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Computer simulation and numerical analysis of compressible flow problems
Kubera, Petr
The thesis deals with the construction of an adaptive 1D and 2D mesh in the framework of the cell- centered finite volume scheme. The adaptive strategy is applied to the numerical solution of problems governed by the Euler equations, which is a hyperbolic system of PDE's. The used algorithm is applicable to non-stationary problems and consists of three independent parts, which are cyclically repeated. These steps are PDE evolution, mesh adaptation and interpolation of numerical solution from the old mesh to the newly adapted mesh. Owing to this the algorithm can be used also for other hyperbolic systems. The thesis is focused on the development of our mesh adaptation strategy, based on the anisotropic mesh adaptation, which preserves the geometric mass conservation law in each computational step. Several test problems with moving discontinuity are computed to compare our algorithm with Moving Mesh algorithms. Keywords: finite volume method, adaptive methods, geometric mass conservation law
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Use of numerical simulation for reduction of scrap from Al alloys
Doležal, Petr ; Lána, Ivo (referee) ; Krutiš, Vladimír (advisor)
This thesis deals with the possibilities of current simulation software and their use in technical practice. The aim of the thesis is to describe the process of the simulation; summarise the required initial parameters of the cast in order to achieve a credible simulation, and to describe the possibilities of the use of simulation software in the area of casting defect prediction. This theoretical analysis is applied on a specific cast, which is subject to a simulation trying to find an ideal inflow system, as well as predicting the formation of possible defects. The accuracy of this simulation will be proved by analysing an actual cast product.
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Discontinuous Galerkin method for the solution of compressible viscous flow
Česenek, Jan
Title: Discontinuous Galerkin method for solving compressible viscous flow Author: Jan Česenek Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Miloslav Feistauer, DrSc., dr.h.c., Department of Numerical Mathematics Abstract: The subject of this PhD thesis is the numerical simulation of the interaction of two-dimensional compressible viscous flow and a vibrating airfoil. We consider a solid airfoil with two degrees of freedom which can rotate around the elastic axis and oscillate in the vertical direction. The numerical simulation of this problem consist of the dis- continuous Galerkin finite element method solving Navier-Stokes equations coupled with a system of nonlinear ordinary differential equations describing the airfoil motion. The time-dependent domain is taken into account with the aid of the Arbitrary Lagrangian- Eulerian(ALE) formulation. Theoretical part of this paper is concerned with error esti- mates of the space-time discontinuous Galerkin method for scalar nonstationary equations with nonlinear convection and nonlinear diffusion. Keywords: convection-diffusion problems, discontinuous Galerkin method, interaction of a fluid with a vibrating airfoil, ALE method
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Wavelet-based Realized Variation and Covariation Theory
Baruník, Jozef ; Vošvrda, Miloslav (advisor) ; Kočenda, Evžen (referee) ; Di Matteo, Tiziana (referee) ; Veredas, David (referee)
English Abstract The study of volatility and covariation has become one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This dissertation contains a complete theory for realized variation and covariation estima- tion, generalizing current knowledge and taking the estimation into the time-frequency domain for the first time. The first part of the theory presents a wavelet-based realized variation theory, while the second part introduces its multivariate counterpart, a wavelet- based realized covariation theory. The results generalize the popular realized volatility framework by bringing robustness to noise as well as jumps and the ability to measure realized variation and covariation not only in the time domain, but also in the frequency domain. The theory is also tested in a numerical study of the small sample performance of the estimators and compared to other popular realized variation estimators under dif- ferent simulation settings with changing noise as well as jump level. The results reveal that our wavelet-based theory is able to estimate the realized measures with the greatest precision. Another notable contribution lies in the application of the presented theory. Our time-frequency estimators not only produce more efficient...
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Computer simulation and numerical analysis of compressible flow problems
Kubera, Petr ; Felcman, Jiří (advisor) ; Knobloch, Petr (referee) ; Fürst, Jiří (referee)
The thesis deals with the construction of an adaptive 1D and 2D mesh in the framework of the cell- centered finite volume scheme. The adaptive strategy is applied to the numerical solution of problems governed by the Euler equations, which is a hyperbolic system of PDE's. The used algorithm is applicable to nonstationary problems and consists of three independent parts, which are cyclically repeated. These steps are PDE evolution, then mesh adaptation and recovery of numerical solution from the old mesh to the newly adapted mesh. Owing to this the algorithm can be used also for other hyperbolic systems. The thesis is focused on the development of our mesh adaptation strategy, based on the anisotropic mesh adaptation, which preserves the geometric mass conservation law in each computational step. The proposed method is suitable to solve problems with moving discontinuities. Several test problems with moving discontinuity are computed to compare our algorithm with Moving Mesh algorithms.
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Ionizing radiation shielding simulation using MCNP code
Konček, Róbert ; Košťál,, Michal (referee) ; Katovský, Karel (advisor)
Radiation is defined as ionizing if it has enough energy to remove electrons from atoms or molecules when it passes through or collides with matter. This ability implies potentially detrimental effects on living tissue. Ionizing radiation shielding is therefore a discipline of great practical importance. The thesis builds upon the author's previous work on the topic and widens the scope of discussion with theoretical and practical issues of advanced shielding calculations. The theoretical part of the thesis describes several approaches to calculating fluence or absorbed dose at an arbitrary point in space. Point-kernel methods provide sufficiently accurate results for simpler shielding problems. In many practical cases, however, calculations based on the transport theory are necessary. There are two basic types of transport calculations: deterministic transport calculations in which the linear Boltzmann equation is solved numerically, and Monte Carlo calculations in which a simulation is made of how particles migrate stochastically through the problem geometry. Advantages and disadvantages of both methods are discussed. In the practical part are the results of radiation shielding calculations performed with a major Monte Carlo code - MCNP6, compared with those obtained in the experiments, which were carried out at the Ionizing Radiation Laboratory at Department of Electrical Power Engeneering, FEEC BUT. The experiments consisted of placing a cobalt-60 radioisotope source at three different positions inside a lead collimator, and counting pulses with two different scintillation detectors positioned in front of the opening of the collimator, alternately with or without lead shield located between the source and the used detector. Agreement of the calculations and the data from the measurements is reasonable, given the inherent uncertainties of the experimental set-up. Performed sensitivity analysis shows relative importances of different parameters used as inputs in simulations, such as densities of materials, or dimensions of the scintillation crystals. Annotated MCNP input files used for simulation are also part of the thesis.
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