Complex Fluid-structure Interaction Research Articles

A coupled smoothed particle hydrodynamics-finite volume approach for shock capturing in one-dimension

A novel approach coupling the finite volume method code Pyro2 and the smoothed particle hydrodynamics code PySPH is introduced and applied to one-dimensional shock problems. The finite volume mesh models the bulk of the system, while regions with discontinuous fluid values are identified and populated with PySPH particles to model the fluid around shocks. The approaches are coupled with boundary cells and ghost particles, with linear interpolation used to extract fluid properties at each timestep in the respective boundary regions. Results from three shock problems using Pyro2, PySPH, and a hybrid approach are presented. The hybrid approach preserves accuracy and computational efficiency in strong shock problems. Additionally, the coupling approach provides a potential avenue for including SPH functionality in FVM simulations, including modeling complex geometries and fluid-structure interaction. The preliminary investigation of the hybrid approach in one dimension highlights the potential efficiency gains of applying coupled FVM-SPH methods to larger blast simulations in two and three dimensions.

Wake control of a square cylinder: Impinging the vortex cores with dual flexible splitter plates

Numerous works have been conducted to study the wake control of a bluff body and more efficient strategies are still what we seek for. This paper studies the complex fluid–structure interaction (FSI) problem of a square cylinder mounted with dual flexible splitter plates from a new perspective: impinging the vortex core with flapping plate tip. The Reynolds number (Re) based on the side length of the square cylinder is fixed at 332.6. The splitter plates are attached at both sides of the square cylinder. Structural parameters, such as plate length and bending stiffness, are considered to achieve an optimal arrangement of this configuration. Compared to the traditional single splitter plate arrangement, only a short splitter length is needed for this dual splitter plates configuration. Flow visualization indicates that the drag reduction is associated with the increase of base pressure and the lift suppression is related to the inhabitation of the interaction of the shear layer and split effect of the tip vortices. The dimensionless bending stiffness plays a vital role in determining the behavior of the splitter plate. Two vibration modes, i.e., off-center vibration and asymmetry vibration modes are captured and the up and down splitter plates tend to vibration in-phase. The Lissajous trajectories of the free tip mainly exhibits arc-shape and sickle-shape. Given the performance of the square cylinder-dual splitter plates configuration, splitter length of l/L=1.5 is an optimal configuration, which is less affected by flexural rigidity. The maximum drag reduction could reach 23.1% and the lift force exerting on this configuration does not increase significantly, which is beneficial for the structural stability.

Turbulent flow interacting with flexible trawl net structure including simulation catch in flume tank

The interaction between fluid and the midwater trawl with stocked catches is extremely complex, but essential to improve the understanding of the drag force acting on the trawl, the behavior of the fishing structure during a trawling process, and to predict its selectivity process. The present study assesses the turbulent characteristics inside and around the midwater trawls with catch and without catch linked to its fluttering motion. The analysis is based on three-dimensional electromagnetic current velocity meter measurements performed in the multiple points inside and outside different parts of a 1/35 scaled midwater trawl model with the aim of access the main turbulent flow structure inside and around the gear. Time-averaged normalized flow velocity fields and turbulent flow parameters were analyzed from the measured flow data. Furthermore, Fourier analysis was conducted by watching the time–frequency Power spectrum content of instantaneous flow velocities fields, the fluttering trawl motions, turbulent kinetic energy, and momentum flux. Based on successive analyzes of mean flow characteristics and turbulent flow parameters, it has been demonstrated that the presence of catch inside the trawl net impacts the evolution of unsteady turbulent flow by creating large trawl fluttering motions that strongly affect the flow passage. The results showed that the time-averaged normalized streamwise and transverse flow velocities inside and around the trawl net with catch were 12.41% lower compared with that obtained inside and around the trawl without catch. The turbulent length scale and turbulent Reynolds number obtained in the different part of the trawl net with catch were about 33.05% greater than those obtained on the trawl net without catch, confirming that the unsteady turbulent flow developing inside and around the midwater trawl is influence by the catch and liner. It is observed that the motions of both the trawl without catch and the trawl with catch are mainly of a low-frequency activity and another component related to unsteady turbulent flow street. A complex fluid–structure interaction is then demonstrated where the fluttering motions of the trawl net affect the fluid flow inside and around trawl net, the fluid force, turbulent pattern, and simultaneously, the periodic unsteady turbulent flow influence the trawl motions.

Fast Aero-Structural Model of a Leading-Edge Inflatable Kite

Soft-wing kites for airborne wind-energy harvesting function as flying tensile membrane structures, each of whose shape depends on the aerodynamic load distribution and vice versa. The strong two-way coupling between shape and loading poses a complex fluid-structure interaction problem. Since computational models for such problems do not yet meet the requirements of being accurate and at the same time fast, kite designers usually work on the basis of intuition and experience, combined with extensive iterative flight testing. This paper presents a fast aero-structural model of leading-edge inflatable kites for the design phase of airborne wind-energy systems. The fluid-structure interaction solver couples two fast and modular models: a particle system model to capture the deformation of the wing and bridle-line system and a 3D nonlinear vortex step method coupled with viscous 2D airfoil polars to describe the aerodynamics. The flow solver was validated with several wing geometries and proved to be accurate and computationally inexpensive for pre-stall angles of attack. The coupled aero-structural model was validated using experimental data, showing good agreement in the deformations and aerodynamic forces. Therefore, the speed and accuracy of this model make it an excellent foundation for a kite design tool.

Flow-induced vibration modeling of bluff bodies with data assimilation

Vortex-induced vibration (VIV) and galloping are two typical flow-induced vibration (FIV) problems of bluff bodies, which often cause fatigue damage or destruction of structures. Therefore, the accurate and effective FIV prediction has become a requirement of the industry in order to prevent structural damage and guide design. Although the semi-empirical model (such as the wake oscillator model) is an efficient FIV prediction tool, the precision ability of existing models is constrained due to empirical parameters and unideal mathematical equations. Generally, the numerical simulation and wind tunnel experiments are relatively accurate methods, but for complex fluid–structure interaction problems, their cost is too high. As a result, a data-driven FIV prediction model is proposed to accomplish effective and high-precision prediction in this study. The Ensemble Kalman filter (ENKF) data assimilation (DA) technique is used to combine the experimental data with a semi-empirical model. First, the sensitivity of empirical parameters is analyzed, and the most sensitive ones are selected as the target parameters for data assimilation. The mean deviation of ensemble (MDE) is proposed to represent the sensitivity of parameters. Then DA-based model is used to predict the galloping and VIV of a rectangular cylinder. The results indicate that the accuracy of the DA-based model is up to 10 times greater than that of the initial semi-empirical model. With the data-driven technology, the typical ‘quasi-steady’ theory of galloping has been improved for low Scruton number values. For the wake oscillator model, assimilating the parameters of the acceleration and velocity coupled terms can improve the prediction accuracy of VIV. Also, this modeling procedure can be regarded as a new parameter identification method from forced and free vibration.

Along-wind and across-wind coupling analysis of high-rise buildings: Modeling and parameter identifications

High-rise buildings, with similar natural frequencies of sway modes in two orthogonal directions, can have coupled vibrations when exposed to strong wind exhibiting complex fluid-structure interaction and aero-elastic effects. This paper studies this coupled vibration with proposing of a mathematical model for both the in-plane and out-of-plane self-excitation force. A single-degree-of-freedom (SDOF) and two-degree-of-freedom (2DOF) aero-elastic square section high-rise building models are tested in wind tunnel to provide data for the analytical modeling. A new strategy to estimate the aerodynamic parameters and self-excitation forces is proposed. Parametric studies show that the self-excitation forces of the SDOF and 2DOFs models have significant difference. The out-of-plane self-excitation force acting in the along-wind direction induced by the across-wind vibration can become dominating inducing large amplitude vibration in the along-wind direction. The wind induced coupling vibrations for other tall buildings can similarly be studied in detail with the proposed strategy.

SPHydro: Promoting smoothed particle hydrodynamics method toward extensive applications in ocean engineering

This paper aims at presenting a general-purpose-oriented and fully parallelized meshless framework to simulate complex Fluid–Structure Interaction (FSI) problems in ocean engineering. In this framework, a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) solver is combined with several advanced pre- and post-processing techniques. Based on the framework, we have been developing our in-house WCSPH-FSI package named SPHydro for solving hydrodynamic problems involving complex FSI processes in an accurate, efficient, and convenient manner. Three benchmarks are performed to qualitatively and quantitatively validate the accuracy and convergence of SPHydro. In addition, several practical applications are also provided to further highlight the generality and applicability of SPHydro in ocean engineering simulations. It is demonstrated that SPHydro holds satisfactory performance in solving complex FSI problems in ocean engineering and that the present framework can be further developed to tackle more complex FSI problems for general engineering applications due to its high flexibility and extensibility.

Theory of rain–wind induced vibration of stay cables: Toward unsteady and fully coupled modeling

Large-amplitude rain–wind induced vibration (RWIV) is a complex fluid–structure interaction process that may develop if light rainfall and moderate wind act concurrently on long stay cables of a cable-stayed bridge. However, its dynamic characteristics and excitation mechanism are remained an open question. Recently, a theoretical framework for the analysis of RWIV was proposed, based on a quasi-steady-state approximation of the movement of upper rivulet, to reveal the main features of the dynamic process of RWIV. In the present study, we further consider the unsteady and dynamic behaviors of the moving upper rivulet and its coupling effects with the cable movement. The periodic mass, circumferential movement of the upper rivulet was modeled based on experimental observations. The theoretical results are then validated by comparison with experimental results. In addition, some parameters that influence RWIV are investigated in detail. The augmented theory in the present study gives a more accurate model and promotes more reliable evaluations of the dynamic behaviors of RWIV of stay cables.

Coupled Multiphysics Simulation using FEA for Complex Fluid-Structure Interaction Problems

In the realm of mechanical engineering, the accurate prediction of fluid-structure interaction (FSI) is paramount for the design and analysis of systems where fluids and structures coexist and interact. This research paper presents a novel approach to address complex FSI problems using coupled multiphysics simulation through Finite Element Analysis (FEA). The proposed methodology integrates advanced computational algorithms to capture the intricate interplay between fluid dynamics and structural mechanics, ensuring a more holistic representation of real-world scenarios. The developed framework was tested on a variety of benchmark problems, ranging from aeroelastic flutter in aircraft wings to blood flow-induced stresses in arterial walls. Results indicate a significant enhancement in prediction accuracy and computational efficiency compared to traditional decoupled methods. Furthermore, the study delves into the challenges faced during the coupling process, offering solutions to mitigate numerical instabilities and enhance convergence rates. The findings of this research not only pave the way for improved design and safety protocols in industries such as aerospace, biomedical, and civil engineering but also underscore the potential of Multiphysics simulation in unravelling the complexities of the natural world.

From Simulation to Reality: A Learning Framework for Fish-Like Robots to Perform Control Tasks

The fish-like robot is one of the typical underwater robots, which has the advantage of high maneuverability with low noise due to its bioinspired structure and biomimetic locomotion. However, it is challenging to efficiently design motion controllers for such robots to achieve satisfactory performance on specific control tasks in the real underwater environment, since the complex fluid-structure interaction exists during their swimming and exact dynamic models are absent. In this article, we propose a learning framework, incorporating a simulation system and a training methodology, to autonomously and fast train in simulation to create control policies that are capable of directly applying to a type of physical fish-like robots to perform motion control tasks. First, we construct a simulation system combining a data-driven environment and a computational fluid dynamics (CFD)-based environment, thus well balancing the simulation accuracy and the calculation speed. Second, we design a training methodology to train deep reinforcement learning (DRL)-based policies for the robot in our constructed simulation system to perform a specific control task. Then, we use two typical motion control tasks to verify our proposed framework. One is the path-following control task, which is a one-objective problem with dense rewards, while the other is the pose control task which is a two-objective problem with sparse rewards. For each task, the DRL-based control policy trained by our learning framework is directly deployed on the physical fish-like robot to perform the task in the real world. Experimental results show that the policies trained in simulation still work well in the real world, and perform even better in terms of control accuracy and stability compared with the traditional control methods, thus demonstrating the effectiveness of our learning framework.

Multi-level adaptive particle refinement method with large refinement scale ratio and new free-surface detection algorithm for complex fluid-structure interaction problems

Fluid-Structure Interaction (FSI) is a crucial problem in ocean engineering. The smoothed particle hydrodynamics (SPH) method has been employed recently for FSI problems in light of its Lagrangian nature and its advantage in handling multi-physics problems. The efficiency of SPH can be greatly improved with the Adaptive Particle Refinement (APR) method, which refines particles in the regions of interest while deploying coarse particles in the left areas. In this study, the APR method is further improved by developing several new algorithms. Firstly, a new particle refinement strategy with the refinement scale ratio of 4 is employed for multi-level resolutions, and this dramatically decreases the computational costs compared to the standard APR method. Secondly, the regularized transition sub-zone is deployed to render an isotropic particle distribution, which makes the solutions between the refinement zone and the non-refinement zone smoother and consequently results in a more accurate prediction. Thirdly, for complex FSI problems with free surface, a new free-surface detection method based on the Voronoi diagram is proposed, and the performance is validated in comparison to the conventional method. The improved APR method is then applied to a set of challenging FSI cases. Numerical simulations demonstrate that the results from the refinement with scale ratio 4 are consistent with other studies and experimental data, and also agree well with those employing the refinement scale ratio 2. A significant reduction in the computational time is observed for all the considered cases. Overall, the improved APR method with a large refinement scale ratio and the new free-surface detection strategy shows great potential in simulating complex FSI problems efficiently and accurately.

Machine-learning prediction of aerodynamic damping for buildings and structures undergoing flow-induced vibrations

Aerodynamic damping, as the principal determinant of wind-induced vibrations, bears vast significance in building engineering. This study presents a new modular framework, called the Deep Neural Network-Genetic Algorithm (DNN-GA) architecture, to predict aerodynamic damping directly from surface pressure measurement while serving as one of the earliest references for GA applications in aerodynamic damping predictions. The accurate prediction can give building engineers better insights into potential designs' feasibility at substantially reduced costs, benefiting building design and engineering implementations. The DNN-GA is demonstrated on an aeroelastic tapered prism—a nonlinear bi-directional fluid-structure interaction (FSI) system with solid connections to building design—with synchronous, high-fidelity wind tunnel data for training and prediction. With pressure input, the DNN module predicts tip response as the intermediate product, based on which the GA module optimizes for aerodynamic damping in a fully automated workflow. Results showed that the DNN-GA outperformed six benchmark machine learning algorithms by at least 400%. A comparison between the GA module and the traditional Random Decrement Technique (RDT) showed an accuracy improvement of at least 700%. Finally, the DNN-GA predicted the aerodynamic damping for the Vortex-Induced Vibration (VIV), Galloping, and VIV-Galloping regimes with the maximum root-mean-squared and mean-absolute errors of only 3.874 × 10−3 and 3.053 × 10−3, attesting to the method's excellent accuracy and suitability to complex, nonlinear, and many types FSI vibrations. Given its data-driven nature, the DNN-GA is also applicable to experimental, numerical, and even field data, making it an attractive tool for building engineering applications.

An efficient explicit immersed boundary-reconstructed lattice Boltzmann flux solver for isothermal fluid-structure interaction problems with large deformations and complex geometries

In this paper, a novel approach for isothermal fluid-structure interaction (FSI) problems is proposed that not only inherits the advantages of a reconstructed lattice Boltzmann flux solver (RLBFS) in solving the fluid field, but also retains the efficiency found in the explicit boundary condition-enforced immersed boundary method (EIB) for implementation of boundary conditions on the solid wall. Hence, the new approach (EIB-RLBFS) is highly suitable for complex FSI problems such as large deformations and complex geometries. Furthermore, the arbitrary Lagrangian-Eulerian (ALE) approach is integrated with EIB-RLBFS to solve moving boundary problems efficiently. The structural dynamics are solved by a finite difference method for moving objects and flexible structures. The overall framework of EIB-RLBFS is simple yet robust, where a fractional method is applied to split the FSI process into a predictor step and a corrector step. The RLBFS is applied in the predictor step to predict the intermediate flow field, while the EIB is invoked in the corrector step to impose the no-slip boundary conditions within the flow field, thereby, correcting the predicted flow field to satisfy the no-slip boundary conditions. The proposed approach (EIB-RLBFS) has been tested and evaluated extensively in terms of accuracy and efficiency on several benchmark cases such as, a 2D self-propelled unconstrained flapping/undulatory foil, a 2D filament, a 3D streamwise rotating sphere, and a 3D flapping flag. Results obtained using the proposed approach are in good agreement with previous studies, substantiating the capability and flexibility of EIB-RLBFS for solving FSI problems.

The immersed boundary method for confined flows: Numerical diffusion and simulation accuracy of a boundary retraction scheme

Diffuse-interface immersed boundary methods (IBM) have been successfully applied to numerous complex fluid–structure interaction problems because of their simple and efficient implementation. Despite their ability to suppress numerical oscillations significantly compared to sharp-interface methods, the diffuse interface is likely to reduce simulation accuracy of the flow field around the solid boundary. The present work investigates the diffusive effects of IBM and the mitigation method for surface-confined particulate flows by comparing results to sharp-interface methods. It is found that increasingly-confined geometries accentuate interface diffusion effects and decrease simulation accuracy. To minimise the diffusive effects of IBM, a boundary retraction scheme is used and its effectiveness is examined, in particular for particles in close contact where the diffuse interfaces overlap. It is shown that this simple implementation is capable of alleviating interface diffusion errors, thus increasing accuracy while limiting computational costs. With an optimal boundary retraction scheme, IBM can successfully capture fluid–structure interactions at different degrees of confinement, comparable to sharp-interface methods.

Aeroelastic characterisation of a bio-inspired flapping membrane wing

Natural fliers like bats exploit the complex fluid–structure interaction between their flexible membrane wings and the air with great ease. Yet, replicating and scaling the balance between the structural and fluid-dynamical parameters of unsteady membrane wings for engineering applications remains challenging. In this study, we introduce a novel bio-inspired membrane wing design and systematically investigate the fluid–structure interactions of flapping membrane wings. The membrane wing can passively camber, and its leading and trailing edges rotate with respect to the stroke plane. We find optimal combinations of the membrane properties and flapping kinematics that out-perform their rigid counterparts both in terms of increased stroke-average lift and efficiency, but the improvements are not persistent over the entire input parameter space. The lift and efficiency optima occur at different angles of attack and effective membrane stiffnesses which we characterise with the aeroelastic number. At optimal aeroelastic numbers, the membrane has a moderate camber between 15% and 20% and its leading and trailing edges align favourably with the flow. Higher camber at lower aeroelastic numbers leads to reduced aerodynamic performance due to negative angles of attack at the leading edge and an over-rotation of the trailing edge. Most of the performance gain of the membrane wings with respect to rigid wings is achieved in the second half of the stroke when the wing is decelerating. The stroke-maximum camber is reached around mid-stroke but is sustained during most of the remainder of the stroke which leads to an increase in lift and a reduction in power. Our results show that combining the effect of variable stiffness and angle of attack variation can significantly enhance the aerodynamic performance of membrane wings and has the potential to improve the control capabilities of micro air vehicles.

Validation of a Fluid Structure Interaction Model for TAVR using Particle Image Velocimetry

Abstract The implantation of a transcatheter aortic valve replacement (TAVR) in patients with severe aortic stenosis improves pathologic blood flow through the aortic valve, but still alters hemodynamics in comparison to a healthy native aortic valve. The hemodynamic characteristics of TAVR are associated with hypo-attenuating leaflet thickening and prosthetic leaflet thrombosis, which may reduce the durability of TAVR. For this reason we developed a numerical model to identify pro-thrombotic regions of TAVR based on the velocity field. In silico models have already been proven to be an effective tool for device optimization in other medical device applications. However, when using an in silico model, it is important to validate the model assumptions with experimental data or analytical solutions to confirm the accuracy of the model. In this study, we present an approach to validate a complex numerical Fluid Structure Interaction (FSI) model used to simulate leaflet kinematics and flow in the vicinity of a TAVR. Based on the recommendation of ISO 5840 (2021), a combined validation of the kinematic and fluid dynamic parameters was performed for this purpose. The leaflet kinematic was investigated via high-speed recordings and evaluated based on the Geometric Orifice Area (GOA). The velocity field of the TAVR was determined experimentally using Particle Image Velocimetry (PIV). The evaluation of the GOA showed a good agreement of the in silico model with the in vitro data for the systolic duration. The occurring velocities were qualitatively compared during peak systole for three planes and showed similar flow characteristics. The maximum velocity was 1.1 m/s in the in vitro and in silico model. Based on the results, it can be assumed that the numerical FSI model of the TAVR can be used for thrombosis risk assessment.

Construction of a peridynamic model for viscous flow

We derive the Eulerian formulation for a peridynamic (PD) model of Newtonian viscous flow starting from fundamental principles: conservation of mass and momentum. This formulation is nonlocal, different from viscous flow models that utilize numerical methods like, e.g., the so-called “peridynamic differential operator” to approximate solutions of the classical Navier-Stokes equations. We show that the classical continuity equation is a limiting case of the PD one, assuming certain smoothness conditions. The PD model for viscous flow is calibrated by enforcing linear consistency for the viscous stress term with the classical Navier-Stokes equations. Couette and Poiseuille flows, and incompressible fluid flow past a regular lattice of cylinders are used to verify the new formulation, at low Reynolds numbers. The constructive approach in deriving the model allows for a seamless coupling with peridynamic models for corrosion or fracture for simulating complex fluid-structure interaction problems in which solid degradation takes place, such as in erosion-corrosion, hydraulic fracture, etc. Moreover, the new formulation sheds light on the relationships between local and nonlocal models.

3D fluid–structure interaction with fracturing: A new method with applications

This paper presents a methodology for simulating general, three-dimensional fluid–structure interaction problems involving fracturing. Ordinary state-based peridynamics is used to describe the mechanical behaviour of the solid phase in a Lagrangian framework. The governing equations of peridynamics are coupled via a multi-direct immersed boundary method with the incompressible formulation of the Navier–Stokes equations, which are used to govern the dynamics of the fluid phase. The synchronization of the solution is achieved via a fully explicit, weak-coupling strategy that allows for fast and efficient computations. A detailed description of the methodology is provided, together with the results of several validation benchmarks. The qualitative results of the unsteady hydraulic fracture of a porous medium are also presented to show the potential of the proposed approach. The authors believe that the numerical technique described in this paper contributes to advance the capability of models in reproducing complex fluid–structure interaction and hydraulic fracture problems, providing a very detailed description of both the fluid and solid mechanics of the processes involved.

Coupled PD-SPH modeling for fluid-structure interaction problems with large deformation and fracturing

A simple and accurate coupled peridynamics (PD) and smoothed particle hydrodynamics (SPH) strategy based on virtual particles and repulsive forces is proposed to simulate fluid-structure interaction (FSI) problems with large deformation and fracturing. In the coupling framework, SPH method is employed to model fluid domain, and peridynamic theory is applied to describe the deformation and fracture of structure. To deal with the fluid-structure interfacial region, the peridynamic particles within the support domain of fluid particles are treated as virtual particles through which full kernel support of fluid particles are ensured, different boundary conditions on fluid particles can be imposed and repulsive forces preventing penetration are exerted. For momentum conservation, peridynamic particles acting forces on fluid particles are simultaneously subjected to opposite forces. Validation studies for the peridynamic model of pure solid structure and the coupled PD-SPH model of FSI involving large deformation and fracture have been performed, all presenting close agreement with analytical solutions, available experimental data, and/or other numerical results. Finally, the proposed approach is employed to study water-jetting rock fragmentation problems and the results further demonstrate that the proposed coupled PD-SPH model is capable of handling complex FSI problems with fluid-induced solid breaking.

Seismic response of cylinder assemblies in axial flow

Earthquakes are a great challenge for the safety of nuclear reactors. To address this challenge, we need to better understand how the reactor core responds to seismic forcing. The reactor core is made of fuel assemblies, which are themselves composed of flexible fuel rods immersed in a strong axial flow. This gives rise to strongly coupled fluid–structure interactions whose accurate modelling generally requires high computational costs. In this paper, we introduce a new model able to capture the mechanical response of the reactor core subjected to seismic forcing with low computational costs. This model is based on potential flow theory for the fluid part, and Euler–Bernoulli beam theory for the structural part, allowing us to predict the response to seismic forcing in presence of axial flow. The linear equations are solved in the Fourier space to decrease computational time. For validation purposes, first we use the proposed model to compute the response of a single cylinder in axial flow. We then implement a multiple-cylinder geometry made of four fuel assemblies, each made of $8\times 8$ cylinders, corresponding to an experimental facility available at CEA. The comparison between numerical results and experiments shows good agreement. The model can predict correctly the added mass. It can also capture qualitatively the coupling between assemblies and the effect of confinement. This shows that a potential flow approach can give insight into the complex fluid–structure interactions within a nuclear reactor and, in particular, be used to predict the response to seismic forcing at low computational cost.