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Mathematical analysis of equations describing the flow of compressible heat conducting fluids / Mathematical analysis of equations describing the flow of compressible heat conducting fluidsAxmann, Šimon January 2016 (has links)
Title: Mathematical analysis of equations describing the flow of compressible heat conducting fluids Author: Šimon Axmann Department: Mathematical Institute of Charles University Supervisor: doc. Mgr. Milan Pokorný, Ph.D., Mathematical Institute of Charles University Abstract: The present thesis is devoted to the mathematical analysis of equa- tions describing the flow of viscous compressible newtonian fluid in various time regimes. In particular, we present existence results for three problems arising as special cases of a general model derived in the introductory part. The first chap- ter deals with time-periodic solutions to the full Navier-Stokes-Fourier system for heat-conducting fluid. The second chapter contains the proof of existence of steady solutions to a system arising from phase field model for two-phase com- pressible fluid. Finally, in the last section we study steady strong solutions to the Navier-Stokes equations under the additional assumption that the fluid is suffi- ciently dense. For each problem a different concept of the solution is considered, on the other hand in all cases an essential role is played by the crucial quantity effective viscous flux. Keywords: compressible Navier-Stokes system; weak solution; entropy variational solution; large data
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Numerické modelování nestabilit při obtékání zahřívaných těles / Numerical modelling of unstable fluid flow past heated bodiesPech, Jan January 2016 (has links)
Title: Numerical modeling of unstable fluid flow past heated bodies Author: Jan Pech Department: Mathematical Institute of Charles University Supervisor: prof. Ing. František Maršík, DrSc., Mathematical Institute of Charles University Abstract: Presented work brings new results to numerical computations of flow influenced by temperature changes. Constructed numerical algorithm takes into account variable coefficients of the differential operators in the system of in- compressible Navier-Stokes equations coupled with thermal heat equation. The spatial discretisation of the problem targets to application of high order method, the spectral element method. Phenomenons connected with high order approxi- mations are discussed on a number of examples and comparisons with methods of lower order, which are more common. Results were achieved for two fluids with opposite response to heating, air and water. The observed quantity is par- ticularly a frequency of vortex shedding, the Strouhal number, as dependent on temperature and Reynolds number. The calculated values were compared with experimental results and exhibit a good coincidence. Numerical analysis of sep- aration angle in flow around heated circular cylinder may give a new impulse to verification of accuracy and reliability of the developed method. Keywords:...
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Stlačitelné Navier-Stokes-Fourierovy rovnice pro adiabatický koeficient blízko jedničky / Compressible Navier-Stokes-Fourier system for the adiabatic coefficient close to oneSkříšovský, Emil January 2019 (has links)
In the present thesis we study the compressible Navier-Stokes-Fourier sys- tem. This is a system of partial differential equations describing the evolutionary problem for an adiabatic flow of a heat conducting compressible viscous fluid in a bounded domain. Here we consider the problem in two dimensions with zero Dirichlet boundary conditions for velocity. The cold pressure term in the pressure law for the momentum equation is here considered in the form pC(ϱ) ∼ ϱ logα (1+ϱ) for some α > 0, for which we need to work on the scale of Orlicz spaces in order to obtain useful estimates and in those space we formulate the problem weakly and also establish the weak compactness of the solution. The main result of this thesis is Theorem 6.1 where we show the existence of a weak solution with no assumptions on the size of the data and on arbitrary large time intervals. 1
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Konjugovaná funkce / Konjugovaná funkceBathory, Michal January 2016 (has links)
Using interpolation methods, new results on the boundedness of quasilinear joint weak type operators on Lorentz-Karamata (LK) spaces are established. LK spaces generalize many function spaces introduced before in literature, for example, the generalized Lorentz- Zygmund spaces, the Zygmund spaces, the Lorentz spaces and, of course, the Lebesgue spaces. The focus is mainly on the limiting cases of interpolation, where the spaces involved are, in certain sense, very close to the endpoint spaces. The results contain both necessary and sufficient conditions for the boundedness of the given operator on LK spaces. The complete characterization of embeddings of LK spaces is also included and the optimality of achieved results is then discussed. Finally, we apply our results to the conjugate function operator, which is known to be bounded on $L_p$ only if $1<p<\infty.$ Powered by TCPDF (www.tcpdf.org)
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Počítačem generované hologramy / Computer Generated HologramsTvarog, Drahoslav January 2010 (has links)
The presented Diploma thesis deals with the computer-generated diffractive structures or rather called computer generated holograms (CGH). We follow basic principles of classical holography and in the context of which we define a synthetic holography. We then show various types of digital holograms and methods of measurement of their quality. We deal with several iterative algorithms useful for computation of the Fourier transform as well as with methods of phase quantization. In the second part of the work, we describe briefly our computer code for iterative Fourier transform computation. With respect to the mentioned techniques, we further present the usability of the method for design of computer generated holograms in reflection regime. After a short introduction to the electron beam lithography and its exploitation for the origination of computer generated diffractive optical elements. We analyze reconstructions of produced holograms and evaluate its quality.
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