Structure Interaction Problems Research Articles

On the Local Existence of Solutions to the Fluid–Structure Interaction Problem with a Free Interface

We address a system of equations modeling an incompressible fluid interacting with an elastic body. We prove the local existence when the initial velocity belongs to the space H1.5+ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^{1.5+\\epsilon }$$\\end{document} and the initial structure velocity is in H1+ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^{1+\\epsilon }$$\\end{document}, where ϵ∈(0,1/20)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon \\in (0, 1/20)$$\\end{document}.

Accurate simulations of moving flexible objects with an improved immersed boundary-lattice Boltzmann method

Accurately capturing boundaries is crucial for simulating fluid–structure interaction (FSI) problems involving flexible objects undergoing large deformations. This paper presents a coupling of the immersed boundary-lattice Boltzmann method with a node-based partly smoothed point interpolation method (NPS-PIM) to enhance the accuracy of simulating moving flexible bodies in FSI problems. The proposed method integrates a multiple relaxation time scheme and employs a force correction technique to address boundary capturing inaccuracies. The effect of virtual fluid is accounted for through a Lagrangian point approximation, ensuring precise FSI force calculations for unsteady solid motions. NPS-PIM is utilized as the solid solver, constructing a moderately softened model stiffness by combining the finite element method (FEM) with the node-based smoothed PIM (NS-PIM). Simulations of flow fields near flexible objects with large deformations demonstrate that the proposed approach reduces numerical errors, improves computational efficiency compared to traditional FSI models using FEM and NS-PIM, and accurately captures the behavior of moving flexible bodies and detailed flow fields.

Estimation of added effects and their frequency dependence in various fluid–structure interaction problems

This paper focuses on a fluid–structure interaction topic—the determination of added effects caused by fluid forces acting on a body, considering the standard linear equation of motion. We present various problems that assume small-displacement oscillations of single and multiple bodies in inviscid irrotational (potential) flow or viscous incompressible flow in both closed domain and external flow. For inviscid flow, effects of geometric parameters on the added effects were studied. The presented results extend results known from the literature. For viscous flow, frequency dependence of the added effects was studied for a wide range of frequency. The added effects were computed from data from numerical simulations of fluid flow, where the body oscillations were modeled using the dynamic mesh approach. Effects of the phase shift caused by the dynamic mesh were addressed. The added mass was compared with the corresponding value determined for inviscid flow where applicable. The results show strong dependence of the added effects on many parameters, making their proper computation challenging even for simplified cases.

Active control of transonic airfoil flutter using synthetic jets through deep reinforcement learning

This paper presents a novel framework for the active control of transonic airfoil flutter using synthetic jets through deep reinforcement learning (DRL). The research, conducted in a wide range of Mach numbers and flutter velocities, involves an elastically mounted airfoil with two degrees of freedom of pitching and plunging oscillations, subjected to transonic flow conditions at varying Mach numbers. Synthetic jets with zero-mass flux are strategically placed on the airfoil's upper and lower surfaces. This fluid–structure interaction (FSI) problem is treated as the learning environment and is addressed by using the arbitrary Lagrangian–Eulerian lattice Boltzmann flux solver (ALE-LBFS) coupled with a structural solver on dynamic meshes. DRL strategies with proximal policy optimization agents are introduced and trained, based on the velocities probed around the airfoil and the dynamic responses of the structure. The results demonstrate that the pitching and plunging motions of the airfoil in the limited cycle oscillation (LCO) can be effectively alleviated across an extended range of Mach numbers and critical flutter velocities beyond the initial training conditions for control onset. Furthermore, the aerodynamic performance of the airfoil is also enhanced, with an increase in lift coefficient and a reduction in drag coefficient. Even in previously unseen environments with higher flutter velocities, the present strategy is achievable satisfactory control results, including an extended flutter boundary and a reduction in the transonic dip phenomenon. This work underscores the potential of DRL in addressing complex flow control challenges and highlights its potential to expedite the application of DRL in transonic flutter control for aeronautical applications.

A Circular Touch Mode Capacitive Rainfall Sensor: Analytical Solution and Numerical Design and Calibration

A circular capacitive rainfall sensor can operate from non-touch mode to touch mode; that is, under the action of enough rainwater, its movable electrode plate can form a circular contact area with its fixed electrode plate. Therefore, the weight of rainwater is borne by only its movable electrode plate in non-touch mode operation but by both its movable and fixed electrode plates in touch mode operation, and the total capacitance of its touch mode operation is much larger than that of its non-touch mode operation. Essential to its numerical design and calibration is the ability to predict the deflection shape of its moveable electrode plate to determine its total capacitance. This requires the analytical solution to the fluid–structure interaction problem of its movable electrode plate under rainwater. In our previous work, only the analytical solution for the fluid–structure interaction problem before its movable electrode plate touches its fixed electrode plate was obtained, and how to numerically design and calibrate a circular non-touch mode capacitive rainfall sensor was illustrated. In this paper, the analytical solution for the fluid–structure interaction problem after its movable electrode plate touches its fixed electrode plate is obtained, and how to numerically design and calibrate a circular touch mode capacitive rainfall sensor is illustrated for the first time. The numerical results show that the total capacitance and rainwater volume when the circular capacitive rainfall sensor operates in touch mode is indeed much larger than that when the same circular capacitive rainfall sensor operates in non-touch mode, and that the average increase in the maximum membrane stress per unit rainwater volume when the circular capacitive rainfall sensor operates in touch mode can be about 20 times smaller than that when the same circular capacitive rainfall sensor operates in non-touch mode. This is where the circular touch mode capacitive rainfall sensor excels.

Multi-dimensional modeling of solitary wave–structure interaction problems by using a [formula omitted]-LES-SPH model

The interaction mechanisms between waves and marine structures are a popular research topic. This paper applies the weakly compressible smoothed particle hydrodynamics (WCSPH) method to study the dynamics of green water overtopping. To enhance the accuracy of the simulations, the SPH method coupled with the large eddy simulation (LES) model is employed for numerical investigations. Initially, we validate the effectiveness of the model by simulating the generation of solitary waves and irregular waves, as well as numerically reproducing the water surface morphology during the interaction between solitary waves and the deck. Subsequently, the validated model is used to study the dynamic characteristics of different types of waves overtopping, revealing significant variations in their motion. Furthermore, we investigate the effect of deck roughness during the entire green water overtopping process in terms of both protrusions extent and distribution, confirming that a reasonable setting of the protrusions can greatly reduce the wave impact loads on the deck, thereby protecting the structure. Additionally, a three-dimensional model is developed to study the green water problem, and we find that the turbulence phenomenon is more pronounced in the three-dimensional scenario.

An immersed multi-material arbitrary Lagrangian–Eulerian finite element method for fluid–structure-interaction problems

Fluid–structure-interaction (FSI) phenomena are widely concerned in engineering practice and challenge current numerical methods. In this article, the finite element method is strongly coupled with the multi-material arbitrary Lagrangian–Eulerian (MMALE) method to develop a monolithic FSI method named the immersed multi-material arbitrary Lagrangian–Eulerian finite element method (IALEFEM). By immersing the finite elements in the MMALE computational grid, the fluid–solid interface is directly tracked by the element boundary with accurate normal directions. The fluid–structure-interaction is implicitly implemented by assembling the nodal variables and updating the Lagrangian momentum equation on the MMALE grid. Combining the advantages of both MMALE and FEM with the immersed boundary method, the IALEFEM is effective for solving complicated FSI problems with multi-material fluid flow. A slip fluid–structure-interaction method is also proposed to enhance the computational accuracy in simulating FSI problems with significantly different velocity fields. The accuracy and effectiveness of the IALEFEM are verified and validated by several benchmark numerical examples including the shock-cylinder obstacle interaction, flexible panel deformation induced by shock wave, dam break problem with large structural deformation, water entry of a wedge, fragmentation of a cylinder shell induced by blast, response of elastic plate subjected to spherical near-field explosion and structural damage of open-frame building under blast loading.

Numerical methods for shape optimal design of fluid–structure interaction problems

We consider the method of mappings for performing shape optimization for unsteady fluid–structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes several theoretical results into account, such as regularity requirements on the transformations and a differential geometrical point of view on the manifold of shapes. Moreover, we discretize the problem such that we can compute exact discrete gradients. This allows for the use of general purpose optimization solvers. We focus on problems derived from an FSI benchmark to validate our numerical implementation. The method is used to optimize parts of the outer boundary and the interface. The numerical simulations build on FEniCS, dolfin-adjoint and IPOPT. Moreover, as an additional theoretical result, we show that for a linear special case the adjoint attains the same structure as the forward problem but reverses the temporal flow of information.

Global stability analysis of flow-induced-vibration problems using an immersed boundary method

In this work, a numerical framework for global stability analysis of rigid-body-motion fluid–structure-interaction problems is presented. The Jacobian matrices which arise in the linearization procedure are derived numerically via the first-order finite difference scheme. The linearized fluid–structure coupled equations are solved using an immersed boundary method. The linear stability solver is first tested on two canonical cases, i.e., the flow past a stationary cylinder and the flow past an isolated elastically mounted cylinder. An excellent agreement between the results obtained here and those from available published research is achieved. The solver is then used to study the linear stability of the flow past two elastically mounted cylinders in tandem arrangement. The variations in growth rate and frequency of two leading modes with reduced velocity are examined. The mechanisms of lock-in and galloping phenomena observed in nonlinear simulation are elucidated from the perspective of linear instabilities in the leading modes.

Interaction leads to symmetry breaking in an array of cantilever plates in oscillatory cross flow

By using a computational model based on the immersed-boundary framework, a new mode of symmetry breaking is discovered in a fluid–structure interaction problem featuring an array of cantilever plates in a cross flow whose strength and direction varies sinusoidally with time. Specifically, within the physical parameters considered in this study, the motion of a single plate remains symmetric, whereas a system containing multiple plates can move asymmetrically so that the symmetry-breaking instability comes from fluid-dynamic interactions among individual plates. Further examination suggests that vortices shed from the free ends of the plates play an important role. Indeed, symmetry breaking occurs only when these vortices are sufficiently strong and when the distance between plates lies within certain range. If the distance is too small, a vortex shed from one plate can only stay in the gap between this plate and its neighboring plate for a short time so that it does not have the chance to interact extensively with the neighbor. On the other hand, if the distance is too large it is also difficult for this vortex to interact with the neighbor since it has to travel a long distance to reach there while the background flow keeps changing its direction. In either case, the system does not display asymmetric behavior.

A poroelastic [formula omitted]-SPH model for modeling biofilm deformation and sloughing in microfluidic channels

We present a poroelastic fluid–structure interaction δ-SPH model for simulating biofilm deformation and sloughing in microfluidic channels. Based on the mixture theory, this model accurately handles large deformations of solid structures and simultaneously simulates seepage flow within the porous biofilm and external flow. A key advantage of the model is its reliance on the solid phase material properties rather than the averaged properties of the biofilm, enabling the modeling of changes in porosity and biofilm material properties induced by loads. Model verification is achieved through two benchmark problems, followed by application to biofilm deformation and sloughing studies. The Young’s modulus of biofilms is a key parameter of interest in many studies. Calibration of the biofilm’s solid material elasticity modulus by using the presented model yields a value of 200 Pa, aligning with previous reports in literature. Additionally, the model is capable of simulating the sloughing process by evaluating local von Mises equivalent stress, reproducing different detachment patterns corresponding to various material strengths. This δ-SPH model offers an efficient numerical tool for biofilm analysis and is extendable to simulate other fluid–structure interaction problems involving porous media with large deformations, such as soil, debris flow, and biological tissues.

Navigating speed–accuracy trade-offs for multi-physics simulations

AbstractThis paper introduces a novel approach aimed at addressing persistent challenges inherent in conventional multiphysics modeling methodologies. Existing techniques, such as numerical modeling and analytical calculations, often suffer from time-consuming and computationally intensive processes, leading to inefficiencies, particularly in intricate simulations. The proposed methodology employs regression machine learning algorithms as a black-box solution to anticipate errors and execution times in multiphysics simulations. Diverging from conventional methods, this approach streamlines the exploration of simulation options, providing discernible choices for balancing speed and precision. The efficacy of the methodology is exemplified through successful applications to heat transfer and fluid–structure interaction problems, illustrating its adaptability across diverse scenarios. Notably, the approach upholds the integrity of physics equations and simulation convergence while markedly reducing the trial-and-error efforts and computational burdens associated with traditional methodologies. In summary, the proposed approach emerges as an innovative and promising solution to augment the accuracy, efficiency, and dependability of multiphysics simulations.

A formulation for fluid–structure interaction problems with immersed flexible solids: Application to splitters subjected to flow past cylinders with different cross-sections

In the finite element method framework, a fluid–structure formulation is developed by coupling an Eulerian fixed-mesh fluid approach with a Lagrangian deforming-mesh description for a flexible solid. The coupled formulation is solved using a staggered scheme during time. For the fluid solution stage, the solid walls are considered as a time-variable internal boundary. The velocity and pressure fields are obtained by solving the weak form of the fluid dynamic equations in which the solid velocity is imposed on the internal boundary via a penalization term. For the solid solution stage, the displacement field is obtained by solving the discrete solid dynamic equations which consider traction forces computed by integrating pressures and viscous stresses on the nodes belonging to the solid walls. This novel technique is firstly applied to analyze a flexible splitter under the shedding of a flow past square cylinder due to this problem is considered as a benchmark in the literature. The present solutions agree with those computed using body-fitted techniques, thus validating the proposal. Secondly, flexible splitter motions under the shedding of flow past cylinders with different cross-sections and splitter lengths are comprehensively studied. Overall, the computed results confirmed that the hydrodynamic coefficients on the cylinders were reduced because of the presence of the splitter.

A micromechanical study on sand − FRP interface subjected to cyclic loading

Fibre-reinforced polymer (FRP) is a promising composite to be used in construction in coastal and marine environments to resist seawater corrosion that deteriorates the properties of conventional civil engineering materials. A classical ground or seabed − structure interaction problem that is involved in the design of FRP structures, is however less understood when the soft nature of FRP is in subjection to the cyclic loadings from traffic, wind, wave and currents, causing penetration and abrasion at the soft FRP − soil interface. This study has downscaled the preceding problem into a micromechanical study at a benchmark sand grain − FRP interface. A large number of cyclic loading is applied, for the first time, at the sand − FRP composite interface, focusing on the development of the elastoplastic behaviour in the normal direction and the evolution of friction and energy dissipation in the tangential direction. The study combines the understanding from the tribology with the knowledge of civil engineering involved in the sand − FRP interaction, suggesting that a larger stick zone at the contact subjected to cyclic shearing is a key triggering of the simultaneous occurrence of the increased coefficient of friction and reduced damping ratio.

Forced vibration of liquid-filled composite laminated shell container considering fluid–structure interaction by the scaled boundary finite element method

In this paper, the scaled boundary finite element method (SBFEM) is first applied to the forced vibration analysis of partially liquid-filled composite laminated shell structure considering fluid–structure interaction. In comparison with the finite element method, the SBFEM only requires discretization of the boundary of the solution domain, which can reduce the spatial dimension of the problem by one and provide the radial analytical expressions for the variables within the solution domain. The structure consists of a multi-layered fiber-reinforced composite laminated shell and incompressible, inviscid, and irrotational liquid. After separately describing the basic expressions for the fluid and composite laminated shell, which includes the transformation of three coordinate systems and the establishment of the constitutive equations for the shell, the governing equations for the fluid and shell structure using the scaled boundary finite element method and modified SBFEM based on scaling surface transformation are formulated, respectively. Meanwhile, the Newmark method and synchronous solution algorithm are employed for the fluid–structure interaction analysis. Subsequently, two validation cases are conducted to assess the accuracy and convergence of the model. Finally, two numerical examples are employed to perform a parameter analysis on the model, involving the response of the system to ground horizontal harmonic excitation and seismic load. The results indicate that the SBFEM, as a semi-analytical high-precision numerical method, can be effectively used to simulate fluid–structure interaction problem of partially liquid-filled laminated composite shell structures.

An unconditionally stable scheme for the immersed boundary method with application in cardiac mechanics

The stability of the immersed boundary (IB) method is a challenge in simulating fluid–structure interaction problems, where time step constraints are significantly stricter than in pure fluid simulations. We propose a novel unconditionally stable scheme for the immersed boundary finite element (IBFE) method. The structure is handled implicitly and characterized by strain energy functions, rather than being modeled as fibers or membranes. Through energy estimate, we prove the unconditional stability of the fully discrete approximation in the absence of the convective term. In real simulations of cardiac mechanics problems, the time step is much larger, only limited by the Courant–Friedrichs–Lewy condition of the fluid. The novelty of this work lies in the combination of dual interpolation and distribution operators, the Jacobian-free Newton–Krylov method for solving nonlinear algebraic systems, and the semi-Lagrangian method for handling the convective term. To validate the effectiveness and accuracy of our approach, we present various benchmarks and conduct a quasi-static simulation of a three-dimensional real left ventricular model. We have shown that the numerical stability of our scheme is very robust even with much larger time step compared to conventional explicit IB methods. Our work paves the way for further works on efficient solvers of the IBFE method.

POD–ANN as digital twins for surge line thermal stratification

This paper describes a hybrid proper orthogonal decomposition (POD) and artificial neural network (ANN) strategy to construct digital twins of a pressurizer surge line under thermal stratification conditions. The one-way coupled conjugate heat transfer and thermal stress analysis was conducted by use of parametric modeling and the introduction of the inverse distance weighted interpolation for the grid mapping, which allows for the mapped grids to have the same number of nodes regardless of variations of surge line geometries. A snapshot-based POD was utilized to obtain truncated lower-order modes and the full-order system response was projected onto these modes with reduced state coefficients. Then the ANN was employed to establish a surrogate model between the five chosen design variables of interest and the reduced state coefficients, resulting in a surrogate-assisted digital twin for a pressurizer surge line. Prediction of fluid–structure interface temperature and thermal stress distribution was thus achieved in an in-line real-time manner for a wide range of parameter variations. We publicly share all code implementations, and we believe that our efforts open a door for the digital twining of thermo–fluid–structure interaction problems

On the Immersed Boundary Method with Time-Filter-SAV for Solving Fluid–Structure Interaction Problem

On the Immersed Boundary Method with Time-Filter-SAV for Solving Fluid–Structure Interaction Problem

Non-intrusive reduced order models for partitioned fluid–structure interactions

The main goal of this work is to develop a data-driven Reduced Order Model (ROM) strategy from high-fidelity simulation result data of a Full Order Model (FOM). The goal is to predict at lower computational cost the time evolution of solutions of Fluid–Structure Interaction (FSI) problems. For some FSI applications, the elastic solid FOM (often chosen as quasi-static) can take far more computational time than the fluid one. In this context, for the sake of performance one could only derive a ROM for the structure and try to achieve a partitioned FOM fluid solver coupled with a ROM solid one. In this paper, we present a data-driven partitioned ROM on two study cases: (i) a simplified 1D-1D FSI problem representing an axisymmetric elastic model of an arterial vessel, coupled with an incompressible fluid flow; (ii) an incompressible 2D wake flow over a cylinder facing an elastic solid with two flaps. We evaluate the accuracy and performance of the proposed ROM-FOM strategy on these cases while investigating the effects of the model’s hyperparameters. We demonstrate a high prediction accuracy and significant speedup achievements using this strategy.

Space–time finite element method with domain reduction techniques for dynamic soil–structure interaction problems

AbstractDesign of earth structures, such as dams, tunnels, and embankments, against the vibrational loading caused by high‐speed trains, road traffic, underground explosions, and, more importantly, earthquake motion, demands solutions of the dynamic soil–structure Interaction (SSI) problem. This paper presents a velocity‐based space–time finite element procedure, v‐ST/finite element method (FEM), to solve dynamic SSI problems. The main goal of this study is to present the computation details of implementing viscous boundary conditions of Lysmer–Kuhlemeyer to truncate the unbounded soil domain. Furthermore, additional time‐dependent boundary conditions, in terms of the free‐field response, are included to facilitate energy flow from the far field to the computation domain at the vertical truncated boundaries. In the FEM, seismic input motion is applied to an effective nodal force vector, which can be obtained explicitly in the numerical simulations. Finally, the response of a concrete gravity dam resting on an elastic half‐space to the horizontal component of earthquake motion is computed and successfully compared with the results of semidiscrete FEM using the Newmark‐ method.