This work extends a previously developed finite-volume overset-grid fluid flow solver to enable the characterisation of rigid-body-fluid interaction problems. To this end, several essential components have been developed and blended together. The inherent time-dependent nature of fluid-solid interaction problems is captured through the laminar transient incompressible Navier-Stokes equations for the fluid, and the Euler-Newton equations for rigid-body motion. First and second order accurate time discretisation schemes have been implemented for the former, whereas second and third order accurate time discretisation schemes have been made available for the latter. Without doubt the main advantage the overset-grid method offers regarding moving entities is the avoidance of the time consuming grid regeneration step, and the resulting grid distortion that can often cause numerical stability problems in the solution of the flow equations. Instead, body movement is achieved by the relative motion of a body fitted grid over a suitable background mesh. In this case, the governing equations of fluid flow are formulated using a Lagrangian, Eulerian, or hybrid flow description via the Arbitrary Lagrangian-Eulerian method. This entails the need to guarantee that mesh motion shall not disturb the flow field. With this in mind, the space conservation law has been hard-coded. The compliance of the space conservation law has the added benefit of preventing spurious mass sources from appearing due to mesh deformation. In this work, two-way fluid-solid interaction problems are solved via a partitioned approach. Coupling is achieved by implementing a Picard iteration algorithm. This allows for flexible degree of coupling specificationby the user. Furthermore, if strong coupling is desired, three variants of interface under-relaxation can be chosen to mitigate stability issues and to accelerate convergence. These include fixed, or two variants of Aitken’s adaptive under-relaxation factors. The software also allows to solve for one-way fluid-solid interaction problems in which the motion of the solid is prescribed. Verification of the core individual components of the software is carried out through the powerful method of manufactured solutions (MMS). This purely mathematically based exercise provides a picture of the order of accuracy of the implementation, and serves as a filter for coding errors which can be virtually impossible to detect by other means. Three instances of one-way fluid-solid interaction cases are compared with simulation results either from the literature, or from the OpenFOAM package. These include: flow within a piston cylinder assembly, flow induced by two oscillating cylinders, and flow induced by two rectangular plates exhibiting general planar motion. Three cases pertaining to the class of two-way fluid-interaction problems are presented. The flow generated by the free fall of a cylinder under the action of gravity is computed with the aid of an intermediate ‘motion tracking’ grid. The solution is compared with the one obtained using a vorticity based particle solver for validation purposes. Transverse vortex induced vibrations (VIV) of a circular cylinder immersed in a fluid, and subject to a stream are compared with experimental data. Finally, the fluttering motion of a rectangular plate under different scenarios is analysed.

New approach for computational modeling of the dynamic behavior of elastic body immersed in incompressible viscous stagnant fluid is described in this work. It is based on determination of added effects (added mass and added damping). This effects are inserted into computational model and it replace influence of the fluid. Commonly used commercial computational software may be used. Approach is based on assumption appropriate for the linear flow. Two pressure field are determined. One for movement of the unite acceleration of the fluid boundary and the second for unite velocity. Nonlinear model (Navier-Stokes equation in ALE form) had to be used for determination of the added damping, hence results are valid only for pre-selected amplitude of vibration.

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.

<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>

Title: Numerical solution of flows in time dependent domains with elastic walls Author: Martin Hadrava Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Miloslav Feistauer, DrSc., dr. h. c. Supervisor's e-mail address: feist@karlin.mff.cuni.cz Abstract: This work is devoted to the numerical solution of flow in time dependent domains with elastic walls. This problem has several applications in engineering and medicine. The flow is described by the system of Navier-Stokes equations supplemented with suitable initial and boundary conditions. A part of the boundary of the region oc- cupied by the fluid is represented by an elastic wall, whose deformation is described by a hyperbolic partial differential equation with initial and boundary conditions. Its right- hand side represents the force by which the fluid flow acts on the elastic wall. The goal of this work is to elaborate a numerical method for solving this coupled problem based on the finite element method and the ALE formulation of the equations describing flow. A for- mulation and analysis of the problem together with discretization, algorithmisation and programming of modules, which were added to an existing software package, is presented. The method that was worked out is applied to solve test problems. Keywords: interaction of flow and an...

This work is concerned with the theoretical analysis of the space-time discontinuous Galerkin method applied to the numerical solution of nonstationary nonlinear convection-diffusion problem in a time- dependent domain. At first, the problem is reformulated by the use of the arbitrary Lagrangian-Eulerian (ALE) method, which replaces the classical partial time derivative by the so-called ALE derivative and an additional convection term. Then the problem is discretized with the use of the ALE space-time discontinuous Galerkin method. On the basis of a technical analysis we obtain an unconditional stability of this method. An important step in the analysis is the generalization of a discrete characteristic function associated with the approximate solutionin a time-dependentdomainand the derivationof its properties. Further we derive an a priori error estimate of the method in terms of the interpolation error, as well as in terms of h and tau. Finally, some practical applications of the ALE space-time discontinuos Galerkin method in a time-dependent domain are given. We are concerned with the numerical solution of a nonlinear elasticity benchmark problem and moreover with the interaction of compressible viscous flow with elastic structures. The main attention is paid to the modeling of flow induced vocal fold...

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...

<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><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><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> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished