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Titel
Numerical continuation for periodic pipe flow with finite element method / von Dominik Worf
Weitere Titel
Numerische Pfadverfolgung für periodische Strömungen mit Finite Elemente Methoden
Verfasser / Verfasserin Worf, Dominik
Begutachter / BegutachterinKühn, Christian
ErschienenWien, 2018
Umfangx, 84 Seiten : Illustrationen, Diagramme
HochschulschriftTechnische Universität Wien, Diplomarbeit, 2018
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Zusammenfassung in deutscher Sprache
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Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers
SpracheEnglisch
DokumenttypDiplomarbeit
Schlagwörter (EN)numerical continuation / Navier Stokes / bifurcation / FEM
URNurn:nbn:at:at-ubtuw:1-108205 Persistent Identifier (URN)
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 Das Werk ist frei verfügbar
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Numerical continuation for periodic pipe flow with finite element method [1.2 mb]
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Zusammenfassung (Englisch)

This thesis is concerned with the continuation theory of incompressible periodic pipe flow. For describing the dynamics of incompressible fluids we use the incompressible Navier-Stokes equation. For a better understanding of it we'll look at its derivation. For a long time now the consensus has been that the laminar solution is linearly stable for all Reynolds numbers. The original idea of this thesis was to adapt a numerical continuation procedure to see if it is possible to jump from the laminar solution branch onto a turbulent one, as it happens in practical experiments. Therefore we inspect the different numerical methods that are used in this procedure. Especially we look at a preconditioner for the linearized problem as the matrix given by the finite element method, using Hood-Taylor elements, becomes less well conditioned as the Reynolds number increases. Prompted by this we look at the convection-diffusion equation and the streamline diffusion discretisation to be able to use it in a multigrid method. To motivate the use of the continuation procedure we look at bifurcation theory, with Fredholm operators and Crandall-Rabinowitz' theorem. We also take a short look at the Allen-Cahn equation to test if the algorithm is correctly defined.

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