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Fluid-structure interaction of compressible flow

Hasnedlová, Jaroslava

German Title: Fluid-Struktur Interaktionen von verdichtbar Strömung

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Abstract

The presented work is split into two parts. The first part is devoted to the theory of the discontinuous Galerkin finite element (DGFE) method for the space-time discretization of a nonstationary convection-diffusion initial-boundary value problem with nonlinear convection and linear diffusion. The DGFE method is applied separately in space and time using, in general, different space grids on different time levels and different polynomial degrees p and q in space and time discretization. The main result is the proof of error estimates in L^2(L^2)-norm and in DG-norm formed by the L^2(H^1)-seminorm and penalty terms. The second part of the thesis deals with the realization of fluid-structure interaction problem of the compressible viscous flow with the elastic structure. The time-dependence of the domain occupied by the fluid is treated by the ALE (Arbitrary Lagrangian-Eulerian) method, when the compressible Navier-Stokes equations are formulated in the ALE formulation. The deformation of the elastic body, caused by the aeroelastic forces, is described by the dynamical elasticity equations. Both these systems are coupled by the transmission conditions. For the space discretization of the flow problem the DGFE method is used. The time-discretization is realized by the backward difference formula. The structural problem is discretized by conforming finite element method and the Newmark method. The fluid-structure interaction is realized via weak or strong coupling algorithms. The developed technique is tested by numerical experiments and applied to the simulation of vibrations of vocal folds during phonation onset.

Translation of abstract (other)

Pøedkládaná práce je rozdìlena do dvou èástí. První èást se zabývá teorií nespojité Galerkinovy metody koneèných prvkù (DGFEM) pro èasoprostorovou diskretizaci nestacionárního problému konvekce-difuze s nelinearní konvekcí a linearní difuzí. DGFEM je aplikována oddìlenì v èase a prostoru s užitím obecnì rozdílných sítí na rùzných èasových úrovních a polynomù obecnì rozdílných øádù p a q pro prostorovou a èasovou diskretizaci. Hlavním zájmem této èásti je dùkaz odhadu chyby metody v L^2(L^2)-normì a v DG-normì. Druhá èást práce pojednává o problému interakce stlaèitelného vazkého proudìní s elastickým tìlesem. Èasová závislost oblasti vyplnìné tekutinou je brána v potaz pomocí ALE metody a stlaèitelné Navierovy-Stokesovy rovnice jsou formulovány v ALE tvaru. Deformace elastického tìlesa zpùsobená aerodymickými silami je popsána pomocí dynamických rovnic elastického tìlesa. Oba systémy jsou propojeny pøechodovými podmínkami. Diskretizece proudìní je v prostoru provedena pomocí DGFEM a v èase s využitím metody zpìtných diferencí. Problém elastické struktury je diskretizován pomocí metody koneèných prvkù a Newmarkovy metody. Interakce je realizována pomocí silné a slabé vazby. Vyvinutá technika je testována na numerických experimentech a aplikována na simulaci vibrací lidských hlasivek na zaèátku fonace.

Item Type: Dissertation
Supervisor: Rannacher, Prof. Dr. Rolf
Date of thesis defense: 5. September 2012
Date Deposited: 20. Sep 2012 09:51
Date: 2012
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Controlled Keywords: Fluid-Struktur-Wechselwirkung, Finite-Elemente-Methode, Computersimulation
Uncontrolled Keywords: Discontinuous Galerkin finite element method , fluid-structure interaction , computer simulation
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