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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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Adaptive space-time discontinuous Galerkin method for the solution of non-stationary problems
Vu Pham, Quynh Lan ; Dolejší, Vít (advisor) ; Feistauer, Miloslav (referee)
This thesis studies the numerical solution of non-linear convection-diffusion problems using the space- time discontinuous Galerkin method, which perfectly suits the space as well as time local adaptation. We aim to develop a posteriori error estimates reflecting the spatial, temporal, and algebraic errors. These estimates are based on the measurement of the residuals in dual norms. We derive these estimates and numerically verify their properties. Finally, we derive an adaptive algorithm and apply it to the numerical simulation of non-stationary viscous compressible flows. Powered by TCPDF (www.tcpdf.org)
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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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Adaptive space-time discontinuous Galerkin method for the solution of non-stationary problems
Vu Pham, Quynh Lan ; Dolejší, Vít (advisor) ; Feistauer, Miloslav (referee)
This thesis studies the numerical solution of non-linear convection-diffusion problems using the space- time discontinuous Galerkin method, which perfectly suits the space as well as time local adaptation. We aim to develop a posteriori error estimates reflecting the spatial, temporal, and algebraic errors. These estimates are based on the measurement of the residuals in dual norms. We derive these estimates and numerically verify their properties. Finally, we derive an adaptive algorithm and apply it to the numerical simulation of non-stationary viscous compressible flows. Powered by TCPDF (www.tcpdf.org)
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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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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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Comparison of Differences in Seasonality of Demographic Time Series of The Selected Countries in EU
Morávek, David ; Šimpach, Ondřej (advisor) ; Miskolczi, Martina (referee)
In the theoretical level this thesis describes some of the statistical methods using for time series analysis with seasonal component and some of the statistical methods using only for analysis of seasonal component. In the analytical level, these statistical methods are applied to demographic time series. The seasonal component is analysed in more detail, and the progress and type of the seasonal component is compared between several european country. This thesis brings and shows some of the interesting trends, which are appeared in analysed demographic time series. Last but not least, this thesis also provides the preview on the application of some not usually using statistical methods.
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