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Modelling of flow and pressure characteristics in the model of the human upper respiratory tract under varying conditions
Karlíková, Adéla ; Forjan,, Mathias (referee) ; Paštěka, Richard (advisor)
Cílem této diplomové práce je vytvořit 3D model horních dýchacích cest podle originálního modelu segmentovaného z CT dat, aplikovat různé podmínky na průtok vzduchu v modelu, a poté hodnotit změnu charakteristik rychlosti a tlaku. Model horních dýchacích cest byl vytvořen v prostředí softwaru ANSYS, který využívá výpočetní dynamiku tekutin, a byly použity Navier-Stokesovy rovnice pro modelování průtoku vzduchu v modelu. Nejprve byl vytvořen jednoduchý 2D model za účelem seznámení se s prostředím ANSYS. Dále byl zkonstruován 3D model horních dýchacích cest a byly modelovány charakteristiky rychlosti a tlaku za různých podmínek. Tyto podmínky zahrnují různé umístění a množství míst pro odběr vzorků v modelu a výběr různých kombinací vstupů. Nakonec byly prezentovány a hodnoceny výsledky spolu s ilustracemi modelů modelovaných za různých podmínek. 3D model lze považovat ze kompromis mezi výpočetní náročností a složitostí modelu a lze jej použít jako základ pro další výzkum.
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Modification of Navier_Stokes equations asuming the quasi-potential flow
Navrátil, Dušan ; Pochylý, František (referee) ; Fialová, Simona (advisor)
The master's thesis deals with Navier-Stokes equations in curvilinear coordinates and their solution for quasi-potential flow. The emphasis is on detailed description of curvilinear space and its expression using Bézier curves, Bézier surfaces and Bézier bodies. Further, fundamental concepts of hydromechanics are defined, including potential and quasi-potential flow. Cauchy equations are derived as a result of the law of momentum conservation and continuity equation is derived as a result of principle of mass conservation. Navier-Stokes equations are then derived as a special case of Cauchy equations using Cauchy stress tensor of Newtonian compressible fluid. Further transformation into curvilinear coordinates is accomplished through differential operators in curvilinear coordinates and by using curvature vector of space curve. In the last section we use results from previous chapters to solve boundary value problem of quasi-potential flow, which was solved by finite difference method using Matlab environment.
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Magnus force acting upon a rotating sphere passing in an incompressible viscous flow
Beck, Dominik ; Martinec, Zdeněk (advisor) ; Čadek, Ondřej (referee)
Classical results of hydrodynamics such as Stokes' force law and Kirchhoff's mo- ment (torque) law are re-derived for laminar viscous flow in the framework of modern compact simplified vector calculus notation. First perturbations of these laws are found and compared visually with experiments. The Magnus drag force on a rotating and moving sphere surrounded by an incompressible viscous New- tonian fluid is derived from the perturbation series of the Navier-Stokes equations in low speed regimes with a small Reynolds number.
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Volumetric Efects Accelerated on GPU
Kubovčík, Tomáš ; Tóth, Michal (referee) ; Starka, Tomáš (advisor)
This thesis deals with simulation and rendering of fluid based volumetric effects, especially effect of fire and smoke. Computations are accelerated on graphics card using modern graphics API with motivation to achieve realistic visual results as well as physically correct calculations. Implemented volumetric effects are distributed as dynamic library which allows addition of these effects to existing applications.
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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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Fluid-structure interaction
Kosík, Adam ; Feistauer, Miloslav (advisor) ; Richter, Thomas (referee) ; Fürst, Jiří (referee)
In this thesis we are concerned with the numerical simulation of the in- teraction of compressible viscous flow and an elastic structure in 2D. For the elastic deformation we use a 2D linear model and nonlinear St. Venant- Kirchhoff and neo-Hookean models. The flow is described by the compressible Navier-Stokes equations written in the arbitrary Lagrangian-Eulerian (ALE) form in order to take into account the time-dependence of the flow domain. The discretization of both the flow problem and the elasticity problem is re- alized by the discontinuous Galerkin finite element method (DGM). We focus on testing the DGM applied to the solution of the flow and elasticity prob- lems. Furthermore, we discuss the coupling algorithm and the technique, how to deal with the deformation of the computational domain for the fluid flow problem. Our work is motivated by the biomedical applications. Numerical experiments include numerical simulation of vibrations of human vocal folds induced by the compressible viscous flow.
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Interaction of flow and an elastic body
Kosík, Adam
In the submitted work we are concerned with the numerical simulation of fluid flow and elastic body interaction. This is a coupled problem of the equations of two kinds, equations describing the flow and equations describing dynamical behaviour of the elas- tic body, which is partly surrounded by the fluid. These systems are coupled by suitable transmission conditions. The fluid flow is described by the Navier-Stokes equations, which are reformulated by the ALE method because of the deformation of the computational domain caused by the body movement. The deformation of the elastic body is described by the linear elasticity system with the generalized Hooke's law. We solve the problem by the finite element method. The developed methods are tested on the physical model of human vocal folds. 1
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Numerical simulation of compressible flows using the parallel computing
Šíp, Viktor ; Dolejší, Vít (advisor) ; Felcman, Jiří (referee)
In the present work we implemented parallel version of a computational fluid dynamics code. This code is based on Discontinuous Galerkin Method (DGM), which is due to its favourable properties suitable for parallelization. In the work we describe the Navier-Stokes equations and their discretization using DGM. We explain the advantages of usage of the DGM and formulate the serial algorithm. Next we focus on the parallel implementation of the algorithm and several particular issues connected to the parallelization. We present the numerical experiments showing the efficiency of the parallel code in the last chapter.
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Numerical simulation of compressible flows with the aid of multigrid methods
Živčák, Andrej ; Dolejší, Vít (advisor) ; Knobloch, Petr (referee)
We deal with the numerical solution of the Navier-Stokes equations describing a motion of viscous compressible flows. The governing equations are discretized with the aid of discontinuous Galerkin finite element method which is based on a discontinuous piecewise polynomial approximation. The discretizations leads to a large nonlinear algebraic system. In order to solve this system efficiently, we develop the so-called p-multigrid solution strategy which employ as a projec- tion and a restriction operators the L2 -projection in the spaces of polynomial functions on each element separately. The p-multigrid technique is studied, deve- loped and implemented in the code ADGFEM. The computational performance of the method is presented.
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Compressible fluid motion in time dependent domains
Sýkora, Petr ; Feireisl, Eduard (advisor) ; Pokorný, Milan (referee)
In this work we study the existence of weak solutions for compressible Navier-Stokes equations in unbounded time dependent domains. Using the methods introduced in Feireisl E. Dynamics of Viscous Compressible Fluids we extend the results of article Feireisl E. Neustupa J. Stebel J., Convergence of a Brinkman-type penalization for compressible fluid flows, which studies the flow with a "no-slip" boundary condition on bounded domains. Next, we extend results of article Feireisl E. Kreml O. Nečasová Š. Neustupa J. Stebel J., Weak solutions to the barotropic Navier- Stokes system with slip boundary conditions in time dependent domains, which studies flow with compete Navier boundary condition. Finally, we discuss solutions for rotating fluid system. In this case, there are new members in momentum equation, representing the Coriolis and centrifugal force, which cause problems.
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