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Numerical simulation of incompressible fluid flow by the spectral element method
Pokorný, Jan ; Hlavička, Rudolf (oponent) ; Čermák, Libor (vedoucí práce)
The thesis presents the spectral element method and its application to a steady 2-D laminar flow of an incompressible Newtonian fluid. Main features of this method are presented in the thesis. The flow is governed by the steady Navier-Stokes equation. Together with boundary data they form the steady Navier-Stokes problem. Its weak form is a starting point for the method. A space discretization is applied and it results into a nonlinear system of equations. Due to this, the nonlinearity has to be treated. To obtain a linear system of equations is the Newton iteration method used. This algorithm forms the kernel of a Navier-Stokes solver that is implemented in Matlab. Finally, there are presented two examples: the lid driven cavity flow and the flow over a cylinder. The first one is solved for Reynolds numbers from 1 to 1000 and the second one for Reynolds numbers from 1 to 100.
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Použití metody spektrálních elementů ve výpočtech nestlačitelného turbulentního proudění
Jiříček, David ; Pech, Jan (vedoucí práce) ; Dolejší, Vít (oponent)
Práce se zabývá modelováním nestlačitelného turbulentního proudění pomocí metody spektrálních elementů (SEM, spectral element method). Jsou zde představeny principy této metody, kterou můžeme chápat jako kombinaci spektrální metody a metody konečných prvků. Turbulentní proudění je popsáno dvou rovnicovým k-ω modelem turbulence, konkrétně Kolmogorovovým modelem a Wilcoxovým modelem. V práci jsou objasněny důvody této volby. Oba modely ve verzi pro 2D výpočty jsou implementovány do Nektar++, již existujícího C++ frameworku pro řešení rovnic metodou spektrálních elementů. Byla nalezena analytická řešení Navier-Stokesových rovnic s proměnnou viskozitou. Tato řešení byla následně použita pro otestování implementace. Simulovali jsme turbulentní proudění v rovinném kanálu a porovnali jsme výsledky s přímou numerickou simulací. 1
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Numerical simulation of incompressible fluid flow by the spectral element method
Pokorný, Jan ; Hlavička, Rudolf (oponent) ; Čermák, Libor (vedoucí práce)
The thesis presents the spectral element method and its application to a steady 2-D laminar flow of an incompressible Newtonian fluid. Main features of this method are presented in the thesis. The flow is governed by the steady Navier-Stokes equation. Together with boundary data they form the steady Navier-Stokes problem. Its weak form is a starting point for the method. A space discretization is applied and it results into a nonlinear system of equations. Due to this, the nonlinearity has to be treated. To obtain a linear system of equations is the Newton iteration method used. This algorithm forms the kernel of a Navier-Stokes solver that is implemented in Matlab. Finally, there are presented two examples: the lid driven cavity flow and the flow over a cylinder. The first one is solved for Reynolds numbers from 1 to 1000 and the second one for Reynolds numbers from 1 to 100.
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Computation of flow around heated cylinder
Pech, Jan
Results of two dimensional numerical simulation of flow around heated cylinder will be presented. The focus is on frequency of vortex shedding in regime of low Reynolds numbers. Computational method based on scheme of spectral elements for Navier-Stokes equations, modified to involve temperature dependent viscosity.
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2D Numerical simulations of wake behind cylinder using spectral element method
Pech, Jan
We investigated 2D numerical simulation of wake in the flow behind circular cylinder. The main object of observance was the frequency of vortex shedding (Strouhal number (St)) depending on the Reynolds number (Re). Using spectral element method we performed a set of simulations to check the onset of vortex shedding, e.g. the critical Reynolds number and relation St-Re. Model of wake behind heated cylinder was computed using commercial software.
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