A generic time and space accurate numerical approach to closely coupled fluid-structure interaction problems

Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, flow in elastic pipes and blood vessels and extrusion of metals through dies. However a comprehensive computational model of these multi-physics phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply even to the extent in metal forming, for example, that the deformation of the die is totally ignored. More recently, strategies for solving the full coupling between the fluid and soild mechanics behaviour have developed. Conventionally, the computational modelling of fluid structure interaction is problematical since computational fluid dynamics (CFD) is solved using finite volume (FV) methods and computational structural mechanics (CSM) is based entirely on finite element (FE) methods. In the past the concurrent, but rather disparate, development paths for the finite element and finite volume methods have resulted in numerical software tools for CFD and CSM that are different in almost every respect. Hence, progress is frustrated in modelling the emerging multi-physics problem of fluid structure interaction in a consistent manner. Unless the fluid-structure coupling is either one way, very weak or both, transferring and filtering data from one mesh and solution procedure to another may lead to significant problems in computational convergence. Using a novel three phase technique the full interaction between the fluid and the dynamic structural response are represented. The procedure is demonstrated on some challenging applications in complex three dimensional geometries involving aircraft flutter, metal forming and blood flow in arteries.

Plasma ionization through wave-particle interaction in a capacitively coupled radio-frequency discharge

Phase resolved optical emission spectroscopy, with high temporal resolution, shows that wave-particle interactions play a fundamental role in sustaining capacitively coupled rf plasmas. The measurements are in excellent agreement with a simple particle-in-cell simulation. Excitation and ionization mechanisms are dominated by beam-like electrons, energized through the advancing and retreating electric fields of the rf sheath. The associated large-amplitude electron waves, driven by a form of two-stream instability, result in power dissipation through electron trapping and phase mixing. (c) 2007 American Institute of Physics.

Liquid monomer-powder particle interaction in acrylic bone cement

It is known that the method used to mix the liquid monomer and powder of PMMA bone cement influences the quality of the cement that is used in total joint replacements. Mixing theory indicates that the interaction between the liquid monomer and the powder is affected by a number of parameters, such as cement viscosity and degree of agitation, with this knowledge utilized in the design of cement mixing devices. Therefore, the objectives of this study were to: (i) obtain information on the interaction of the liquid monomer and the powder in the case of an PMMA bone cement, (ii) show how this knowledge can be applied to the design of an automated cement mixing device, and (iii) compare the porosity, bending modulus, and bending strength of one commercially-available cement prepared using the automated mixer and prepared using a conventional mixer that is in current clinical use. Experimental data indicated that increasing the velocity and decreasing the viscosity of the systems produced cement that improved mechanical properties, which may contribute to better mechanical integrity and, hence, reduced tendency for aseptic loosening, of cemented hip implants.

Development and validation of Fluid Structure Interaction Methods for an Oscillating Wave Surge Converter

The term fatigue loads on the Oyster Oscillating Wave Surge Converter (OWSC) is used to describe hydrostatic loads due to water surface elevation with quasi-static changes of state. Therefore a procedure to implement hydrostatic pressure distributions into finite element analysis of the structure is desired. Currently available experimental methods enable one to measure time variant water surface elevation at discrete locations either on or around the body of the scale model during tank tests. This paper discusses the development of a finite element analysis procedure to implement time variant, spatially distributed hydrostatic pressure derived from discretely measured water surface elevation. The developed method can process differently resolved (temporal and spatial) input data and approximate the elevation over the flap faces with user defined properties. The structural loads, namely the forces and moments on the body can then be investigated by post processing the numerical results. This method offers the possibility to process surface elevation or hydrostatic pressure data from computational fluid dynamics simulations and can thus be seen as a first step to a fluid-structure interaction model.

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).

Fluid-Structure Interaction in Civil Engineering Structures

The problems being addressed involve the dynamic interaction of solids (structure and foundation) with a liquid (water). Various numerical procedures are reviewed and employed to solve the problem of establishing the expected response of a structure subjected to seismic excitations while duly accounting for those interactions. The methodology is applied to the analysis of dams, lock gates, and large storage tanks, incorporating in some cases a comparison with the results produced by means of simplified analytical procedures.

Analysis of Meshfree Methods for Lagrangian Fluid-Structure Interaction

In this dissertation a new numerical method for solving Fluid-Structure Interaction (FSI) problems in a Lagrangian framework is developed, where solids of different constitutive laws can suffer very large deformations and fluids are considered to be newtonian and incompressible. For that, we first introduce a meshless discretization based on local maximum-entropy interpolants. This allows to discretize a spatial domain with no need of tessellation, avoiding the mesh limitations. Later, the Stokes flow problem is studied. The Galerkin meshless method based on a max-ent scheme for this problem suffers from instabilities, and therefore stabilization techniques are discussed and analyzed. An unconditionally stable method is finally formulated based on a Douglas-Wang stabilization. Then, a Langrangian expression for fluid mechanics is derived. This allows us to establish a common framework for fluid and solid domains, such that interaction can be naturally accounted. The resulting equations are also in the need of stabilization, what is corrected with an analogous technique as for the Stokes problem. The fully Lagrangian framework for fluid/solid interaction is completed with simple point-to-point and point-to-surface contact algorithms. The method is finally validated, and some numerical examples show the potential scope of applications.

Fluid-solid interaction in arteries incorporating the autoregulation concept in boundary conditions

In pre-surgery decisions in hospital emergency cases, fast and reliable results of the solid and fluid mechanics problems are of great interest to clinicians. In the current investigation, an iterative process based on a pressure-type boundary condition is proposed in order to reduce the computational costs of blood flow simulations in arteries, without losing control of the important clinical parameters. The incorporation of cardiovascular autoregulation, together with the well-known impedance boundary condition, forms the basis of the proposed methodology. With autoregulation, the instabilities associated with conventional pressure-type or impedance boundary conditions are avoided without an excessive increase in computational costs. The general behaviour of pulsatile blood flow in arteries, which is important from the clinical point of view, is well reproduced through this new methodology. In addition, the interaction between the blood and the arterial walls occurs via a modified weak coupling, which makes the simulation more stable and computationally efficient. Based on in vitro experiments, the hyperelastic behaviour of the wall is characterised and modelled. The applications and benefits of the proposed pressure-type boundary condition are shown in a model of an idealised aortic arch with and without an ascending aorta dissection, which is a common cardiovascular disorder.