Two aspects of solving the incompressible Navier-Stokes equations are described in the thesis. The preconditioning of the algebraic systems arising from the Finite Element Method discretization of the Navier-Stokes equations is complex due to the saddle point structure of the resulting algebraic problems. The Pressure Convection Diffusion Reaction and the Least Squares Commutator preconditioners constitute two possible choices studied in the thesis. Solving the flow problems in time-dependent domains requires special numerical methods, such as the Fictitious Boundary method and the Arbitrary Lagrangian Eulerian formulation of Navier-Stokes equations which are used in the thesis. The problems examined in the thesis are simulations of experiments conducted in liquid Helium at low temperatures. These simulations can be used to establish a relationship between vorticity and new quantity pseudovorticity in an experiment-like setting.

The dynamic response of long structures (e.g., pavements) subjected to moving loads is generally difficult to simulate using conventional methods like the finite element method in the Lagrangian setting. This is because the entire length of the structure in the path of the moving load would need to be discretized, and in turn would require large meshes. Additionally, if improvement in quality of results through the use of finer mesh sizes is sought, the entire region of the mesh in the load path would require refinement. As a direct result, long simulation run-times can be expected when using conventional methods. To overcome these drawbacks, and improve the efficiency of the finite element simulations, the Arbitrary Lagrangian Eulerian (ALE) approach can be used to simulate pavement structures, provided longitudinal homogeneity is assumed. This contribution uses an extension of the quasi-static ALE framework to the transient domain, enabling the study of the dynamic response of pavement structures subjected to moving loads. In this work, some case studies are considered to highlight the capabilities of this dynamic ALE framework.

This work describes the implementation of a novel dynamic Arbitrary Lagrangian Eulerian (ALE) formulation for the simulation of pavement structures loaded by rolling tires in a finite element framework. The proposed formulation enables the simulation of dynamic effects like acceleration, deceleration and variation of the wheel load on the pavement. The ALE scheme is described for a hyperelastic St. Venant-Kirchhoff material capable of finite deformations. With the adoption of this dynamic ALE formulation, a significant improvement in terms of speed and efficiency of the simulation is achieved in comparison to a classical transient Lagrangian formulation. This is primarily because only the relevant portion of the mesh around the applied load needs to be discretized and simulated. Another benefit is that a cumbersome moving load formulation does not need to be implemented. The results show satisfactory agreement with a conventional Lagrangian simulation with a moving load.

Cette recherche a pour but d’expliquer l’évolution du Groupe des Verts/ale en matière de stratégies et de poids politique au sein du parlement européen. C’est par le biais de l’utilisation de la théorie de la Mise à l’Agenda ainsi que de la théorie de la crise des crises de Schattschneider que ce travail tente de montrer qu’il existe une corrélation forte entre population et institution, notamment en ce qui concerne les enjeux climatiques et lors des périodes de crise. Cette analyse du groupe des Verts/Ale basée sur des entretiens semi-dirigés permet notamment de mieux comprendre les multiples stratégies des verts de mise à l’agenda européen, les mécanismes de contrôle et d’instrumentalisation parlementaire, les rapports interinstitutionnels européens et les formations de coalitions entre groupes politiques. La conclusion de cette recherche est que si les comportements et stratégies du groupe des verts/ale ont porté leurs fruits jusqu’en 2020, le processus de mise à l’agenda est majoritairement influencé par les périodes de crise qui viennent redéfinir les priorités politiques des dirigeants européens. / The aim of this research is to explain the evolution of the Green/EFA Group in terms of strategies and political weight within the European Parliament. Using the Agenda Setting theory and Schattschneider's Crisis of Crises theory, this work attempts to show that there is a strong correlation between population and institution, particularly in terms of climate issues and during periods of crisis. This analysis of the Greens/EFA group, based on semi-structured interviews, provides a better understanding of the multiple strategies used by the green political group to put issues on the European agenda, the mechanisms of parliamentary control and instrumentalization, European inter-institutional relations and the formation of coalitions between political groups. The conclusion of this research is that, while the behaviors and strategies of the Greens/EFA group have shown good results up to 2020, the process of agenda setting is mainly influenced by periods of crisis that redefine the political priorities of European leaders.

O presente trabalho consiste no uso do Método dos Elementos Finitos (MEF) para a análise de interação fluido-estruturas de barras com foco em problemas transientes envolvendo explosões ou outras ações com propagação de ondas de choque. Para isso é necessário o estudo de três diferentes aspectos: a dinâmica das estruturas computacional, a dinâmica dos fluidos computacional e o problema do acoplamento. No caso da dinâmica das estruturas computacional deve-se identificar em função da cinemática de deformações, quais são os requisitos para que um elemento seja adequado para analisar tais problemas, tendo em vista que a formulação deve admitir grandes deslocamentos. Para evitar problemas relacionados com aproximações de rotações finitas, opta-se por empregar uma formulação descrita em termos de posições e que leva em consideração os efeitos de empenamento da seção transversal. No caso da dinâmica dos fluidos computacional, busca-se uma formulação para escoamentos compressíveis que seja estável e ao mesmo tempo sensível ao movimento da estrutura, sendo empregado um algoritmo de integração temporal explícito baseado em características com as equações governantes descritas na forma Lagrangeana-Euleriana Arbitrária (ALE). No que se refere ao acoplamento, busca-se modularidade e versatilidade, empregando-se um modelo particionado fraco (explícito) de acoplamento e técnicas de transferência das condições de contorno (Dirichlet-Neummann), sendo estudados os efeitos de utilizar transferência bidirecional ou unidirecional dessas condições de contorno. / This work consists in the use of the Finite Element Method (FEM) for numerical analysis of fluid-bar structures, focusing on transient problems involving explosions or other actions with shock waves propagation. For this purpose, one needs to study three different aspects: the computational structural dynamics, the computational fluid dynamics and the coupling problem. Regarding computational structural dynamics, one need firstly to identify the requirements for an element to be adequate to analyze such problems, taking into account the fact that such element should admit large displacements. In order to avoid problems related to finite rotation approximations and to give a realist representation of a 3D bar structure, we chose a formulation defined in terms of positions and that considers the cross-section warping effects. Regarding computational fluid dynamics, we seek for a stable formulation for compressible flows, and at same time, sensitive to the movement of the structure, leading to an explicit time integration algorithm based on characteristics with governing equations described in the Arbitrary Lagrangian-Eulerian (ALE) form. Regarding to coupling, we chose to use a weak (explicit) partitioning coupling model in order to ensure modularity and versatility. The developed coupling scheme is bases on boundary conditions transfer techniques (Dirichlet-Neummann), and we study the effects of using bidirectional or unidirectional boundary conditions transfers.

Die künstliche Grundwasserabsenkung stellt eine wichtige Maßnahme für die Entwässerung von Baugruben und bergbaulich genutzten Flächen dar. Eine erfolgreiche und zielgerichtete Absenkung des Grundwasserspiegels setzt ein zweckmäßiges Design und die richtige Auswahl der genutzten Absenkungstechniken voraus. Dabei sind insbesondere die Dimension des abzusenkenden Bereichs, die Untergrundbeschaffenheit sowie zu erfüllende umweltschutzrechtliche Regelungen zu berücksichtigen. Zur Grundwasserabsenkung kommen üblicherweise verschiedene Ausführungen und Anordnungen von Pumpbrunnen zum Einsatz. Konventionelle Pumpbrunnen, welche für Absenkungsmaßnahmen eingesetzt werden, entnehmen Grundwasser aus dem Aquifer. Durch das fortwährende Abpumpen von in der Regel erheblichen Wassermengen können jedoch Umweltprobleme entstehen, und es ist mit zusätzlichen Entsorgungskosten für die Ableitung des geförderten Wassers zu rechnen. Im Gegensatz hierzu stellen vertikale Zirkulationsbrunnen (VCW) einen innovativen Ansatz dar, der eine lokale Grundwasserabsenkung ohne Nettowasserentnahme aus dem Aquifer erlaubt. Ein VCW kann als ein Einbohrlochsystem aufgefasst werden, bei dem im oberen Bereich eines Brunnens Wasser entnommen und dieses in einem separaten, weiter unten installierten Brunnenbereich wieder injiziert wird. Die erfolgreiche Anwendung dieser neuen Grundwasserabsenkungstechnik erfordert die genaue Kenntnis der Faktoren, welche für die Grundwasserströmungsverhältnisse relevant sind und somit die Absenkung bestimmen. Traditionelle Berechnungsansätze vernachlässigen oft vertikale Grundwasserbewegungen und sind deshalb für die Beschreibung der komplexen Strömungsverhältnisse in unmittelbarer Nähe eines VCW nicht geeignet. Aus diesem Grund steht die systematische Untersuchung der Grundwasserströmung unter Berücksichtigung vertikaler Strömungskomponenten im Hauptfokus dieser Arbeit. Die Untersuchungen beschäftigen sich in erster Linie mit der Entwicklung einer geeigneten Simulationsmethode, mit der Evaluierung des Einflusses relevanter hydrogeologischer Parameter sowie mit der Durchführung und Auswertung von Pumpversuchen an einem Feldstandort. Die hier vorgestellte neue Simulationsmethode koppelt den sogenannten Arbitrary‐Lagrangian‐Eulerian‐(ALE)‐Algorithmus mit der Grundwasserströmungsgleichung. Die Simulationsergebnisse werden mit mehreren analytischen Lösungen verglichen und verifiziert. Das entwickelte numerische Modell berücksichtigt auch Vertikalströmungen und eignet sich somit zur Simulation der Grundwasserströmung in der Nähe von VCW. Folglich kann nun die Lage des Grundwasserspiegels, vor allem für ungespannte Grundwasserleiter, präzise berechnet werden. Nach erfolgter Kalibrierung des numerischen Modells anhand von Felddaten wurde eine Sensitivitätsanalyse relevanter Parameter im Hinblick auf die erzielte Absenkung und deren Auswirkungen auf die Grundwasserströmungssituation durchgeführt. Die dabei erhaltenen Ergebnisse zeigen, dass die Grundwasserabsenkung proportional zur Pumprate, indirekt proportional zur hydraulischen Leitfähigkeit und fast unabhängig von der Anisotropie des Grundwasserleiters um den VCW ist. Des Weiteren zeigte sich, dass die Lage des oberen Entnahmepunktes einen größeren Einfluss auf die Absenkung als die Lage des darunter liegenden Injektionspunktes hat. Die Größe des von der Grundwasserzirkulation beeinflussten Bereiches hängt dagegen neben dem Abstand dieser beiden Punkte hauptsächlich auch von der Anisotropie des Aquifermaterials ab. Um den Einfluss der Hydrostratigraphie auf die Grundwasserströmung zu untersuchen, wurden die Eigenschaften der einzelnen Schichten genau charakterisiert. Hierfür wurden Direct‐Push‐, Pump‐, Injektions‐ sowie Zirkulationsversuche an einem Feldstandort durchgeführt. Zudem wurden Bohrkerne entnommen und mithilfe von Siebanalysen vertikale Korngrößenverteilungsprofile im Labor bestimmt. Die eingesetzten experimentellen Methoden stellen in Kombination mit numerischen Simulationsrechnungen eine gute Basis dar, um die Rolle der Schichtstruktur im Aquifer besser beurteilen zu können. Die Untersuchungen leisten somit einen wichtigen Beitrag für das zukünftige Design und den Betrieb von VCW für Grundwasserabsenkungszwecke in ungespannten Grundwasserleitern. Zudem zeigt die hier vorliegende Arbeit das große Potential dieser neuen Grundwasserabsenkungstechnik als vielversprechende Alternative zu konventionellen Absenkungsverfahren auf.

Title: Fluid-structure interaction of compressible flow Author: RNDr. Jaroslava Hasnedlová Department: Department of Numerical Mathematics, Institute of Applied Mathematics Supervisors: Prof. RNDr. Miloslav Feistauer, DrSc., Dr. h. c., Prof. Dr. Dr. h. c. Rolf Rannacher Supervisors' e-mail addresses: feist@karlin.mff.cuni.cz, rannacher@iwr.uni-heidelberg.de 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 sep- arately 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 L2 (L2 )-norm and in DG-norm formed by the L2 (H1 )-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 compress- ible Navier-Stokes equations are formulated in...

O presente trabalho consiste no uso do Método dos Elementos Finitos (MEF) para a análise de interação fluido-estruturas de barras com foco em problemas transientes envolvendo explosões ou outras ações com propagação de ondas de choque. Para isso é necessário o estudo de três diferentes aspectos: a dinâmica das estruturas computacional, a dinâmica dos fluidos computacional e o problema do acoplamento. No caso da dinâmica das estruturas computacional deve-se identificar em função da cinemática de deformações, quais são os requisitos para que um elemento seja adequado para analisar tais problemas, tendo em vista que a formulação deve admitir grandes deslocamentos. Para evitar problemas relacionados com aproximações de rotações finitas, opta-se por empregar uma formulação descrita em termos de posições e que leva em consideração os efeitos de empenamento da seção transversal. No caso da dinâmica dos fluidos computacional, busca-se uma formulação para escoamentos compressíveis que seja estável e ao mesmo tempo sensível ao movimento da estrutura, sendo empregado um algoritmo de integração temporal explícito baseado em características com as equações governantes descritas na forma Lagrangeana-Euleriana Arbitrária (ALE). No que se refere ao acoplamento, busca-se modularidade e versatilidade, empregando-se um modelo particionado fraco (explícito) de acoplamento e técnicas de transferência das condições de contorno (Dirichlet-Neummann), sendo estudados os efeitos de utilizar transferência bidirecional ou unidirecional dessas condições de contorno. / This work consists in the use of the Finite Element Method (FEM) for numerical analysis of fluid-bar structures, focusing on transient problems involving explosions or other actions with shock waves propagation. For this purpose, one needs to study three different aspects: the computational structural dynamics, the computational fluid dynamics and the coupling problem. Regarding computational structural dynamics, one need firstly to identify the requirements for an element to be adequate to analyze such problems, taking into account the fact that such element should admit large displacements. In order to avoid problems related to finite rotation approximations and to give a realist representation of a 3D bar structure, we chose a formulation defined in terms of positions and that considers the cross-section warping effects. Regarding computational fluid dynamics, we seek for a stable formulation for compressible flows, and at same time, sensitive to the movement of the structure, leading to an explicit time integration algorithm based on characteristics with governing equations described in the Arbitrary Lagrangian-Eulerian (ALE) form. Regarding to coupling, we chose to use a weak (explicit) partitioning coupling model in order to ensure modularity and versatility. The developed coupling scheme is bases on boundary conditions transfer techniques (Dirichlet-Neummann), and we study the effects of using bidirectional or unidirectional boundary conditions transfers.

Problems governed by partial differential equations (PDEs) in deformable domains, t Rd; d = 2; 3; are of fundamental importance in science and engineering. They are of particular relevance in the design of many engineering systems e.g., aircrafts and bridges as well as to the analysis of several biological phenomena e.g., blood ow in arteries. However, developing numerical scheme for such problems is still very challenging even when the deformation of the boundary of domain is prescribed a priori. Possibility of excessive mesh distortion is one of the major challenge when solving such problems with numerical methods using boundary tted meshes. The arbitrary Lagrangian- Eulerian (ALE) approach is a way to overcome this difficulty. Numerical simulations of convection-dominated problems have for long been the subject to many researchers. Galerkin formulations, which yield the best approximations for differential equations with high diffusivity, tend to induce spurious oscillations in the numerical solution of convection dominated equations. Though such spurious oscillations can be avoided by adaptive meshing, which is computationally very expensive on ne grids. Alternatively, stabilization methods can be used to suppress the spurious oscillations. In this work, the considered equation is designed within the framework of ALE formulation. In the first part, Streamline Upwind Petrov-Galerkin (SUPG) finite element method with conservative ALE formulation is proposed. Further, the first order backward Euler and the second order Crank-Nicolson methods are used for the temporal discretization. It is shown that the stability of the semi-discrete (continuous in time) ALE-SUPG equation is independent of the mesh velocity, whereas the stability of the fully discrete problem is unconditionally stable for implicit Euler method and is only conditionally stable for Crank-Nicolson time discretization. Numerical results are presented to support the stability estimates and to show the influence of the SUPG stabilization parameter in a time-dependent domain. In the second part of this work, SUPG stabilization method with non-conservative ALE formulation is proposed. The implicit Euler, Crank-Nicolson and backward difference methods are used for the temporal discretization. At the discrete level in time, the ALE map influences the stability of the corresponding discrete scheme with different time discretizations, and it leads to schemes where conservative and non-conservative formulations are no longer equivalent. The stability of the fully discrete scheme, irrespective of the temporal discretization, is only conditionally stable. It is observed from numerical results that the Crank-Nicolson scheme induces high oscillations in the numerical solution compare to the implicit Euler and the backward difference time discretiza-tions. Moreover, the backward difference scheme is more sensitive to the stabilization parameter k than the other time discretizations. Further, the difference between the solutions obtained with the conservative and non-conservative ALE forms is significant when the deformation of domain is large, whereas it is negligible in domains with small deformation. Finally, the local projection stabilization (LPS) and the higher order dG time stepping scheme are studied for convection dominated problems. The analysis is based on the quadrature formula for approximating the integrals in time. We considered the exact integration in time, which is impractical to implement and the Radau quadrature in time, which can be used in practice. The stability and error estimates are shown for the mathematical basis of considered numerical scheme with both time integration methods. The numerical analysis reveals that the proposed stabilized scheme with exact integration in time is unconditionally stable, whereas Radau quadrature in time is conditionally stable with time-step restriction depending on the ALE map. The theoretical estimates are illustrated with appropriate numerical examples with distinct features. The second order dG(1) time discretization is unconditionally stable while Crank-Nicolson gives the conditional stable estimates only. The convergence order for dG(1) is two which supports the error estimate.

<p align="justify">This work deals with the development of numerical methods for compressible flow simulation with application to the interaction of fluid flows and structural bodies.</p> <p align="justify">First, we develop numerical methods based on multidimensional upwind residual distribution (RD) schemes. Theoretical results for the stability and accuracy of the methods are given. Then, the RD schemes for unsteady problems are extended for computations on moving meshes. As a second approach, cell centered and vertex centered finite volume (FV) schemes are considered. The RD schemes are compared to FV schemes by means of the 1D modified equation and by the comparison of the numerical results for scalar problems and system of Euler equations. We present a number of two and three dimensional steady and unsteady test cases, illustrating properties of the numerical methods. The results are compared with the theoretical solution and experimental data.</p> <p align="justify">In the second part, a numerical method for fluid-structure interaction problems is developed. The problem is divided into three distinct sub-problems: Computational Fluid Dynamics, Computational Solid Mechanics and the problem of fluid mesh movement. The problem of Computational Solid Mechanics is formulated as a system of partial differential equations for an anisotropic elastic continuum and solved by the finite element method. The mesh movement is determined using the pseudo-elastic continuum approach and solved again by the finite element method. The coupling of the problems is achieved by a simple sub-iterative approach. Capabilities of the methods are demonstrated on computations of 2D supersonic panel flutter and 3D transonic flutter of the AGARD 445.6 wing. In the first case, the results are compared with the theoretical solution and the numerical computations given in the references. In the second case the comparison with experimental data is presented.</p>