Structure Interaction Problems Research Articles

On the Choice of Interface Parameters in Robin–Robin Loosely Coupled Schemes for Fluid–Structure Interaction

We consider two loosely coupled schemes for the solution of the fluid–structure interaction problem in the presence of large added mass effect. In particular, we introduce the Robin–Robin and Robin–Neumann explicit schemes where suitable interface conditions of Robin type are used. For the estimate of interface Robin parameters which guarantee stability of the numerical solution, we propose a new strategy based on the optimization of the reduction factor of the corresponding strongly coupled (implicit) scheme, by means of the optimized Schwarz method. To check the suitability of our proposals, we show numerical results both in an ideal cylindrical domain and in a real human carotid. Our results showed the effectiveness of our proposal for the calibration of interface parameters, which leads to stable results and shows how the explicit solution tends to the implicit one for decreasing values of the time discretization parameter.

Direct numerical simulations of flutter instabilities over a vibrating turbine blade cascade

This paper presents direct numerical simulations (DNS) on unsteady turbulent flow in a vibrating low-pressure turbine blade cascade to predict the flutter instabilities and explores the effects of blade oscillations on the flow structure and flow separation point. The spectral/hp element method is employed for the three-dimensional simulations of the domain. This method enables capturing more details about the flow structure and vortex generations compared to the URANS methods. The method can aid in understanding the physics of these complex fluid–structure interaction problems while it requires much less computational time compared to the other DNS models. The blade vibration frequency is varied from 5.2 Hz to 10.3 Hz with maximum vibration amplitude of 3% of chord length at the blade tip. The results illustrate that the vortex generation becomes stronger over the blades with higher vibration frequencies compared to the stationary ones. The main reason for the additional vortex generation and recirculations over the oscillating blades is the additional flow disturbance due to blade vibration and its interactions with the shear-layer on the turbine blade cascade. It is seen that the vortex shedding is growing around the trailing edge and become stronger on the suction surface of the vibrating blade. The flow separation over the suction surface of the stationary blade occurs at Ssep∕S0=0.391, while it occurs at 0.372 over the oscillating blade with f=5.2Hz.

A novel smoothed particle hydrodynamics and finite element coupling scheme for fluid–structure interaction: The sliding boundary particle approach

A novel numerical formulation for solving fluid–structure interaction (FSI) problems is proposed where the fluid field is spatially discretized using smoothed particle hydrodynamics (SPH) and the structural field using the finite element method (FEM). As compared to fully mesh- or grid-based FSI frameworks, due to the Lagrangian nature of SPH this framework can be easily extended to account for more complex fluids consisting of multiple phases and dynamic phase transitions. Moreover, this approach facilitates the handling of large deformations of the fluid domain respectively the fluid–structure interface without additional methodological and computational efforts. In particular, to achieve an accurate representation of interaction forces between fluid particles and structural elements also for strongly curved interface geometries, the novel sliding boundary particle approach is proposed to ensure full support of SPH particles close to the interface. The coupling of the fluid and the structural field is based on a Dirichlet–Neumann partitioned approach, where the fluid field is the Dirichlet partition with prescribed interface displacements and the structural field is the Neumann partition subject to interface forces. To overcome instabilities inherent to weakly coupled schemes an iterative fixed-point coupling scheme is employed. Several numerical examples in form of well-known benchmark tests are considered to validate the accuracy, stability, and robustness of the proposed formulation. Finally, the filling process of a highly flexible thin-walled balloon-like container is studied, representing a model problem close to potential application scenarios of the proposed scheme in the field of biomechanics.

Refactorization of Cauchy’s Method: A Second-Order Partitioned Method for Fluid–Thick Structure Interaction Problems

This work focuses on the derivation and the analysis of a novel, strongly-coupled partitioned method for fluid-structure interaction problems. The flow is assumed to be viscous and incompressible, and the structure is modeled using linear elastodynamics equations. We assume that the structure is thick, i.e., modeled using the same number of spatial dimensions as fluid. Our newly developed numerical method is based on generalized Robin boundary conditions, as well as on the refactorization of the Cauchy's one-legged `theta-like' method, written as a sequence of Backward Euler-Forward Euler steps used to discretize the problem in time. This family of methods, parametrized by theta, is B-stable for any theta in [0.5,1] and second-order accurate for theta=0.5+O(tau), where tau is the time step. In the proposed algorithm, the fluid and structure subproblems, discretized using the Backward Euler scheme, are first solved iteratively until convergence. Then, the variables are linearly extrapolated, equivalent to solving Forward Euler problems. We prove that the iterative procedure is convergent, and that the proposed method is stable provided theta in [0.5,1]. Numerical examples, based on the finite element discretization in space, explore convergence rates using different values of parameters in the problem, and compare our method to other strongly-coupled partitioned schemes from the literature. We also compare our method to both a monolithic and a non-iterative partitioned solver on a benchmark problem with parameters within the physiological range of blood flow, obtaining an excellent agreement with the monolithic scheme.

Vibrations of Nonlinear Elastic Structure Excited by Compressible Flow

This study deals with the development of an accurate, efficient and robust method for the numerical solution of the interaction of compressible flow and nonlinear dynamic elasticity. This problem requires the reliable solution of flow in time-dependent domains and the solution of deformations of elastic bodies formed by several materials with complicated geometry depending on time. In this paper, the fluid–structure interaction (FSI) problem is solved numerically by the space-time discontinuous Galerkin method (STDGM). In the case of compressible flow, we use the compressible Navier–Stokes equations formulated by the arbitrary Lagrangian–Eulerian (ALE) method. The elasticity problem uses the non-stationary formulation of the dynamic system using the St. Venant–Kirchhoff and neo-Hookean models. The STDGM for the nonlinear elasticity is tested on the Hron–Turek benchmark. The main novelty of the study is the numerical simulation of the nonlinear vocal fold vibrations excited by the compressible airflow coming from the trachea to the simplified model of the vocal tract. The computations show that the nonlinear elasticity model of the vocal folds is needed in order to obtain substantially higher accuracy of the computed vocal folds deformation than for the linear elasticity model. Moreover, the numerical simulations showed that the differences between the two considered nonlinear material models are very small.

Dynamic mode decomposition-based reconstructions for fluid–structure interactions: An application to membrane wings

Four data-driven low-order modeling approaches, Dynamic mode decomposition (DMD) and three other variations (optimal mode decomposition, total-least-squares DMD and high-order DMD), are used to capture the spatio-temporal evolution of fluid–structure interactions. These methods are applied to experimental data obtained in a flow over a flexible membrane wing and its elastic deformation. Spectral coherence indicates there exists an interaction between the flow and structural deformation at a single frequency for this problem (depending on the angle of attack and/or the presence of a ground). It is therefore an ideal dataset to assess the performance of the four different methods in terms of the relevant modes/frequencies and reconstruction of flow and structural deformation. We show that the four methods detect the same dominant frequency (within Fourier resolution) and qualitatively the same associated mode. However, the modes appear to be heavily damped or amplified preventing a successful flow and structure reconstruction (except when using high-order DMD). This problem persists even if the damping coefficients are set to 0 due to imprecision in the estimation of the dominant frequency. The reconstruction is assessed by means of the average correlation between the real and reconstructed fields corresponding to 0.42 and 0.85 for the fluid and membrane deformation respectively when using high-order DMD (and virtually 0 for the other three methods). Based on the analysis, we conclude that high-order DMD, particularly for when fluid and structural data are modeled simultaneously, is the most suitable method to generate linear low-order models for fluid–structure interaction problems. Further, we show that this modeling is not dependent on the relative energies of fluid and membrane deformation.

Centrifuge application of fibre Bragg gratings: pile axial loads and wall bending moments

One challenge for geotechnical centrifuge testing of soil–structure interaction problems is the reliable measurement of induced structural strains/forces. This paper presents a novel application of fibre Bragg grating (FBG) sensors for strain measurement within geotechnical centrifuge tests. FBG sensors have several advantages for centrifuge testing, in particular their small size and minimal self-weight. This paper gives an overview of recently developed installation and calibration procedures for FBG sensors within buried centrifuge model structures. The effect of thermal expansion/contraction of the materials (including both the fibre and structures) is considered and assessed. The precision and reliability of the FBG sensors are demonstrated using verification tests. The application of the FBG sensors is considered for two geotechnical problems, namely, pile jacking and a ‘retaining wall’ adjacent to a tunnel (acting as a protective wall to prevent an adjacent structure from tunnelling-induced ground movement). The results demonstrate that the FBG sensors can provide reliable measurements of pile axial strains/forces and protective wall bending moments. The paper provides evidence to support the routine adoption of FBG sensors for strain/force measurement of structures in geotechnical centrifuge modelling.

An immersed boundary fluid–structure interaction method for thin, highly compliant shell structures

A parallel computational method for simulating fluid–structure interaction problems involving large, geometrically nonlinear deformations of thin shell structures is presented and validated. A compressible Navier-Stokes solver utilizing a higher-order finite difference immersed boundary method is coupled with a geometrically nonlinear computational structural dynamics solver employing the mixed interpolation of tensorial components formulation for thin triangular shell elements. A weak fluid–structure coupling strategy is used to advance the numerical solution in time. The thin shell structures are represented in the fluid domain by a geometry mesh with a finite thickness at or below the size of the local grid spacing in the fluid domain. The methodologies for load and displacement transfer between the disparate geometry and structural meshes are detailed considering a parallel computing environment. The coupled method is validated for canonical simulation-based test cases and experimental fluid–structure interaction problems considering large deformations of thin shell structures, including a shock impinging on a cantilever plate, a fixed cylinder with a flexible trailing filament in channel flow, a thin, clamped plate in wall-bounded flow, and a flag waving in viscous crossflow. The FSI method is then demonstrated on a compliant circular sheet with a clamped center exposed to crossflow and finally applied to the inflation of a spacecraft disk-gap-band parachute inflating in supersonic flow conditions resembling the upper Martian atmosphere, where comparison with experimental data is provided.

Coupling total Lagrangian SPH–EISPH for fluid–structure interaction with large deformed hyperelastic solid bodies

In this work, we propose a two-way coupling technique between a total Lagrangian smoothed particle hydrodynamics (SPH) method for Solid Mechanics and the explicit incompressible SPH (EISPH) to simulate fluid–structure interaction problems. In the solid part, the total Lagrangian framework guarantees that the particle distribution keep stable to correctly calculate the deformation gradient and thus the elastic forces. The constitutive model follows hyperelastic formulations, and the stability of the method is enforced by a Jameson–Schmidt–Turkel (JST) stabilization procedure. For the fluid part, we applied an EISPH formulation, which is a fully explicit incompressible scheme based on a projection method capable of providing accurate pressure distributions for free-surface flows, while avoiding costly linear equations. The coupling scheme follows the same manner as the fixed wall ghost particle (FWGP) approach, which was here adapted to include moving walls. In addition, the non-penetration condition is rigorously reinforced through a numerical algorithm to avoid penetration of every fluid particle, including free-surface particles. Our method for solid is then verified through a large deformed tension plate numerical test, and our coupling forces through a series floating tests and hydrostatic water column over a thin infinite plate. Then, the method is validated comparing it with experimental data of a dam break test in which the water column attacks a thin rubber plate.

Modelling finger propagation in elasto-rigid channels

Abstract

Time domain phenomenological formulation for the sound generation in corrugated pipes

The study deals with a possibility to formulate the complex fluid–structure interaction problem of noise generation due to the unsteady flow in corrugated pipes by phenomenological formulation. Although the details of fluid dynamics are not accessible this way, the computational framework is much less demanding and the key features are still present. The van der Pol-like equations serve as a model of self-sustained sources coupled to the acoustic resonances of the tube. The effects of the sound field convection are discussed. A closer case-study investigation using linear stability analysis and a semi-analytical solution is presented. Numerical analysis investigating the flow velocity sweeps and fitting the model to the experimental data follows. The proposed system exhibits the key features known from experiments such as mode-locking and hysteresis and is capable of capturing the experimental data correctly.

Adaptive High-Order Fluid-Structure Interaction Simulations with Reduced Mesh-Motion Errors

This paper demonstrates an adaptive approach for solving fluid–structure interaction problems using high-fidelity numerical methods along with a detailed analysis of mesh-motion errors. A high-order partitioned approach is applied to couple the fluid and the structural subsystems, where the fluid subsystem is discretized using a discontinuous Galerkin finite-element method, while the structures solver uses a continuous Galerkin discretization. An explicit mapping is used as the primary mesh deformation algorithm. High-order time-integration schemes are used by the coupled solver to march forward in time, and the space-time mesh of the fluid subsystem is adapted using output-based methods. The error estimates for the unsteady outputs are evaluated by calculating the uncoupled, unsteady adjoint of the fluid subsystem. Adaptive meshing is used to demonstrate the importance of mesh-motion errors on output convergence, and a comprehensive analysis is conducted to control such errors arising from the mesh deformation algorithm. The benefits of adaptive meshing are demonstrated on a cantilevered Euler–Bernoulli beam placed in a low-Reynolds number flow and on a two-dimensional pitching–plunging airfoil in a high-Reynolds number flow.

ELL for 3D FSI problems with thin flexible structures based on the continuum-based shell element

This paper extends the Eulerian–Lagrangian–Lagrangian (ELL) method to solve the three-dimensional (3D) fluid–structure interaction (FSI) problems with flexible thin solids. The continuum-based (CB) shell element is adopted to model the flexible, thin-shell structure that undergoes large deformation. Several benchmarking problems, including a 3D cylinder-beam problem, vertical beam bending, and flapping flag, are solved to validate the present ELL approach incorporates the CB shell model. The results show that the ELL approach in this work has good agreement with references. A flapping butterfly with flexible wings is calculated to show the capability of the ELL to analyze more complex FSI problems in biomechanics.

Extending the Particle Finite Element Method for sediment transport simulation

The present work extends the capabilities of the Particle Finite Element Method (PFEM), which allows modeling of soil–fluid–structure interaction problems, to allow the modeling of sediment transport and scouring effects. This is accomplished by implementing scouring rules on an evolving scourable-interface, i.e. the interface surface between fluid and soil. The proposed method improves upon previous proposals by jointly capturing both the temporal and spatial scales of scouring evolution, as shown in the presented validation exercise, and also because its parametrization is conforms with commonplace engineering procedures for scouring prediction. The extension preserves desirable PFEM properties such as conservation of mass, mesh-size independence, and stability of the numerical solution of the PFEM equations and adds a negligible computational overhead to the PFEM implementation.

Existence for a Quasi-Static Interaction Problem Between a Viscous Fluid and an Active Structure

We consider a quasi-static fluid–structure interaction problem where the fluid is modeled by the Stokes equations and the structure is an active elastic material. More precisely, the displacement of the structure satisfies the equations of elasticity with an additional active stress, which models the presence of internal biological motors in the structure. Under smallness assumptions on the data, we prove the existence of a solution for this strongly coupled system.

Modelling of acoustic waves in homogenized fluid-saturated deforming poroelastic periodic structures under permanent flow

Acoustic waves in a poroelastic medium with periodic structure are studied with respect to permanent seepage flow which modifies the wave propagation. The effective medium model is obtained using the homogenization of the linearized fluid–structure interaction problem while respecting the advection phenomenon in the Navier–Stokes equations. For linearization of the micromodel, an acoustic approximation is introduced which yields a problem for the acoustic fluctuations of the solid displacements, the fluid velocity and pressure. An extended Darcy law of the macromodel involves the permeability and advection tensors which both depend on an assumed stationary perfusion of the porous structure. The monochromatic plane wave propagation is described in terms of two quasi-compressional and two quasi-shear modes. Two alternative problem formulations in the frequency domain are discussed. The one defined in terms of displacement and velocity fields leads to generalized eigenvalue problems involving non-Hermitean matrices whose entries are constituted by the homogenized coefficients depending on the incident wave frequencies, whereby degenerate permeabilities can be accounted for. The homogenization procedure and the wave dispersion analysis have been implemented to explore the influence of the advection flow and the microstructure geometry on the wave propagation properties, namely the phase velocity and attenuation. Numerical examples are reported.

Variability response function approach for foundation reliability

This paper explores the applicability of variability response functions to nonlinear soil–structure interaction problems, focusing on the impacts of spatially variable soil properties on foundation reliability regarding the settlement response. An estimation scheme is proposed to obtain the response functions, which involves a periodic function to approximate the relationship between foundation response and phase angles representing the soil variability patterns. Using a single set of realizations, the response function approach enables the evaluation of foundation reliability under various spatial variability patterns, including different autocovariance distances in three dimensions and the rotated anisotropy features of soil variations. This leads to significant reductions in computational demands compared to previous attempts of random field modelling, which often involved individual Monte Carlo simulations for each combination of spatial variability parameters. The proposed approach is applied to both shallow foundation and piled foundation cases, illustrating its range of applicability. For linear-elastic systems, the approach is shown to be effective for various coefficients of variation in soil variability. For elastic–plastic pile group analyses, the approach leads to efficient evaluation of the statistics of average and differential settlements of the pile group, both of which compare favourably with conventional random field simulation techniques. Since it does not require multiple random field realizations, the approach is particularly efficient in identifying the worst-case scenario of autocovariance distances that corresponds to the largest uncertainty in foundation response. This can become a useful tool for conservative reliability assessments under a project setting, since site-specific estimates of random field parameters are often imprecise due to limited site data.

Numerical Investigation of the Dynamical Behavior of a Fluid-Filled Microparticle Suspended in Human Arteriole.

The study of artificial microparticles (capsules and vesicles) has gained a growing interest with the emergence of bio-engineering. One of their promoting applications is their use as therapeutic vectors for drug delivery, when capsules and vesicles release their capacity in a targeted environment. The dynamic behavior of capsules and vesicles in confined or unbounded flows was widely studied in the literature and their mechanical response was truthfully described using constitutive laws with good agreement with experiences. However, in a context of biological application, to our knowledge, none of published studies investigating the mechanical response of deformable microparticle took into account the real physiological conditions: the rheological properties of blood such as carrying fluid and the mechanical properties of blood vessels. In this paper, we consider a hyperelastic microparticle suspended in human arteriole. We investigate the deformation of the microparticle resulting from its interaction with blood flow and the arteriolar wall using various capillary numbers and respecting physiological properties of blood and arterial wall. The influence of the blood viscosity model (Newtonian versus shear thinning) is investigated and a comparison with a rigid microchannel and a muscle-embedded arteriole is carried out. The fluid structure interaction (FSI) problem is solved using arbitrary Lagrangian Eulerian (ALE) method. Our simulations have revealed that the arteriolar wall distensibility deeply influences both the deformation and velocity of the microparticle: the deformation strongly increases while the velocity decreases in comparison to an infinitely rigid wall. In the context of therapeutic procedure of targeted drug-delivery, a particular attention should be addressed to these observations, in particular for their implication in the burst mechanism.

Transient Response Analysis of Underwater Structures Based on Total Field Formulas and Modified High-order Transmission Boundary

The scaled boundary finite element method (SBFEM) has obvious advantages in simulating both finite and infinite domains. However, the present high-order transmission boundary of SBFEM has a problem in numerical stability, especially for 3D fluid–structure interaction (FSI) problems. In this paper, a modified method is put forward to improve the numerical stability of the high-order transmission boundary and the total field formulas of the modified high-order transmission boundary are derived. In the transient response analysis, the nonreflecting characteristics of the infinite fluid domain are simulated by the modified high-order transmission boundary, while the impacts loading is calculated by the total field formulas. Several numerical examples are presented to prove the validity of the modified high-order transmission boundary and the total field formulas.

A generic smoothed wall boundary in multi-resolution particle method for fluid–structure interaction problem

Dealing with complex geometry boundaries is a challenge for particle boundary conditions. Since the effective area of the fluid particle is cut off by the boundary, it is difficult to obtain accurate results near the boundary, especially for complex geometry shapes. Things become more complicated when dealing with multiple sizes of particles in multi-resolution particle methods. In this paper, a generic smoothed wall (GSW) boundary is proposed by using single layer particles to accurately discretize the boundary. The boundary weight function is transformed to a distance function to fill the vacancy of the particle number density of fluid particles. The GSW boundary can be applied in the static, moving and non-linear deforming wall conditions. It also can be used to effectively handle complex geometric boundaries, since simulation results are not affected by changes in the number and size of wall particles. In addition, the GSW boundary also shows good results when combined with multi-resolution methods solving problems with multiple sizes of particles. In this paper, the MPS–DEM coupling method with GSW boundary model is applied to solve non-linear FSI problem. Several cases have been calculated to validate the accuracy, convergency and stability of the GSW boundary model. Compared with dummy particle boundary, results show that the proposed GSW boundary model can improve the numerical accuracy near the boundary, and handle arbitrary moving boundaries with high efficiency.