Complex Fluid-structure Interaction Research Articles

Numerical analysis and data-driven optimization of energy harvesting efficiency from wake-induced vibration in a multi-cylinder configuration

Wake-induced vibrations (WIV) in multi-cylinder configurations have demonstrated greater energy harvesting efficiency in hydrokinetic applications compared to conventional vortex-induced vibrations (VIV) of a single cylinder. However, the complex fluid-structure interactions make it challenging to identify optimal configurations for maximum power output, as extensive simulations across numerous parameter combinations lead to substantial computational costs with traditional computational fluid dynamics (CFD) methods. To address this challenge, we developed a data-driven model using automated machine learning (AutoML) techniques, focusing on four key parameters: spacing, diameter, damping, and reduced velocity. Trained on comprehensive datasets from validated CFD simulations, this model integrates multiple algorithms to predict the power efficiency of WIV systems with high accuracy. Our approach enables rapid and precise evaluations of power efficiency across a broad range of configurations, significantly reducing the computational burden compared to traditional CFD approaches. The results indicate that optimal configurations, characterized by larger upstream cylinder diameters, higher damping ratios, and ideal spacing ratios, can achieve power generation efficiencies of up to 59.15%. Further analysis of vorticity contours reveals that synchronized interactions between upstream vortex shedding and downstream structure motions enhance WIV, thereby improving energy harvesting efficiency.

An optimized anisotropic pressure fluctuation model for the simulation of turbulence-induced vibrations

A significant aspect of the economic performance and safety of a nuclear reactor involves maintaining the integrity of the fuel rods, which are susceptible to Turbulence-Induced Vibrations (TIV) resulting from the axial flow of the coolant. TIV can instigate severe repercussions, including structural damage such as fatigue and wear. TIV can be studied numerically, using Fluid–Structure Interaction( FSI) simulations. However, high-resolution approaches are computationally too expensive to use for complex FSI simulations, while Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations severely underpredict the displacement amplitudes of the vibrations as they only resolve the mean flow. Evolving from this shortfall, this paper focuses on a recently developed Anisotropic Pressure Fluctuation Model (AniPFM). This model generates a synthetic velocity fluctuations field, which is used to solve for the pressure fluctuations. Using this model, together with URANS, is a possible way to simulate the excitation mechanisms of TIV of fuel rods in a computationally cheaper way. While previous research has highlighted the potential of this model, there are parameters, definitions, and constants whose impacts on the model are not yet fully understood. Therefore, a comprehensive effort is undertaken to fine-tune the model, optimize its performance, improve understanding of it and further validate it. This is done by applying AniPFM to both pure flow and FSI cases, using high-resolution numerical and experimental data as reference and for comparison. With the optimized model, a substantial decrease in average difference from the experimental data is found for the FSI case under consideration, when compared with the unoptimized version of AniPFM.

Vortex-induced vibrations of flexible cylinders predicted by wake oscillator model with updated relative velocity parameters and a varying axial tension model

This study developed a numerical analysis model for predicting three-dimensional vortex-induced vibrations (VIV) on flexible cylinders by incorporating updated relative velocity parameters and a varying axial tension model. The research seeks to enhance the precision of VIV predictions for flexible cylinders under complex fluid-structure interactions. The trigonometric functions of the attack angle and the relative velocity magnitude have been refined to achieve more accurate hydrodynamic force calculations. The axial tension is computed by accounting for the wet weight and the bending deflection resulting from cylinder vibrations in both cross-flow (CF) and in-line (IL) directions. The present work simulates a series of cases and compares the outcomes with the experimental data and numerical results of other investigators. The results demonstrate that the present model agrees well with the experimental data and exhibits superiority over previous studies in certain aspects. This work enhances the understanding and prediction of VIV phenomena in flexible structures, with potential applications in ocean engineering and offshore structures.

Simulation of fluid-structure interaction using the density smoothing B-spline material point method with a contact approach

Fluid-structure interaction (FSI) problems with strong nonlinearity and multidisciplinarity pose challenges for current numerical FSI algorithms. This work proposes a monolithic strategy for solving the equations of motion for both the fluid and structural domains under the unique Lagrangian framework of the B-spline material point method (BSMPM). A node-based density smoothing BSMPM (referred to as ds-BSMPM) is proposed to eliminate pressure instability and oscillation in the simulation of weakly compressible fluids, which is straightforwardly implemented using B-spline basis functions without the need for any sophisticated particle search algorithm. The interaction between the fluid and structure is conducted using the Lagrangian multiplier method on the tensor product grid, whose actual position is determined by the Greville abscissa and is used to detect contact. The proposed method is verified and validated against existing numerical approaches and experimental results, demonstrating the effectiveness of the proposed method in eliminating the oscillations of water pressure and solid stress, and avoiding premature and erroneous contact. In particular, this work presents a promising monolithic approach for achieving high-fidelity solutions to complex FSI problems.

A Peridynamics-Smoothed Particle Hydrodynamics Coupling Method for Fluid-Structure Interaction

Ice–water interaction is a critical issue of engineering studies in polar regions. This paper proposes a methodology to simulate fluid–ice interactions by employing a structure modeled using ordinary state-based peridynamics (OSB-PD) within a smoothed particle hydrodynamics (SPH) framework, effectively representing a deformable moving boundary. The forces at the fluid–structure interface are delineated by solving the fluid motion equations for normal forces exerted by the fluid on the structure, grounded in the momentum conservation law. Upon validating the PD and SPH methods, a dam break flowing through an elastic gate was simulated. When compared with experimental results, the model exhibited discrepancies of 3.8%, 0.5%, and 4.6% in the maximum horizontal displacement, maximum vertical displacement, and the waterline deviation (W = 0.05 m), respectively. Moreover, the method demonstrated a high degree of accuracy in simulating the fracture of in-situ cantilever ice beams, with deflection closely matching experimental data and a 7.4% error in maximum loading force. The proposed PD-SPH coupling approach demonstrates its effectiveness in capturing the complex fluid–structure interactions and provides a valuable tool for studying the deformation and fracture of structures under the influence of fluid forces.

Cytoplasmic stirring by active carpets

Large cells often rely on cytoplasmic flows for intracellular transport, maintaining homeostasis, and positioning cellular components. Understanding the mechanisms of these flows is essential for gaining insights into cell function, developmental processes, and evolutionary adaptability. Here, we focus on a class of self-organized cytoplasmic stirring mechanisms that result from fluid-structure interactions between cytoskeletal elements at the cell cortex. Drawing inspiration from streaming flows in late-stage fruit fly oocytes, we propose an analytically tractable active carpet theory. This model deciphers the origins and three-dimensional spatiotemporal organization of such flows. Through a combination of simulations and weakly nonlinear theory, we establish the pathway of the streaming flow to its global attractor: a cell-spanning vortical twister. Our study reveals the inherent symmetries of this emergent flow, its low-dimensional structure, and illustrates how complex fluid-structure interaction aligns with classical solutions in Stokes flow. This framework can be easily adapted to elucidate a broad spectrum of self-organized, cortex-driven intracellular flows.

A Review of the Hydrodynamic Damping Characteristics of Blade-like Structures: Focus on the Quantitative Identification Methods and Key Influencing Parameters

Abstractcean energy has progressively gained considerable interest due to its sufficient potential to meet the world’s energy demand, and the blade is the core component in electricity generation from the ocean current. However, the widened hydraulic excitation frequency may satisfy the blade resonance due to the time variation in the velocity and angle of attack of the ocean current, even resulting in blade fatigue and destructively interfering with grid stability. A key parameter that determines the resonance amplitude of the blade is the hydrodynamic damping ratio (HDR). However, HDR is difficult to obtain due to the complex fluid–structure interaction (FSI). Therefore, a literature review was conducted on the hydrodynamic damping characteristics of blade-like structures. The experimental and simulation methods used to identify and obtain the HDR quantitatively were described, placing emphasis on the experimental processes and simulation setups. Moreover, the accuracy and efficiency of different simulation methods were compared, and the modal work approach was recommended. The effects of key typical parameters, including flow velocity, angle of attack, gap, rotational speed, and cavitation, on the HDR were then summarized, and the suggestions on operating conditions were presented from the perspective of increasing the HDR. Subsequently, considering multiple flow parameters, several theoretical derivations and semi-empirical prediction formulas for HDR were introduced, and the accuracy and application were discussed. Based on the shortcomings of the existing research, the direction of future research was finally determined. The current work offers a clear understanding of the HDR of blade-like structures, which could improve the evaluation accuracy of flow-induced vibration in the design stage.

Exploring kinematic stability of vortex structures: A topological approach to fluid flow around staggered square cylinders

In this study, a detailed fluid dynamics analysis is conducted around two identical square cylinders in a staggered configuration at a Reynolds number (Re) of 40, using a stabilized finite-element method to investigate the kinematic stability of vortex structures. By varying the horizontal spacing (S/D) between 2 and 30 and examining transverse gaps (T/D) of 0.25, 0.8, and 1.25, the research uncovers significant flow behavior variations from the tandem configuration, highlighting complex fluid-structure interactions. The presence of “separation bubbles” at lower S/D values across all T/D ratios indicates the dynamic impact of the upstream cylinder's proximity on the flow field, particularly on the stagnation points of the downstream cylinder. Through a comprehensive topological analysis, the study identifies various flow regimes and topological bifurcations, revealing transitions between stable states that maintain the number of critical points constant, and the kinematic stability of these vortical structures is established by the critical point theory. The effect of cylinder configurations and diverse flow structures on fluid loading is also analyzed by examining surface pressure coefficients. The asymmetry present in the cylinder configuration is manifested through the asymmetric values of lift coefficients.

Chaotic Vortex-Induced Vibrations of Rigid Cylinders with Nonlinear Snapping Support

Vortex-Induced Vibration (VIV) is a complex fluid–structure interaction in offshore structures. Traditionally, this phenomenon is considered periodic; however, many of its signals show chaotic behavior. The basic model already employed by other researchers is a rigid circular cylinder with linear springs and dampers. In this work, nonlinear snapping support is used to model nonlinearity in the system. To numerically simulate the flow, Reynolds-Averaged Navier–Stokes (RANS) equations for two-dimensional incompressible unsteady flows are applied. The degree of nonlinearity of the system can be changed by manipulating [Formula: see text], which is one of the geometric properties of the spring and takes values between 0 and 1. The 0–1 test, Poincaré section, and Fast Fourier Transform are used to analyze the cylinder and lift force behavior. Also, the Hilbert transform is applied to the signals, and the phase shift between displacement and lift force is obtained. The results show that the system behavior consists of branches: branch I and branch II. The large amplitudes occur in branch II. It is found that chaos emerges at the beginning of branch II, regardless of the value of [Formula: see text]. By raising the [Formula: see text] value, the span of branch II becomes more expansive, and its first point is placed at lower reduced velocities. Also, the wake dynamics becomes more regular at the end of branch I and more irregular at the beginning of branch II with the increase in [Formula: see text]. When the cylinder displacement signal is chaotic, the lift force behavior is also chaotic, but not vice versa.

Virtual physical framework reveals vortex-induced vibration “Soar” and “Death” for a bluff body at high Reynolds numbers

Vortex-induced vibration (VIV) of a bluff body is well known as a canonical phenomenon in complex fluid–structure interactions (FSI). However, our understanding and physical theories of this phenomenon are still restricted to a lower Reynolds number (Re) range owing to the limitations of experimental fluid mechanics. Herein, we describe a virtual physical framework (VPF) capable of editing and controlling the physical parameters of an actual physical system with high fidelity by combining numerical disciplinary and mechanical actuators. We demonstrated the effectiveness of applying a VPF to address the experimental fluid mechanical challenges of vortex-induced vibration (VIV) for a bluff body at a high Re by virtualizing a large, flexibly mounted rigid cylindrical system. We observed the VIV evolution of the bluff body at different Re values. Notably, the VIV appears in its “soar” stages with unexpected amplitudes of 2.4 D, nearly 200% higher than the traditionally acknowledged value at approximately Re = 2.0E5, while suddenly entering into its “death” stages with no vibrations over the critical Re region. The dissynchrony changes in the energy dissipation and input with Re caused by drag and excitation forces in the fluid system were further found to result in these VIV phenomena. This discovery upsets previous perceptions of VIVs and raises profound questions regarding related engineering projects. The VPF also opens a promising paradigm in experimental research for accelerating scientific discovery and investigating unaddressed classical physical phenomena.

Estimating nonlinear wind-induced response of roof cable nets by aeroelastic experiments and ML modeling

The paper examines the structural engineering challenges related to the assessment of the wind-induced vertical displacements of lightweight, hyperbolic-paraboloid cable-supported membrane roofs. Analysis and comparisons are conducted using three distinct methods for calculating the roof vertical, out-of-plane displacements. Finite element method (FEM) analysis is employed using: (i) estimated static nodal forces obtained from wind pressure coefficients determined by aerodynamic wind tunnel tests on a rigid building model, and (ii) loads found from wind pressure coefficients, estimated through machine learning (ML) methods, and (iii) measured roof response found from aeroelastic wind tunnel tests on a flexible model. The study examines three different roof geometries (square, rectangular and circular) and two distinct membrane curvatures for each geometry. Furthermore, wind directionality (three mean-wind incidence angles) and Reynolds number effects (seven mean wind velocities) are studied. Comparisons show that the non-linear FEM analysis, based on estimated static wind loads, underestimates the roof displacements at the roof center, compared to the direct measurements on the aeroelastic model. The main contribution of the study consists of a novel application of ML models, and Artificial Neural Networks (ANNs) in particular, which are employed to correct roof displacement estimations, found by simplified aerodynamic test pressure measurements on rigid roof models. The goal is to better describe the complex fluid-structure interaction of the roof membranes, which can only be achieved by direct aeroelastic tests that are difficult to design and execute. Finally, the study demonstrates that ANNs can be used not only for the preliminary design of the full-scale structure but also for construction of wind tunnel scale models.

Wave run-up characteristic on armour layer breakwater using the smoothed particle hydrodynamics (SPH) method

Coastal structures, such as breakwater, play a critical role in protecting shorelines from the erosive forces of waves and currents. Understanding the wave run-up phenomenon on these structures is essential for designing effective coastal defense systems. This research aims to investigate the wave run-up characteristics on an armour layer breakwater using the Smoothed Particle Hydrodynamics (SPH) method (Meshless particle method based on the Lagrangian formulation), a numerical method that captures complex fluid-structure interactions. The SPH method’s inherent ability to handle free-surface flows and dynamic interactions makes it particularly suited for simulating wave run-up. The research employs numerical testing and modelling of a non-overtopping breakwater using the smoothed particle hydrodynamics method simulated with the DualSPHysics program. The wave characteristic data used in this research are the waves on the south coast of Java. The results of this research indicate that the correlation between wave run-up characteristics (Ru/H) and the Iribarren number, both using the numerical SPH method and theory, tends to exhibit a similar pattern. Remarkably, the results from both approaches exhibit a striking similarity, revealing that as the Iribarren number increases, the incremental growth of Ru/H diminishes, eventually stabilizing at a critical threshold. The Coefficient of Determination (R2) between wave run-up characteristics (Ru/H) obtained from numerical simulations using the SPH method and Günbak’s theory is 0.8824.

An efficient partitioned framework to couple Arbitrary Lagrangian-Eulerian and meshless vector form intrinsic finite element methods for fluid-structure interaction problems with deformable structures

The Vector Form Intrinsic Finite Element (VFIFE) is an advanced meshless Lagrangian structural solver. This study introduces a partitioned framework to integrate Arbitrary Lagrangian-Eulerian and VFIFE methods into fluid-structure interaction (FSI) problems featured by large structural displacements and deformations. The VFIFE method enables the FSI simulations with deformable structures due to the nature of Lagrangian particles, which is challenging for traditional computational fluid mechanics techniques. In addition, the VFIFE can be effectively equipped with the partitioned coupling schemes because of the versatility of governing equations. In this algorithm system, several matrix problems in finite element methods and mapping and interpolation in the fluid-structure interface can be avoided. The significant potential of this algorithm in tackling complex FSI problems is demonstrated through various benchmarks, encompassing scenarios like Taylor-Green vortex, flow over a rigid cylinder (Re = 40 ∼ 200), forced vibration of a rigid cylinder, vortex-induced vibration (VIV) of an elastically mounted cylinder, and VIV of a rigid cylinder with an attached flexible cantilever beam. Finally, an experiment on flow past a curtain in a water tank is conducted to further evaluate the precision and stability of the current coupling strategy in three dimensions, demonstrating the feasibility of such methods in flexible structures.

Experimental study of flag fluid–structure interaction in a laminar jet and application of POD

A fluttering flag in a uniform laminar flow exhibits complex fluid–structure interaction (FSI) behavior. This investigation experimentally studied aerodynamic load behavior and its connection to the oscillation behavior, flag envelope and fluid flow parameters, and application of Proper Orthogonal Decomposition (POD) to fluid flow data to elucidate changes in flow behavior associated with the changes in oscillation modes and observed drag coefficient values. For this purpose, three flag models with varying lengths were used. The aerodynamic load forces were measured using a high-precision load cell, and two-dimensional Particle Image Velocimetry (PIV) was used to quantify the flow field around the flag. The Reynolds number (Re), mass ratio (R1), and dimensionless rigidity (R2) values were varied between 4.4×104−12.3×104, 1.48−2.77, and 1.3×10−3−15.1×10−3, respectively. The results showed the linear relationship between drag coefficients with normalized amplitude of oscillation and Strouhal number. The results also showed the connection between observed drag and change in flag oscillation modes. The POD analysis showed that the energy content of the POD modes changed with the change in flag oscillation from mode-2 to mode-3 oscillations. The phase portrait of the first four POD modes also showed a unique interplay of POD modes, resulting in a change in the velocity flow field associated with the change in oscillation modes. The low-order reconstruction using select POD modes and control volume analysis of the velocity flow field showed a connection between POD modes and observed drag.

Shock-wave/turbulent boundary-layer interaction with a flexible panel

The dynamic coupling between a Mach 2.0 shock-wave/turbulent boundary-layer interaction (STBLI) and a flexible panel is investigated. Wall-resolved large-eddy simulations are performed for a baseline interaction over a flat-rigid wall, a coupled interaction with a flexible panel, and a third interaction over a rigid surface that is shaped according to the mean panel deflection of the coupled case. Results show that the flexible panel exhibits self-sustained oscillatory behavior over a broad frequency range, confirming the strong and complex fluid–structure interaction (FSI). The first three bending modes of the panel oscillation are found to contribute most to the unsteady panel response, at frequencies in close agreement with natural frequencies of the mean deformed panel rather than those for the unloaded flat panel. This highlights the importance of the mean panel deformation and the corresponding stiffening in the FSI dynamics. The time-averaged flow shows an enlarged reverse-flow region in the presence of mean surface deformations. The separation-shock unsteadiness is enhanced due to the panel motion, leading to higher wall-pressure fluctuations in the coupled interaction. Spectral analysis of the separation-shock location and bubble-volume signals shows that the STBLI flow strongly couples with the first bending mode of the panel oscillation. This is further confirmed by dynamic mode decomposition of the flow and displacement data, which reveals variations in the reverse-flow region that follow the panel bending motion and appear to drive the separation-shock unsteadiness. Low-frequency modes that are not associated with the fluid–structure coupling, in turn, are qualitatively similar to those obtained for the rigid-wall interactions, indicating that the characteristic low-frequency unsteadiness of STBLI coexists with the dynamics emerging from the fluid–structure coupling. Based on the present results, unsteady FSIs involving STBLIs and flexible panels are likely to accentuate rather than mitigate the undesirable features of STBLIs.

Effect of Archimedes number on the dynamics of free-falling perforated disks

The dynamics of perforated disks falling freely in a large expanse of viscous fluid at rest is investigated numerically. This complex fluid–structure interaction is solved via large eddy simulation. This numerical algorithm is verified and validated with available experimental results. The influence of Archimedes number expressing the ratio between the gravity-buoyancy and viscosity effects is discussed thoroughly, including kinematics and dynamics. Two critical Archimedes numbers are identified, Arcr1≈450 and Arcr2≈950, respectively. At these two critical Archimedes numbers, both kinematic and dynamic variables change trends. In this paper, we focus on the statistics of free-falling perforated disks. With the Archimedes number Ar increasing, the average angle of attack ⟨AoA⟩ and descent velocity ⟨Uz⟩ decrease gradually, and they arrive at a fixed value finally (here, ⟨·⟩ represents a time-average result); On the contrary, the other kinetic variables change violently when Ar is around 900, for example, terminal velocity ⟨Ut⟩. Additionally, phase differences of kinematic and dynamic variables are analyzed. A constant phase difference between the nutation angle θ and normal force FN is identified, about 66°, which is independent of Ar. Vortex structures are visualized using Q-criterion, and triangular vortex is omnipresent around holes. During the descent, a helical vortex always attaches to the perforated disk outer edge. With Ar increasing, complex vortex interaction appears, for example, merging and stretching. Some unusual behaviors in the numerical results are analyzed from the perspective of wake dynamics.

Adaptive control of transonic buffet and buffeting flow with deep reinforcement learning

The optimal control of flow and fluid–structure interaction (FSI) systems often requires an accurate model of the controlled system. However, for strongly nonlinear systems, acquiring an accurate dynamic model is a significant challenge. In this study, we employ the deep reinforcement learning (DRL) method, which does not rely on an accurate model of the controlled system, to address the control of transonic buffet (unstable flow) and transonic buffeting (structural vibration). DRL uses a deep neural network to describe the control law and optimizes it based on data obtained from interaction between control law and flow or FSI system. This study analyzes the mechanism of transonic buffet and transonic buffeting to guide the design of control system. Aiming at the control of transonic buffet, which is an unstable flow system, the control law optimized by DRL can quickly suppress fluctuating load of buffet by taking the lift coefficient as feedback signal. For the frequency lock-in phenomenon in transonic buffeting flow, which is an unstable FSI system, we add the moment coefficient and pitching displacement to feedback signal to observe pitching vibration mode. The control law optimized by DRL can also effectively eliminate or reduce pitching vibration displacement of airfoil and buffet load. The simulation results in this study show that DRL can adapt to the control of two different dynamic modes: typical forced response and FSI instability under transonic buffet, so it has a wide application prospect in the design of control laws for complex flow or FSI systems.

Coupled dynamics of the moving Antarctic krill trawl structure and its hydrodynamics behavior using various catch sizes and door spreads based on wavelet-based and Fourier analysis

Antarctic krill is a key element of the complex ecology of the Antarctic Ocean and a target species for commercial fisheries for aquaculture supply, krill oil production, and as a major food source for various natural predators. Therefore, understanding the interaction between the fluid structures of the Antarctic krill trawl structure is the key factor in solving problems such as selectivity, energy efficiency, catchability, and ecological sustainability in this fishery. Thus, this study experimentally investigated the influence of catch sizes, door spread, and inflow velocities on the bridle tension, trawl motions, trawl deformation, and flow field inside and around a scaled trawl model in flume tank based on the electromagnetic current velocity meter measurements. Fourier analysis using power spectrum density and the continuous wavelet transform is used to analyze the time-frequency contents of the instantaneous flow velocities, bridle tension, and trawl motions; and in the interaction between the unstable turbulent flows and the fluttering trawl motions, wavelet coherency analysis was employed to detect coherent structures. Results indicated that the bridle tension and trawl motions increased as the catch size, door spread, and inflow velocity increased. Owing to the significant trawl deformation, a complex fluid–structure interaction occurred and a strong positive correlation between the bridle tension and trawl motions was obtained. Furthermore, a significant decrease in the flow field occurred inside and outside different parts of the trawl. Fourier and wavelet analysis results showed that the trawl motions and bridle tension are mainly of a low-frequency activity and of another component related to the unsteady turbulent flow street, and decreased with the increasing catch size and door spread. A complex fluid–structure interaction is then demonstrated where the hydrodynamics of the moving Antarctic krill trawl structure are an intricate interplay between trawl fluttering motions and unsteady turbulent flow influenced by catch size and door spread. The knowledge of such trawl hydrodynamic behavior is of great importance to understand and design the optimal structure of trawl nets to maintain the sustainability of the Antarctic krill fishery.

Differentiable hybrid neural modeling for fluid-structure interaction

Solving complex fluid-structure interaction (FSI) problems, which are described by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics based solvers are inadequate to handle the increasing demand for large-scale and long-period simulations. The ever-increasing availability of data and rapid advancement in deep learning (DL) have opened new avenues to tackle these challenges through data-enabled modeling. The seamless integration of DL and classic numerical techniques through the differentiable programming framework can significantly improve data-driven modeling performance. In this study, we propose a differentiable hybrid neural modeling framework for efficient simulation of FSI problems, where the numerically discretized FSI physics based on the immersed boundary method is seamlessly integrated with sequential neural networks using differentiable programming. All modules are programmed in JAX, where automatic differentiation enables gradient back-propagation over the entire model rollout trajectory, allowing the hybrid neural FSI model to be trained as a whole in an end-to-end, sequence-to-sequence manner. Through several FSI benchmark cases, we demonstrate the merit and capability of the proposed method in modeling FSI dynamics for both rigid and flexible bodies. The proposed model has also demonstrated its superiority over baseline purely data-driven neural models, weakly-coupled hybrid neural models, and purely numerical FSI solvers in terms of accuracy, robustness, and generalizability.

Nonlinear WEC modeling using Sparse Identification of Nonlinear Dynamics (SINDy)

Modeling oscillating surge wave energy converter (OSWEC) systems to accurately predict their behavior has been a notoriously difficult challenge for the wave energy field. This is particularly challenging in realistic sea states where nonlinear WEC dynamics are common due to complex fluid-structure interaction, breaking waves, and other phenomena. Common modeling techniques for OSWECs include using potential flow theory to linearize the governing equations and ease computations, or using CFD to solve the full Navier-Stokes equations coupled with rigid body motion. However, both of these options have significant limitations. Potential flow theory breaks down in realistic sea conditions where nonlinear WEC dynamics are present, and CFD is often too computationally expensive for many applications such as real-time state prediction and optimal control, two areas of active research in the wave energy field. In particular, OSWEC dynamics are dominated by diffractive and viscous forces, often making common assumptions and linearization approximations (including small-body approximations) unreasonable, and CFD computationally intractable.
 To bridge this gap in modeling methods, we propose using Sparse Identification of Nonlinear Dynamics (SINDy) to build nonlinear reduced-order models (ROMs) that describe OSWEC behavior in response to large-amplitude regular waves. SINDy is an equation-free, data-driven algorithm that identifies dominant nonlinear functions present in system state dynamics using a library of nonlinear functions created from time series measurement data. The result is an ordinary differential equation (ODE) in time that can be solved from an initial condition to model and predict time behavior of the states. SINDy is parsimonious, meaning it uses a sparsity-promoting hyperparameter with the goal of only including the minimum number of terms to capture dominant dynamics, resulting in interpretable and generalizable results that are not overfit to the data. Using the discovered ROMs and integrating in time, not only can SINDy provide time series models and future state predictions of OSWEC dynamics, it can also give insights into which variables are critical in describing the underlying dynamics of the state. 
 In this study, we use SINDy to describe the nonlinear dynamics of a lab-scale OSWEC in a wave tank subjected to large-amplitude regular waves. We use nonlinear simulation data to generate kinematic, force, and torque data and use it as input to SINDy to identify ODEs that describe the measurement variables in time. We then integrate the ODEs to recreate the time series as well as predict future system behavior. We directly compare the resulting time series to the original data input to assess the accuracy of the SINDy model. We also interpret the dominant terms in the ODEs to gain insight on underlying mechanisms of the observed nonlinearity.
 Early results show SINDy is a promising tool for modeling nonlinear OSWEC dynamics. We are able to build ROMs for variables such as angular kinematics and the moment about the hinge that generate an accurate recreation of data measurements. We found strong dominance in cubic and quintic terms of the ROMs, suggesting higher-order nonlinearities in the system dynamics. These findings inspire future work in identifying underlying mechanisms driving nonlinearity.