnich podminkach uloh. Uka/c-me. /o pornoci Fouriorovy inolody l/.c fosil lako stucionarni ulohy, konkrctno so zabyvanio Laplaccoviju rovnici s okrajovynii podminkami na ruznych oblasloch (kruh. vyscc. vyscc mc/ikru/f, mraikru/i). Klicova slova: Parcialni diforoncialni rovnico, Fouricrova tnot.oda, rovnico vodoni lopla, rovnico sLruny. Title: Fourier method for solving partial differential equations Author: Karel Tuma, Department: Matematicky ustav UK Supervisor: Mgr. Milan Pokorny. Ph.D. Supervisor's e-mail address: pokorny@karlin.raff.cuni.cz Abstract: In the present work we derive the heat equation and the wave equation. They arc- solved in one space...
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Computation of viscous flows due to an oscillating cylinder of rectangular cross section.
Outrata, Ondřej ; Hron, Jaroslav (advisor) ; Tůma, Karel (referee)
Incompressible flows due to an oscillating cylinder of rectangular cross section in viscous fluid are governed by Navier-Stokes equations. In this thesis, these equations will be reformulated in a weak sense and their solution approximated by Finite Element Method. Fictitious Boundary Method is used as a tool to handle time dependent boundary. Behavior of a fluid was computed using these methods and is illustrated for various parameters, especially a behavior of the vortices originated in liquid He II is compared to an experiment.
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Fluid-structure interaction between blood and dissipating artery wall
Fara, Jakub ; Tůma, Karel (advisor) ; Bodnár, Tomáš (referee)
In this thesis we introduce a new fluid-structure interaction model in the Eulerian description. This model is developed for blood flow in viscoelastic artery. For the fluid part a non-Newtonian model Oldroyd-B is used and for the structure part Kelvin-Voigt model is employed. Kelvin-Voigt model will be reached by a limiting process of the Oldroyd-B model. Interface between these two materials is guaranteed by conservative level-set method. Numerical tests of this model is performed by finite element method. This model is used for a simulation of two problems: a two dimensional channel with viscoelastic walls and pulsating inflow and Turek-Hron FSI benchmark. 1
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Modeling of anisotropic viscoelastic fluids
Šípka, Martin ; Tůma, Karel (advisor) ; Průša, Vít (referee)
In this thesis, we aim to create a framework for the derivation of thermodynamically consistent anisotropic viscoelastic models. As an example we propose simple models extending the isotropic Oldroyd-B and Giesekus models to illustrate the models' behavior and the process of finding the correct equations. We show what behavior in sheer we can expect and continue with a 3D simulation inspired by the experiment on a real liquid crystal mixture. Finally, we compare the simulation and the experiment to find similarities and possible further research topics.
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Numerical comparison of two mathematical formulations of viscoelastic Oldroyd-B model
Cach, Jakub ; Tůma, Karel (advisor) ; Hron, Jaroslav (referee)
Viscoelastic fluids are not only interesting for their application in various areas of industry, but are especially important in biological processes, as most biofluids are visco- elastic. The ability to well numerically model such fluids and simulate their behavior is advantageous both in time and money, as there is no need to perform demanding physical experiments. This text presents the thermodynamic derivation of the Oldroyd-B model of a viscoelastic fluid which automatically guarantees the fulfillment of the 2nd law of thermodynamics in two different but equivalent formulations: B and F. As a numerical experiment a simple benchmark of viscoelastic flow past cylinder for different Weissenberg numbers was performed using a program in finite-element FEniCS. In the B-formulation it was possible to reach an agreement with the benchmark, on the other hand in the F- formulation it was not, although this formulation should be more suitable for numerical computations. Analysis and correction of the F-formulation is beyond the scope of this study. 1
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