Original title: Numerické řešení rovnic popisujících dynamiku hejn
Translated title: Numerical solution of equations describing the dynamics of flocking
Authors: Živčáková, Andrea ; Kučera, Václav (advisor)
Document type: Rigorous theses
Year: 2019
Language: slo
Abstract: [eng] [cze]
This work is devoted to the numerical solution of equations describing the dynamics of flocks of birds. Specifically, we pay attention to the Euler equati- ons for compressible flow with a right-hand side correction. This model is based on the work Fornasier et al. (2010). Due to the complexity of the model, we focus only on the one-dimensional case. For the numerical solution we use a semi- implicit discontinuous Galerkin method. Discretization of the right-hand side is chosen so that we preserve the structure of the semi-implicit scheme for the Euler equations presented in the work Feistauer, Kučera (2007). The proposed numeri- cal scheme was implemented and numerical experiments showing the robustness of the scheme were carried out. 1 V tejto práci sa venujeme numerickému riešeniu rovníc popisujúcich dynamiku kŕdľov (hejn) vtákov, takzvaný flocking. Konkrétne venujeme pozornosť systému Eulerových rovníc pre stlačiteľné prúdenie s korekciou pravej strany. Tento model vychádza z práce Fornasier et al. (2010). Pre komplikovanosť modelu sa zame- riavame len na jednodimenzionálny prípad. K numerickému riešeniu používame semi-implicitnú nespojitú Galerkinovú metódu. Diskretizáciu pravej strany vo- líme tak, aby sme zachovali štruktúru semi-implicitnej schémy pre Eulerove rov- nice predstavenej v práci Feistauer, Kučera (2007). Navrhnutá numerická schéma bola implementovaná a boli vykonané numerické experimenty, ktoré preukázali robustnosť schémy. 1
Keywords: discontinuous Galerkin method; Euler equations; flocking; flocks; semi-implicit method; Eulerové rovnice; flocking; kŕdle (česky hejná); nespojitá Galerkinová metóda; semi-implicitná metóda

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/107379

Permalink: http://www.nusl.cz/ntk/nusl-398060


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Rigorous theses