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Mathematical modelling of glass forming process
Chaloupka, Tomáš ; Průša, Vít (advisor) ; Lanzendörfer, Martin (referee)
The thesis focus on modelling of float glass making process using viscose film type approximation. Navier-Stokes equations are averaged over one spatial variable. Then the domain with an a priory unknown shape, where the shape is a part of the solution, is transformed to a fixed computational domain. The problem is solved by finite element method using FEniCS software. In the end is discussed an influence of several parameters such as wheels, which regulates thickness of the glass and enforce an inner condition, boundary conditions or spreading coefficient on the numerical result. 1
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Matematical model of permeability evolution in a fractured porous media due to internal erosion and deposition.
Krajinová, Markéta ; Lanzendörfer, Martin (advisor) ; Zumr, David (referee)
The seepage of fluid through saturated porous media may lead to inner erosion, channelization, preferential flow and transport and deposition of particles. A novel mathematical model was created to describe some of the processes. The model describes a temporal and spatial development of porosity (volume fraction) and permeability (transmissivity) due to erosion and deposition in saturated porous and fractured media. The model calculates the change of permeability and porosity in a direction of different fracture joint sets. The model is based on multi-continua theory, where a region is divided into components (three or more components in this thesis). The components are described by separate differential equations. This approach was used recently by Mahadevan et al. (2012) and Fujisawa et al. (2009) for erosion of porous media. This thesis describes the approaches, assumptions and the equations used in the model. In contrast to the published models, the thesis considers anisotropy. It is characterized by transmissivity tensor (also hydraulic conductivity tensor), which is composed of vectors in the joint sets directions. The model also uses a Dupuit approximation, which allows to approximate flow onto a horizontal plane. The model is also introduced by a numerical simulation using final element...
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Effect of CO2 production on the water level in a closed borehole
Turjaková, Veronika ; Vlček, Josef (advisor) ; Lanzendörfer, Martin (referee)
This thesis is focused on upper mantle originated carbon dioxide exhalations in the area of Western Bohemia, particularly Cheb basin. It describes local geology, current geodynamics, earthquake swarms and related issues. The thesis introduces a simple physical model of gas- water mixture behaviour in a closed borehole. The model was created using elementary physical principles and works as a tool for simplifying the description of events, which were registered at a monitoring borehole HJB-1 at Hartoušov site. Last part of the thesis includes data which were recorded for the verification of the model. These are presented and interpreted at the end of the thesis. Key words: carbon dioxide, Henry's law, Cheb basin
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Inflow and outflow boundary conditions on artificial boundaries
Kubáč, Vojtěch ; Lanzendörfer, Martin (advisor) ; Tůma, Karel (referee)
In the beginning of this thesis we introduce the basic properties of the fluid mechanics, mainly for stationary incompressible flow. In the next section we show the weak formulation of derived (Navier-Stokes) equations and some of the boun- dary conditions. Finally, the biggest part of this thesis is occupied by numerical experiments with simple planar flows. We seek for suitable inflow and outflow boundary conditions on an artificial boundary for the problem of outflow from a long channel or inflow to that channel. 1
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Mathematical modelling of glass forming process
Chaloupka, Tomáš ; Průša, Vít (advisor) ; Lanzendörfer, Martin (referee)
The thesis focus on modelling of float glass making process using viscose film type approximation. Navier-Stokes equations are averaged over one spatial variable. Then the domain with an a priory unknown shape, where the shape is a part of the solution, is transformed to a fixed computational domain. The problem is solved by finite element method using FEniCS software. In the end is discussed an influence of several parameters such as wheels, which regulates thickness of the glass and enforce an inner condition, boundary conditions or spreading coefficient on the numerical result. 1
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Relation between forces induced by fluid flow and dissipative processes in boundary layers
Mináriková, Petra ; Maršík, František (advisor) ; Lanzendörfer, Martin (referee)
Práce se zabývá vlivem disipativních proces· v mezních vrstvách, konkrétně vlivem viskozity tekutiny a dále vlivem difúze vodní páry ve vzduchu na vznik sil p·sobících na obtékaná tělesa. Z Croccovy věty plyne, že gradient entropie má sv·j podíl na vzniku cirkulace a d·sledkem toho i na vznik vztlakové síly. Práce zkoumá vznik vztlakové síly při obtékání rotujícího válce, v soft- waru FEniCS modeluje tuto situaci, porovnává s modelem nevazké nestlačitelné tekutiny a následně i s experimentem provedeným Ing. Zdeňkem Trávníčkem a Ing. Zuzanou Broučkovou. Taktéž zkoumá vznik vztlakové síly při vypařování na horní straně válce a srovnává s případem rotujícího válce. 1
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Flows of incompressible fluids with pressure-dependent viscosity (and their application to modelling the flow in journal bearing)
Lanzendörfer, Martin ; Málek, Josef (advisor) ; Knobloch, Petr (referee) ; Süli, Endré (referee)
Title: Flows of incompressible fluids with pressure-dependent viscosity (and their application to modelling the flow in journal bearing) Author: Martin Lanzendörfer Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, DSc. Abstract: The viscosity of the fluids involved in hydrodynamic lubrication typically depends on pressure and shear rate. The thesis is concerned with steady isothermal flows of such fluds. Generalizing the recent results achieved in the case of homogeneous Dirichlet boundary conditions, the existence and uniqueness of weak solutions subject to the boundary conditions employed in practical applications will be established. The second part is concerned with numerical simulations of the lubrication flow. The experiments indicate that the presented finite element method is successful as long as certain restrictions on the constitutive model are met. Both the restrictions involved in the theoretical results and those indicated by the numerical experiments allow to accurately model real-world lubricants in certain ranges of pressures and shear rates. The last part quantifies those ranges for three representative lubricants. Keywords: existence and uniqueness of weak solutions, finite element method, pressure- thickening, shear-thinning, incompressible fluids,...
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