Stability and asymptotic analysis of a fluid-particle interaction model

We are interested in coupled microscopic/macroscopic models describing the evolution of particles dispersed in a fluid. The system consists in a Vlasov-Fokker-Planck equation to describe the microscopic motion of the particles coupled to the Euler equations for a compressible fluid. We investigate dissipative quantities, equilibria and their stability properties and the role of external forces. We also study some asymptotic problems, their equilibria and stability and the derivation of macroscopic two-phase models.

Finite element modeling of fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins

In order to use the finite element method for solving fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins effectively and efficiently, we have presented, in this paper, the new concept and numerical algorithms to deal with the fundamental issues associated with the fluid-rock interaction problems. These fundamental issues are often overlooked by some purely numerical modelers. (1) Since the fluid-rock interaction problem involves heterogeneous chemical reactions between reactive aqueous chemical species in the pore-fluid and solid minerals in the rock masses, it is necessary to develop the new concept of the generalized concentration of a solid mineral, so that two types of reactive mass transport equations, namely, the conventional mass transport equation for the aqueous chemical species in the pore-fluid and the degenerated mass transport equation for the solid minerals in the rock mass, can be solved simultaneously in computation. (2) Since the reaction area between the pore-fluid and mineral surfaces is basically a function of the generalized concentration of the solid mineral, there is a definite need to appropriately consider the dependence of the dissolution rate of a dissolving mineral on its generalized concentration in the numerical analysis. (3) Considering the direct consequence of the porosity evolution with time in the transient analysis of fluid-rock interaction problems; we have proposed the term splitting algorithm and the concept of the equivalent source/sink terms in mass transport equations so that the problem of variable mesh Peclet number and Courant number has been successfully converted into the problem of constant mesh Peclet and Courant numbers. The numerical results from an application example have demonstrated the usefulness of the proposed concepts and the robustness of the proposed numerical algorithms in dealing with fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins. (C) 2001 Elsevier Science B.V. All rights reserved.

Charged-particle interaction with liquids: Ripplon excitations

We calculate the ripplon field contribution to the self-energy of an electron exterior to a liquid for planar and spherical geometries. We compare the full dielectric calculation of the electron-liquid interaction with the simpler alternative method consisting of integrating the electron-atom static-induced-dipolar potential through the whole liquid volume. We obtain good agreement between both methods for a nonpolar liquid such as 4He but differences up to 40% for a polar liquid such as water. We study the conditions under which the ripplon contribution to the self-energy is a perturbation. For an electron moving parallel to a planar liquid surface, we calculate the ripplon contribution to its stopping power. For this dynamical case, we conclude that the alternative method is a good approximation even for polar liquids.

Fluid-rock interaction during late stages of the Alpine exhumation

Résumé de la thèseLa fracturation des roches au cours de phases compressives ou extensives est un souvent évoquée pour expliquer la circulation de fluide au sein des roches cristallines. Dans le cadre de cette thèse, la circulation des fluides lors de l'exhumation tardive des Alpes a été étudiée en utilisant deux approches différentes: analyses structurales de la déformation fragile d'une part et analyses géochimiques des roches et des minéraux (isotopes stables, datations U/Pb, thermochronologie (U-Th)/He) d'autre part. Cette approche combinée a permis de mieux comprendre l'interaction existante entre les fluides métamorphiques et les fluides météoriques, ainsi que leur interaction avec les roches encaissantes. Le travail a été effectué dans la zone Pennique du Valais suisse.La première partie était focalisée sur la déformation fragile, le but étant de définir les différents types de déformations existantes et de déterminer l'âge relatif des différentes familles de failles. Dans la région d'étude, quatre domaines ont été distingués. Chacun d'eux comportent deux types de structures fragiles, certaines sont minéralisées alors que d'autre non. Au sein de chaque domaine, la direction principale des structures minéralisées correspond à l'orientation des accidents tectoniques majeurs de la région (Aosta- Ranzola Line au Sud, Rhône Line au Nord et Simplon Fault Zone à l'Est), alors que les structures non- minéralisées montrent des orientations plus variables. Ainsi, le premier type de structure est interprété comme résultant d'une dislocation tectonique alors que le deuxième type de structure résulterait d'une dislocation gravitaire locale. Il n'est néanmoins pas possible de classer chronologiquement la formation de ces deux types de structure ni d'attribuer un âge relatif aux changements d'orientation des contraintes majeures.La deuxième étude a été effectuée dans la région de la zone de faille du Simplon. Dans cette zone, la composition isotopique des minéraux ayant cristallisé à l'intérieur des fractures tardives permet de distinguer différents types de circulation de fluide. Les valeurs δ180 du quartz de la roche encaissante ainsi que ceux des veines tardives du bloque inférieur de la faille sont comparables. Ces valeurs indiquent un rééquilibrage et un tamponnage isotopique des fluides tardifs au contact de la roche encaissante lors de la fracturation de cette dernière et de la cristallisation des veines tardives. La même situation est observée dans la partie nord du bloque supérieur ainsi que dans sa partie sud. Ceci n'est néanmoins pas le cas pour la partie centrale du bloque supérieur où les valeurs isotopiques des minéraux dans les veines tardives sont approximativement 3 %o plus basses (avec des valeurs extrêmes négatifs), indiquant une contribution d'eau météorique aux fluides circulant dans les veines. Ces données suggèrent qu'une infiltration d'eau météorique a pu avoir lieu dans le bloque supérieur, où la fracturation des roches est plus intensive car le déplacement relatif le long de la faille y fut plus important, et la température maximale du métamorphisme plus basse. La troisième contribution traite de la géo-thermochronologie de la zone de contact entre la klippe de la Dent Blanche et la nappe de Tsaté. De petits zircons euhédraux ont été trouvés dans un plan de faille minéralisé (parallèle à la Faille du Rhône, voir première partie de l'étude), riche en hématite et quartz, de la zone d'étude. Les analyses U/Pb donnent des âges radiométriques autour de 270 - 280 Ma aux zircons extraits de la minéralisation ainsi que ceux extraits de la roche encaissante, ce qui correspond à l'âge de la nappe de la Dent Blanche et non celui de la nappe du Tsaté qui est elle-même classiquement interprétée comme une ophiolite Jurassique de l'Océan Liguro-Piémontais. Ces données suggèrent que les zircons contenus dans la veine ont été hérités de la roche encaissante. Les résultats (U-Th)/He indiquent un âge de refroidissement différent pour la roche encaissante (25.5 ± 2.0 Ma) que celui de la minéralisation (17.7 ±1.4 Ma). Le thermomètre isotopique quartz-hématite indique une température d'équilibre, et donc de mise en place de la minéralisation, d'environ 170 °C, température très proche de la température de -180 °C de fermeture du zircon pour le système (U-Th)/He. Ceci suggère que l'âge de refroidissement des zircons de la minéralisation correspond aussi à l'âge de formation de la faille.Thesis abstractFluid circulation in fractured rocks is a common process in geology, and it is generally the consequence of faulting and fracturing during both tectonic compression and extension. This thesis is focused on fluid circulation during late stages of the Alpine exhumation. After a structural analysis of the late brittle deformation of the studied samples, several analytical methods (stable isotope investigations, U/Pb radiometric dating, (U-Th)/He thermochronology) have been applied to understand the interaction of metamorphic and meteoric fluids with one another as well as with the host rock. This thesis is articulated around three study directions. All studies were conducted in the Penninic Zone of the Valais, Switzerland. The first study deals with late, brittle deformation and focuses on the different deformation styles and on the relative age of the different families of fractures. In order to do this, late brittle structures observed in four different domains have been subdivided as a function of the existence (or not) and type of mineralization. Comparisons between mineralized and non-mineralized strike directions for all four domains show that mineralized structures follow the strike orientation of major tectonic movements indicated in the Penninic Zone of the Valais (Aosta-Ranzola Line to the S, Rhône Line to the Ν and Simplon Fault Zone to the E), whereas non-mineralized fractures have a more variable strike orientation. This difference could be interpreted as indicative of tectonic-related faulting (mineralized structures) vs. local, collapse-related faulting (non-mineralized fractures), but it is not strong enough to indicate a relative age of the late brittle structures, and/or a change in the orientation of the strain field in post-Miocene times. The second studied area is focused on the Simplon Fault Zone (SFZ). Stable isotope analyses of minerals filling these late fractures indicate that there are two different fluid circulation systems in the footwall and hanging wall of the SFZ. In the footwall, δ180 values of quartz from both the host rock and the late veins range from +10 %o to +12 %o. This is consistent with buffering of circulating fluids by the host rock during fracturing and vein precipitation. In the hanging wall, δΙ80 values for quartz crystals from the host rock and the late veins are similar in both the northern and southern parts of the detachment that are both affected by the same degree of metamorphism (greenschist to the Ν and amphibolite to the S). This is not the case in the central part of the SFZ, where there is a jump from amphibolite facies in the footwall to greenschist facies in the hanging wall. δ,80 values for quartz from the hanging wall late veins are approximately 3.0 %o lower (down to negative values in some cases) than the values observed in the footwall These data suggest that infiltration of meteoric water may have occurred in the most fractured parts of the hanging wall, where relative displacement on the SFZ was the greatest and the peak temperature lower. In the less fractured footwall the δ180 values reflect a host rock-buffered system.The third study is focused on geo-thermochronology at the contact between the Dent Blanche nappe and the Tsaté nappe where small, euhedral zircons were found in a hematite- and quartz-rich mineralization on a late normal fault plane parallel to the Rhône Line (see first part of the study). U/Pb analysis indicates that the zircons - both in the late mineralization and in the host rock - have absolute radiometric ages clustering around 270 - 280 Ma, which is the accepted age for intrusive rocks from the Austroalpine Dent Blanche units but not for the Tsaté nappe. The latter is classically interpreted as an ophiolitic remnant of the Jurassic Liguro-Piemontais Ocean. U/Pb analyses suggest that zircons in late mineralization are all inherited from the host rock; however, results of (U-Th)/He analyses indicate that cooling ages for the host rocks are different to the cooling ages for the zircons in late mineralization. Indeed, the calculated cooling age for the Arolla gneiss is 25.5 ± 2.0 Ma, whilst the cooling age for the associated mineralized fault plane is 17.7 ±1.4 Ma. Oxygen stable isotope fractionation between quartz and hematite in the same late mineralization corresponds to temperatures of about 170 °C. The proximity of the calculated emplacement temperature for the mineralization and the lower accepted closure temperature for zircon in the (U-Th)/He system (-180 °C) imply that the age of 17.7 ± 1.4 Ma can also be interpreted as the formation age of this late brittle fault.Résumé grand publicLa circulation des fluides dans les roches fracturées est typique de nombreux processus géologiques, et très souvent est la conséquence de la fracturation des roches. Cette thèse aborde la question de la circulation des fluides pendant les dernières phases du soulèvement des Alpes. Après une analyse structurale de la fracturation directement sur le terrain, plusieurs méthodes géochimiques ont été appliquées pour comprendre l'interaction entre les différents fluides circulants, et avec leur propre roche mère. L'étude, concentrée sur trois directions principales, a été conduite dans la zone Pennique du Valais suisse. La première partie traite de la déformation cassante dans le secteur cité. L'analyse détaillée des fractures a permis de les subdiviser en structures minéralisées et non-minéralisées, sur quatre domaines différents. La comparaison entre les directions des structures minéralisées et non-minéralisées a permis de montrer que les premières suivent l'orientation des accidents tectoniques majeurs de la région, alors que les structures non- minéralisées ont une orientation plus variable. Cette différence pourrait être interprétée comme indication d'une dislocation tectonique (structures minéralisées) contre une dislocation gravitaire locale (structures non-minéralisées), mais elle n'est pas assez forte pour indiquer un âge relatif des structures tardives et/ou un changement de l'orientation des contraintes après -20 Ma vers le présent.A partir de ces observations, la deuxième étude est concentrée dans la région de la faille du Simplon. Les analyses géochimiques sur les minéraux remplissant les structures tardives indiquent qu'il y a deux différents systèmes de circulation des fluides dans les deux parties (toit et mur) de la faille. Dans le mur, les valeurs isotopiques des minéraux cristallisés à partir d'un fluide tardif sont les mêmes de ceux de la roche mère, donc il y a eu rééquilibration chimique entre fluide et roche pendant la fracturation de cette dernière et la précipitation des minéraux. Dans le toit, les valeurs isotopiques dans la roche mère et dans les minéraux des veines tardives sont comparables dans les parties Ν et S de la faille, où les roches du toit et du mur ont atteint une température maximale - pendant phase prograde de la formation des Alpes - comparable. Au contraire, dans la partie centrale, où le mur a atteint des températures maximales plus élevées par rapport au toit, les valeurs géochimiques des minéralisations tardives du toit sont parfois plus basses que les valeurs observées dans le mur. Ces données suggèrent que l'infiltration de l'eau de surface aurait pu se produire dans la partie plus fracturée du toit, où le déplacement relatif le long de la faille était majeur et les températures maximales mineures. Au contraire, les données géochimiques du mur de la partie centrale indiquent un système isotopique équilibré par la roche mère.La troisième partie de ce travail se base sur l'étude géochimique intégrée des isotopes stables d'Oxygène et radioactifs du Plomb, Uranium, Thorium et Hélium, auprès d'une faille normale minéralisée et des roches de la région à cheval entre deux nappes, la nappe de la Dent Blanche et la nappe de Tsaté. Ici, des petits zircons ont été trouvés dans la minéralisation citée, riche en hématite et quartz. L'analyse radiométrique Uranium/Plomb a montré que les zircons dans la minéralisation et dans les roches autour ont des âges comparables (autour 280 Ma). Cela signifie que les zircons dans la minéralisation tardive ont été hérités de la roche mère pendant la fracturation et la circulation des fluides tardives. De l'autre coté, les résultats des analyses Uranium-Thorium/Hélium indiquent que les âges de refroidissement pour les roches mères sont différents comparés aux âges de refroidissement pour les zircons dans la minéralisation tardive: ces derniers sont plus jeunes d'environ 8 Ma (autour 25 Ma et autour 17 Ma respectivement). Les analyses des isotopes de l'oxygène sur quartz et hématite dans la même minéralisation donnent une température de mise en place de cette dernière d'environ 170° C. La température de fermeture du système chimique des zircons dans le système (Uranium-Thorium)/Hélium est d'environ 180 °C: la proximité de ces deux températures implique que l'âge de refroidissement de la minéralisation tardive peut également être interprété comme âge de formation de la faille.

Modeling of the Fluid-Structure Interaction in Inelastic Piping Systems

In many engineering applications, compliant piping systems conveying liquids are subjected to inelastic deformations due to severe pressure surges such as plastic tubes in modern water supply transmission lines and metallic pipings in nuclear power plants. In these cases the design of such systems may require an adequate modeling of the interactions between the fluid dynamics and the inelastic structural pipe motions. The reliability of the prediction of fluid-pipe behavior depends mainly on the adequacy of the constitutive equations employed in the analysis. In this paper it is proposed a systematic and general approach to consistently incorporate different kinds of inelastic behaviors of the pipe material in a fluid-structure interaction analysis. The main feature of the constitutive equations considered in this work is that a very simple numerical technique can be used for solving the coupled equations describing the dynamics of the fluid and pipe wall. Numerical examples concerning the analysis of polyethylene and stainless steel pipe networks are presented to illustrate the versatility of the proposed approach.

The Fluid Structure Interaction Analysis of a Peristaltic Pump

The thesis work models the squeezing of the tube and computes the fluid motion of a peristaltic pump. The simulations have been conducted by using COMSOL Multiphysics FSI module. The model is setup in axis symmetric with several simulation cases to have a clear understanding of the results. The model captures total displacement of the tube, velocity magnitude, and average pressure fluctuation of the fluid motion. A clear understanding and review of many mathematical and physical concepts are also discussed with their applications in real field. In order to solve the problems and work around the resource constraints, a thorough understanding of mass balance and momentum equations, finite element concepts, arbitrary Lagrangian-Eulerian method, one-way coupling method, two-way coupling method, and COMSOL Multiphysics simulation setup are understood and briefly narrated.

Be analysis of bottom sediments in dynamic fluid-structure interaction problems

[EN] Sediment materials play an important role on the dynamic response of large structures where fluid-soil-structure interaction is relevant and materials of that kind are present. Dam-reservoir systems and harbor structures are examples of civil engineering constructions where those effects are significant.

A 2D BEM-FEM approach for time harmonic fluid-structure interaction analysis of thin elastic bodies.

[EN]This paper deals with two-dimensional time harmonic fluid-structure interaction problems when the fluid is at rest, and the elastic bodies have small thicknesses. A BEM-FEM numerical approach is used, where the BEM is applied to the fluid, and the structural FEM is applied to the thin elastic bodies.

Fluid-structure interaction by a coupled lattice Boltzmann-finite element approach

In this thesis, a strategy to model the behavior of fluids and their interaction with deformable bodies is proposed. The fluid domain is modeled by using the lattice Boltzmann method, thus analyzing the fluid dynamics by a mesoscopic point of view. It has been proved that the solution provided by this method is equivalent to solve the Navier-Stokes equations for an incompressible flow with a second-order accuracy. Slender elastic structures idealized through beam finite elements are used. Large displacements are accounted for by using the corotational formulation. Structural dynamics is computed by using the Time Discontinuous Galerkin method. Therefore, two different solution procedures are used, one for the fluid domain and the other for the structural part, respectively. These two solvers need to communicate and to transfer each other several information, i.e. stresses, velocities, displacements. In order to guarantee a continuous, effective, and mutual exchange of information, a coupling strategy, consisting of three different algorithms, has been developed and numerically tested. In particular, the effectiveness of the three algorithms is shown in terms of interface energy artificially produced by the approximate fulfilling of compatibility and equilibrium conditions at the fluid-structure interface. The proposed coupled approach is used in order to solve different fluid-structure interaction problems, i.e. cantilever beams immersed in a viscous fluid, the impact of the hull of the ship on the marine free-surface, blood flow in a deformable vessels, and even flapping wings simulating the take-off of a butterfly. The good results achieved in each application highlight the effectiveness of the proposed methodology and of the C++ developed software to successfully approach several two-dimensional fluid-structure interaction problems.

Effect of mixing, particle interaction, and spatial dimension on the glass transition

In this thesis, the influence of composition changes on the glass transition behavior of binary liquids in two and three spatial dimensions (2D/3D) is studied in the framework of mode-coupling theory (MCT).The well-established MCT equations are generalized to isotropic and homogeneous multicomponent liquids in arbitrary spatial dimensions. Furthermore, a new method is introduced which allows a fast and precise determination of special properties of glass transition lines. The new equations are then applied to the following model systems: binary mixtures of hard disks/spheres in 2D/3D, binary mixtures of dipolar point particles in 2D, and binary mixtures of dipolar hard disks in 2D. Some general features of the glass transition lines are also discussed. The direct comparison of the binary hard disk/sphere models in 2D/3D shows similar qualitative behavior. Particularly, for binary mixtures of hard disks in 2D the same four so-called mixing effects are identified as have been found before by Götze and Voigtmann for binary hard spheres in 3D [Phys. Rev. E 67, 021502 (2003)]. For instance, depending on the size disparity, adding a second component to a one-component liquid may lead to a stabilization of either the liquid or the glassy state. The MCT results for the 2D system are on a qualitative level in agreement with available computer simulation data. Furthermore, the glass transition diagram found for binary hard disks in 2D strongly resembles the corresponding random close packing diagram. Concerning dipolar systems, it is demonstrated that the experimental system of König et al. [Eur. Phys. J. E 18, 287 (2005)] is well described by binary point dipoles in 2D through a comparison between the experimental partial structure factors and those from computer simulations. For such mixtures of point particles it is demonstrated that MCT predicts always a plasticization effect, i.e. a stabilization of the liquid state due to mixing, in contrast to binary hard disks in 2D or binary hard spheres in 3D. It is demonstrated that the predicted plasticization effect is in qualitative agreement with experimental results. Finally, a glass transition diagram for binary mixtures of dipolar hard disks in 2D is calculated. These results demonstrate that at higher packing fractions there is a competition between the mixing effects occurring for binary hard disks in 2D and those for binary point dipoles in 2D.

Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

Numerical modelling of fluid-structure interaction with application in hemodynamics

The thesis deals with numerical algorithms for fluid-structure interaction problems with application in blood flow modelling. It starts with a short introduction on the mathematical description of incompressible viscous flow with non-Newtonian viscosity and a moving linear viscoelastic structure. The mathematical model consists of the generalized Navier-Stokes equation used for the description of fluid flow and the generalized string model for structure movement. The arbitrary Lagrangian-Eulerian approach is used in order to take into account moving computational domain. A part of the thesis is devoted to the discussion on the non-Newtonian behaviour of shear-thinning fluids, which is in our case blood, and derivation of two non-Newtonian models frequently used in the blood flow modelling. Further we give a brief overview on recent fluid-structure interaction schemes with discussion about the difficulties arising in numerical modelling of blood flow. Our main contribution lies in numerical and experimental study of a new loosely-coupled partitioned scheme called the kinematic splitting fluid-structure interaction algorithm. We present stability analysis for a coupled problem of non-Newtonian shear-dependent fluids in moving domains with viscoelastic boundaries. Here, we assume both, the nonlinearity in convective as well is diffusive term. We analyse the convergence of proposed numerical scheme for a simplified fluid model of the Oseen type. Moreover, we present series of experiments including numerical error analysis, comparison of hemodynamic parameters for the Newtonian and non-Newtonian fluids and comparison of several physiologically relevant computational geometries in terms of wall displacement and wall shear stress. Numerical analysis and extensive experimental study for several standard geometries confirm reliability and accuracy of the proposed kinematic splitting scheme in order to approximate fluid-structure interaction problems.

Dating brittle tectonic movements with cleft monazite: Fluid-rock interaction and formation of REE minerals

[1] Two millimeter-sized hydrothermal monazites from an open fissure (cleft) that developed late during a dextral transpressional deformation event in the Aar Massif, Switzerland, have been investigated using electron microprobe and ion probe. The monazites are characterized by high Th/U ratios typical of other hydrothermal monazites. Deformation events in the area have been subdivided into three phases: (D1) main thrusting including formation of a new schistosity, (D2) dextral transpression, and (D3) local crenulation including development of a new schistosity. The two younger deformational structures are related to a subvertically oriented intermediate stress axis, which is characteristic for strike slip deformation. The inferred stress environment is consistent with observed kinematics and the opening of such clefts. Therefore, the investigated monazite-bearing cleft formed at the end of D2 and/or D3, and during dextral movements along NNW dipping planes. Interaction of cleft-filling hydrothermal fluid with wall rock results in rare earth element (REE) mineral formation and alteration of the wall rock. The main newly formed REE minerals are Y-Si, Y-Nb-Ti minerals, and monazite. Despite these mineralogical changes, the bulk chemistry of the system remains constant and thus these mineralogical changes require redistribution of elements via a fluid over short distances (centimeter). Low-grade alteration enables local redistribution of REE, related to the stability of the accessory phases. This allows high precision isotope dating of cleft monazite. 232Th/208Pb ages are not affected by excess Pb and yield growth domain ages between 8.03 ± 0.22 and 6.25 ± 0.60 Ma. Monazite crystallization in brittle structures is coeval or younger than 8 Ma zircon fission track data and hence occurred below 280°C.

Fluid-structure interaction of an elastic pipe immersed inside a coaxial rigid pipe: a model for the Tullio phenomenon

An axisymmetric, elastic pipe is filled with an incompressible fluid and is immersed in a second, coaxial rigid pipe which contains the same fluid. A pressure pulse in the outer fluid annulus deforms the elastic pipe which invokes a fluid motion in the fluid core. It is the aim of this study to investigate streaming phenomena in the core which may originate from such a fluid-structure interaction. This work presents a numerical solver for such a configuration. It was developed in the OpenFOAM software environment and is based on the Arbitrary Lagrangian Eulerian (ALE) approach for moving meshes. The solver features a monolithic integration of the one-dimensional, coupled system between the elastic structure and the outer fluid annulus into a dynamic boundary condition for the moving surface of the fluid core. Results indicate that our configuration may serve as a mechanical model of the Tullio Phenomenon (sound-induced vertigo).