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Metody vyššího řádu založené na rekonstrukci
Dominik, Oldřich ; Kučera, Václav (advisor) ; Dolejší, Vít (referee)
This work is concerned with the introduction of a new higher order numerical scheme based on the discontinuous Galerkin method (DGM). We follow the methodology of higher order finite volume (HOFV) and spectral volume (SV) schemes and introduce a reconstruction operator into the DGM. This operator constructs higher order piecewise polynomial reconstructions from the lower order DGM scheme. We present two variants: the generalization of standard HOFV schemes, already proposed by Dumbser et al. (2008) and the generalization of the SV method introduced by Wang (2002). Theoretical aspects are discussed and numerical experiments with the focus on a 2D advection problem are carried out. Powered by TCPDF (www.tcpdf.org)
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Numerical modelling of compressible flow using spectral element method
Jurček, Martin ; Dolejší, Vít (advisor) ; Kučera, Václav (referee)
The development of computational fluid dynamics has given us a very powerful tool for investigation of fluid dynamics. However, in order to maintain the progress, it is necessary to improve the numerical algorithms. Nowadays, the high-order methods based on the discontinuous projection seem to have the largest potential for the future. In the work, we used open-source framework Nektar++, which provides the high-order discretization method. We tested the abilities of the framework for computing the compressible sonic and transonic flow. We successfully obtained simulations of the viscous and inviscid flow. We computed the lift and the drag coefficients and showed that for a higher polynomial order we can obtain the same accuracy with less degrees of freedom and lower computational time. Also, we tested the shock capturing method for the computation of the inviscid transonic flow and confirmed the potential of the high order methods. 1
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Metody vyššího řádu založené na rekonstrukci
Dominik, Oldřich ; Kučera, Václav (advisor) ; Dolejší, Vít (referee)
This work is concerned with the introduction of a new higher order numerical scheme based on the discontinuous Galerkin method (DGM). We follow the methodology of higher order finite volume (HOFV) and spectral volume (SV) schemes and introduce a reconstruction operator into the DGM. This operator constructs higher order piecewise polynomial reconstructions from the lower order DGM scheme. We present two variants: the generalization of standard HOFV schemes, already proposed by Dumbser et al. (2008) and the generalization of the SV method introduced by Wang (2002). Theoretical aspects are discussed and numerical experiments with the focus on a 2D advection problem are carried out. Powered by TCPDF (www.tcpdf.org)
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