Original title: Numerická simulace proudění stlačitelných tekutin pomocí multigridních metod
Translated title: Numerical simulation of compressible flows with the aid of multigrid methods
Authors: Živčák, Andrej ; Dolejší, Vít (advisor) ; Knobloch, Petr (referee)
Document type: Master’s theses
Year: 2012
Language: slo
Abstract: [eng] [cze]
We deal with the numerical solution of the Navier-Stokes equations describing a motion of viscous compressible flows. The governing equations are discretized with the aid of discontinuous Galerkin finite element method which is based on a discontinuous piecewise polynomial approximation. The discretizations leads to a large nonlinear algebraic system. In order to solve this system efficiently, we develop the so-called p-multigrid solution strategy which employ as a projec- tion and a restriction operators the L2 -projection in the spaces of polynomial functions on each element separately. The p-multigrid technique is studied, deve- loped and implemented in the code ADGFEM. The computational performance of the method is presented. Skúmame numerické riešenie Navier-Stokesovych rovníc popisujúcich prúdenie viskóznej stlačitel'nej tekutiny. Rovnice sú diskretizované pomocou ne- spojitej Galerkinovej metódy konečných prvkov, ktorá je založená na aproximácii po častiach nespojitými polynomiálnymi funkciami. Diskretizovaná úloha vedie k vel'kému systému nelineárnych algebraických rovníc. S ciel'om vyriešit' tento systém efektívne sme odvodili tzv. p-multigridnú stratégiu riešenia, ktorá používa ako operátory projekcie a restrikcie L2 -projekciu medzi priestorami polynomiál- nych funkcií a to zvlášt' pre každý element. p-Multigridná technika bola študo- vaná, odvodená a implementovaná v kóde ADGFEM. Výpočetný výkon metódy je uvedený.
Keywords: discontinuous Galerkin method; multigrid; Navier-Stokes equations; multigrid; Navier-Stokesove rovnice; nesppojitá Galerkinova metóda

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/40853

Permalink: http://www.nusl.cz/ntk/nusl-459303


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Master’s theses