The precise simulation of three-dimensional fluid-structure interaction (FSI) phenomena has always been a hot topic in computational mechanics. To solve FSI problems, a bidirectional coupling strategy technique between the Smoothed Particle Hydrodynamics (SPH) method and Finite Element Method (FEM) is proposed based on a single-layer particle boundary technique in this paper, enabling efficient three-dimensional coupling between fluid particles and solid elements. Within the proposed SPH-FEM coupling framework, a mapping relationship is constructed between surface meshes and single-layer SPH particles, where the surface meshes share nodes with solid elements to transmit external loads. At the same time, the single-layer particles serve as solid boundaries for the SPH solver. The approach eliminates the need for additional boundary treatments and node arrangements required in conventional SPH-FEM coupling algorithms, significantly improving data exchange efficiency between the SPH and FEM modules. The model introduces a boundary shield algorithm and permits different particle/mesh resolutions at the fluid-structure interface, enabling the simulation of three-dimensional FSI problems with complex geometries. Afterwards, the improved SPH-FEM coupling model is adopted to carry out numerical simulations of typical FSI problems, such as the water impact of a wedge, the deformation of an elastic plate under dam-break flows, the flexible floating body under dam-break flows, and the dynamic response of a flexible ship under waves. The numerical results are compared and verified with reference results, proving the computational accuracy of the SPH-FEM coupling algorithm in the FSI problem and broadening the application prospects of the SPH method in engineering problems.

To address the high computational cost of high-fidelity computational fluid dynamics (CFD) simulations for vortex-induced vibration (VIV), a prediction framework combining proper orthogonal decomposition (POD) and the Informer model is proposed. Validated for cylinders with various mass ratios at reduced velocities Ur = 1-16 and a fixed m*ξ=0.013, the framework forecasts the spatiotemporal evolution of cylinder wake vortices with a relative error of approximately 5% using a limited flow-field training set per case. The transfer learning results suggest improved training efficiency and generalization, while the agreement in energy-transfer loops and phase angles provides evidence that the model reproduces selected signatures of fluid-structure coupling within the tested conditions. Based on the predicted flow field, hydrodynamic forces are derived using the finite-domain vorticity-moment theory, which are then used to calculate the VIV response. The framework is extended to the three-dimensional flexible riser, where the overall vibration response is predicted by forecasting hydrodynamic forces on two-dimensional slices, yielding relative errors that typically stay within 10%. With source-domain data and the pre-trained model, the framework improves efficiency by 98.6% compared to traditional CFD simulations, significantly reducing cost. This study establishes an efficient data-driven alternative to high-fidelity CFD for VIV problems within the tested regime.

The analysis of fluid-structure interaction (FSI) in complex flow fields has traditionally relied on high-fidelity numerical simulations with large-scale refined grids, which entail prohibitive computational costs. This study investigates vortex-induced vibrations (VIV) of a long slender riser under both constant and time-varying top tension conditions using a two-way coupled computational fluid dynamics (CFD) approach at subcritical Reynolds numbers. The spectral proper orthogonal decomposition (SPOD) method is introduced to perform modal decomposition and extract latent space representations. By integrating machine learning (ML) models, multiple SPOD-ML frameworks are developed. These frameworks are capable of predicting the complete spatiotemporal evolution of structural responses and both two- and three-dimensional wake vortex structures from limited temporal data. Building upon the SPOD-ML framework, which captures the underlying physical mechanisms of flow dynamics in VIV problems, this study further incorporates a Transfer Learning (TL) strategy to enhance the training efficiency and robustness of the predictive framework across varying flow conditions. This study conducts a comprehensive evaluation of the prediction performance across various models, with the aim of constructing a data-driven framework that integrates machine learning and transfer learning strategies. The framework significantly reduces computational costs while maintaining high accuracy in short-term forecasting, with prediction errors below 5%. Furthermore, the influence of different prediction strides on model accuracy and stability is systematically investigated.

The horizontal and vertical spacings between fore and aft hydrofoils are critical design parameters for hydrofoil craft. This study combines finite-volume simulations with towing-tank experiments to investigate hydrodynamic interference between fore-and-aft tandem hydrofoils under three-dimensional free-surface conditions. Submergence depth, vertical spacing and horizontal spacing are varied to quantify their effects on lift, drag and the aft-foil inflow. The results show that lift increases nonlinearly with submergence depth, whereas drag increases nearly linearly. As the vertical spacing increases, the aft-foil lift first decreases and then recovers, but increasing the vertical spacing alone does not fully restore the isolated-foil lift. Horizontal spacing changes the aft-foil effective angle of attack and the strength of strut-junction separation vortices, making the lift response either favourable or adverse depending on the relative arrangement, while drag is slightly reduced. Through a combined numerical and experimental investigation, these results indicate that tandem-hydrofoil performance is controlled primarily by wake-position matching and tip-vortex control rather than by simply increasing spacing or depth. An effective layout should ensure adequate submergence, use horizontal spacing to capture favourable upwash, and use vertical spacing to weaken adverse wake interference.

The wake generated by underwater vehicles during operation exhibits various hydrodynamic characteristics, which can provide crucial insights into the orientation, speed, and depth of the vehicle. This study proposes a methodology based on an artificial intelligence surrogate model for wake prediction and navigation parameter inversion of the underwater vehicle. Initially, numerical simulation techniques are employed to establish a hydrodynamic dataset of the underwater vehicle wake. Subsequently, Proper Orthogonal Decomposition (POD) is adopted to reduce the order of the wake data. Combined with physics-informed prior knowledge, a multi-scale decoupled architecture, termed the Trend-Gaussian Process (Trend-GP), is proposed, explicitly isolating macroscopic trends via Ridge Regression before modeling highly non-linear residuals with Gaussian Processes. Evaluations demonstrate exceptional performance within the interpolation dataset. In extrapolation scenarios, this model maintains high precision in large depth extrapolations and reliable accuracy at a 5% speed extrapolation rate, yielding an average wake prediction error of 7.40%, with parameter inversion errors of 3.36% (speed) and 4.80% (depth). Compared to conventional surrogate models, the Trend-GP achieves high accuracy under small-sample constraints, quantifies uncertainty based on Bayesian theory to forewarn sparse boundaries, and enhances extrapolation capabilities through its trend-residual decoupling mechanism, providing a novel strategy for non-acoustic detection in underwater environments.

This paper presents SPHydroDRL, a mesh-free computational framework that couples quasi-Lagrangian Smoothed Particle Hydrodynamics (SPH) with Deep Reinforcement Learning (DRL) for solving Active Flow Control (AFC) problems. Built upon the previously developed SPHydro solver, the framework provides an SPH environment accelerated by graphics processing units and communicates with a DRL agent through a lightweight Python-C++ interface. Three hydrodynamic benchmark cases are considered to assess the numerical accuracy, robustness, and control performance of the coupled framework. The results demonstrate that the proposed SPH-DRL framework provides a practical particle-based route for long-duration AFC simulations involving free-surface flows and moving boundaries, while maintaining good global fluid-volume conservation.

This study presents a coupled thermo-mechanical SPH framework for simulating high-speed multimaterial impacts involving large deformations. The framework consistently integrates reaction heat release, heat conduction, and temperature-dependent constitutive laws and equations of state into the governing equations, enabling accurate modeling of plastic flow, thermal response, and damage evolution. For metallic materials, the Johnson-Cook constitutive model and failure criterion are employed, while a friction- and viscosity-dominated post-failure response is introduced to represent mechanical behavior after melting and fragmentation. To address tensile instability in conventional SPH methods, a novel physically based pressure-limiting technique coupled with temperature evolution is developed. Furthermore, a dynamic particle activation strategy is proposed to efficiently resolve only the shock-affected regions, greatly enhancing computational efficiency. Numerical results show that the proposed framework can robustly capture interface evolution, temperature distribution, and failure patterns in high-speed multimaterial impacts. The findings highlight the crucial role of thermal effects in impact-induced damage processes. Overall, the developed model achieves high accuracy and stability under extreme strain-rate conditions, offering a reliable computational tool for investigating coupled thermal-mechanical behavior and damage mechanisms in high-speed impact events.

This paper numerically investigates the vortex-induced vibration of flexible risers subjected to surge motion of floating platforms. The dynamic boundary condition associated with this degree of freedom is transformed into a superimposed flow composed of shear flow and sheared oscillatory flow. The effects of oscillation frequency and velocity ratio of the equivalent superimposed flow on riser vibration characteristics are examined across different Keulegan-Carpenter number ranges. Numerical results show that increasing the oscillation frequency of the superimposed flow strengthens the dominance of the dominant vibration mode, whereas increasing the velocity ratio enhances the contribution of higher-order modes. The vortex shedding mode at each riser section varies periodically, resulting in five distinct vortex shedding modes. Based on their evolution, mechanistic conclusions are drawn, indicating that the oscillation frequency of the superimposed flow influences the critical velocity governing transitions between high-frequency and low-frequency vortex shedding modes, while the velocity ratio has little effect on the magnitude of the critical velocity but alters its interval.

To address the high sensitivity of propulsion efficiency and stability to attitude variations in near-free-surface bionic propulsion systems, a numerical investigation of the hydrodynamic characteristics of an undulating NACA0012 hydrofoil using the δ+-SPH method is conducted in this study. By introducing angle-of-attack variations from α=−5∘ to 5∘ at a fixed submergence depth of H/L=0.4, the effects of the angle of attack on cruising performance, free-surface response, and wake structure evolution are systematically analyzed. The results indicate that as the angle of attack increases, the cycle-averaged cruising velocity first increases but then decreases, whereas the input power coefficient increases monotonically and the overall propulsion efficiency decreases. The maximum cruising velocity and propulsion efficiency are achieved at α=−3∘ and α=−5∘, respectively. Further analysis of the hydrodynamic loads reveals that at α=−3∘, the force distribution is relatively balanced, thereby promoting stable cruising. Wake analysis demonstrated that the angle of attack controls the dominance and arrangement of positive and negative vortices by altering the relative strength of shear layers on the upper and lower surfaces. As the angle of attack increases, the wake tends to deflect toward the free surface and forms a typical “V”-shaped vortex street at α=5∘. Within the scope of this study, the case of α=−3∘ achieves an optimal balance among propulsion efficiency, cruising velocity, and attitude stability, providing a reference for attitude design and parameter optimization of near-free-surface bionic propulsion systems.

Inspired by the ship roll stabilization fin stabilizers, this paper innovatively proposes an active vibration suppression method by arranging rotating hydrofoil system controlled by Proportional-Integral-Derivative (PID) strategy. Using the computational fluid dynamics (CFD) method, a two-degree-of-freedom (2-DOF) system is established to model the main cylinder-hydrofoil system, aiming to investigate the influence of hydrofoils on the vortex-induced vibration (VIV) response. The effects of hydrofoil quantity, size, and spacing from the cylinder on suppression efficiency were studied to determine an appropriate hydrofoils arrangement strategy. The hydrofoil system achieves vibration suppression by generating counter forces and controlling the wake structure. Theoretical analysis shows that the transverse vibration velocity is more suitable as the feedback signal for the PID controller. Since integral control introduces a phase lag that degrades suppression performance, PD control demonstrates superior temporal efficacy and dynamic stability. Furthermore, phase-averaged pressure fields and spectral proper orthogonal decomposition (SPOD) were employed to extract the dominant flow dynamics. The results conclusively demonstrate that the PID-controlled hydrofoil system significantly reduces the low-pressure region around the main cylinder and primarily attenuates energy transfer to the external flow field, thereby achieving vibration suppression efficiencies of 94-98 % across different reduced velocities. Findings provide valuable insights for the optimal design of this innovative active vibration suppression device.

In this work, a novel hybrid weighted-compact-nonlinear scheme (WCNS) with fifth-order multi-resolution (MR) and low dissipation features is proposed to predict the one/two/three-dimensional (abbreviated as 1D/2D/3D) compressible discontinuous flows, which is motivated by three different state-of-the-art concepts (termed as "H-WCNS-s(+)"). For the improvements of present H-WCNS-s(+): first-step, recently developed succinct local smoothing indicators (SIs) are introduced into the existing WCNS-MR scheme for reducing the computing cost and preserving fifth-order convergence (WCNS-MR-s); second-step, a new global SI is designed referring to an advanced Z-type SI which can result in lower numerical dissipation (H-WCNS-s-I); third-step, following adaptive stencils-selection concept in existing targeted essential non-oscillatory scheme, a new stencils-selection condition is designed to meet the feature of five-three-one center nested stencils, to improve the numerical stability near sharp discontinuity. Moreover, the numerical flux of Harten-Lax-van-Leer is mainly adopted in the present hybrid scheme. In the numerical experiments, first, the spectral properties of the proposed schemes are demonstrated and compared with other existing fifth-order schemes, and the numerical convergence rate of the proposed schemes are also illustrated, which has lower numerical dissipation than existing WCNS-type schemes. Subsequently, several 1D/2D classical or challenge compressible problems accompanied by different shock-wave phenomena (multi-small-scale, blast and implosion, etc.) are simulated to show the precision, robustness and shock-capturing capacity of the proposed schemes. Finally, the 3D compressible inviscid/viscous small-scale vortical structures are predicted to assess the extended capacity and virtue of the proposed scheme for 3D turbulent flow, comparing with other fifth-order WCNS-type schemes. Moreover, the comparisons of computing cost between the present new schemes and other WCNS-type schemes are also considered and discussed, to get that both of the proposed H-WCNS-s(+) and WCNS-MR-s schemes have obviously lower computing cost than the existing MR WCNS-type schemes.

As a key component for offshore oil development, riser safety has long attracted extensive attention. Affected by platform surge, riser's vortex-induced vibration (VIV) shows strong nonlinearity and multimodal characteristics. Machine learning enables efficient processing of massive data, making it significant to develop an intelligent VIV prediction method. Based on the established numerical model, this study adopts superimposed flow parameters and spatial position as input features, and establishes mapping relationships with time-averaged and instantaneous dimensionless amplitude ratios via BP, RBF, GRNN and XGBoost models. The optimal prediction model is selected according to evaluation metrics, and then interpreted using SHapley Additive exPlanations (SHAP) analysis to quantify feature contributions. Key findings indicate that the RBF neural network outperforms other models for both time-averaged and instantaneous amplitude predictions; time-averaged VIV is dominated by the top flow velocity of the shear flow field Vste,top and spatial position z, while instantaneous VIV shows balanced feature contributions and stronger nonlinearity. SHAP analysis further quantifies differential feature effects. This work provides an interpretable and reliable amplitude prediction method for riser VIV under platform-surge coupling conditions, offering certain technical support for structural safety design and vibration control in marine engineering.

Based on the finite volume method, this paper systematically investigates the hydrodynamic performance and wake evolution characteristics of a biomimetic zebrafish at different near-wall distances D* and tail-beat amplitudes A*. The results indicate that while swimming near a wall can achieve higher speed, it comes at the cost of efficiency: as D* decreases, the cruising speed and the input power increase, and the efficiency is reduced. The wall effect is particularly significant when D*≤0.7 and is amplified with increasing tail-beat amplitude. When swimming close to the wall, the fish body experiences an attractive force directed toward the wall. To maintain a constant near-wall distance, a yaw angle adjustment is needed, and this angle increases with increasing tail-beat amplitude. Wake analysis reveals that near the wall, both the circulation strength and the radius of the tail vortex ring increase. Although vortex-ring expansion tends to weaken the induced backward jet, the increase in circulation strength is more pronounced, resulting in an increased Γ/R ratio, which is consistent with the observed increase in swimming speed. This study elucidates the coupling mechanism of the effects of the near-wall distance and tail-beat amplitude on the wall, providing insights for understanding the dynamic characteristics of biomimetic fish swimming in proximity to a wall.

This study investigates the genesis and temporal evolution of turbulent eddies in violent-sloshing flows using a fully meshless computational framework. A quasi-Lagrangian delta δ $\delta$ -large-eddy simulation–smoothed particle hydrodynamics formulation is employed to solve the weakly compressible Navier–Stokes equations, together with a novel methodology to quantify slosh-induced energy dissipation, where delta δ $\delta$ denotes the density-diffusion operator introduced in the delta δ $\delta$ -SPH formulation. Under violent periodic forcing, the flow exhibits a strongly nonlinear free-surface dynamics, characterised by recurrent wave breaking and energetic impacts against the tank walls. By decomposing the total viscous dissipation into enstrophy-related and deformation-related contributions, we find that the enstrophy fraction remains nearly constant, at around 30 percent sign 30 % $30\,\%$ , across the investigated regimes. Moreover, in the absence of surface tension, the enstrophy-related dissipation does not converge under grid refinement; the inclusion of surface tension regularises this behaviour and promotes a shift of the vortex population towards larger coherent structures. High-resolution two-dimensional simulations, spanning a wide range of spatial resolutions, are complemented by fully three-dimensional simulations and by reduced-width three-dimensional configurations, in which the spanwise direction is fully resolved over a limited extent. This combined analysis shows that, for this class of bounded violent free-surface flows, global loads and energy dissipation are primarily governed by free-surface fragmentation and reconnection, rather than by fully three-dimensional turbulent cascade mechanisms. As a result, two-dimensional simulations provide an accurate description of the dynamics controlling the integral quantities of interest. These findings offer new physical insight into the coupling between free-surface fragmentation, vortex dynamics and dissipation mechanisms in violent sloshing, and establish a reference framework for future studies of turbulence generation in confined free-surface flows.

Research on biomimetic propulsion near the free surface offers valuable insights into the design and control of underwater biomimetic vehicles. This study employs the smoothed-particle hydrodynamics method to examine the propulsion of an undulating hydrofoil near the free surface, focusing on the effects of the Froude number (Fr) and the dimensionless submergence depth ( H / L ) on hydrodynamic performance, and analyzing results alongside vortex structures and free surface deformation. The main results indicate that the time-averaged thrust generated by the undulating hydrofoil tends to decrease with decreasing H / L and increasing Fr. At Re = 4000 , when H / L < 1.5 , the hydrofoil achieves the locally optimal propulsion efficiency at F r = 0.2 , while for 1.5 < H/L < 2.5 , it reaches its optimal efficiency at F r = 0.4 . The hydrofoil is attracted to the free surface when Fr = 0.2 and 0.4, whereas it experiences a repulsive force away from the surface when Fr = 0.6 . Additionally, a "P + S" type vortex street forms in the wake when the hydrofoil travels near the free surface. As Re increases, the variation trend of the hydrofoil's hydrodynamic characteristics with respect to H / L remains nearly consistent, while the number of small vortices in the wake gradually increases. The present method provides an effective approach for simulating bionic hydrodynamic problems near the free surface.

IWSI (Ice-Water-Structure Interaction) has consistently held significant importance in ocean engineering. In this work, a 3D numerical ice tank is constructed based on the SPH (Smoothed Particle Hydrodynamics) and PD (Peridynamics) methods as an effective supplement to the physical modeling test to investigate IWSI. The dynamic flow of fluid and the dynamic response of the solid are modeled by SPH and PD, respectively. In terms of spatial multi-resolution coupling, this solver considers particles of different sizes, combining structure-fine particles and fluid-coarse particle interactions, which can model particular physical coupling at multiple scales. As for the temporal multi-resolution coupling, the MSS (Modified Sequential Staggered) algorithm is utilized to reduce the computational cost and improve efficiency. The fluid, structure, and coupled solvers are respectively validated. Several IWSI problems are investigated and this study successfully predicts ice loads and the initiation and propagation of cracks in ice plates. The present study not only develops an accurate numerical model featuring multi-scale physical couplings but also identifies the underlying principles governing ice fracturing mechanisms under dynamic impact in IWSI-related issues.

This study addresses the challenges of weak geometric adaptability and low computational accuracy in Physics-Informed Neural Networks (PINNs) for predicting static mechanical responses of complex shell structures. Despite growing applications of PINNs in shell static analysis, their use for complex geometries like stiffened shells remains hindered by limited network capacity, subpar training accuracy, and ineffective physical constraint enforcement. No reliable PINN solutions currently exist for such complex geometries. We propose an innovative computational framework that deeply integrates the Finite Element Method (FEM) with Physics-Informed Kolmogorov-Arnold Networks (PIKANs). The framework spatially discretizes shell structures using FEM, solves shell governing equations at each grid node, and establishes the neural network's loss function based on these equations. Building on this foundation, an improved High-Order ReLU-KAN (HRKAN) is employed to construct the FEM-PIKAN computational model, which innovatively introduces sigmoid activation functions at the hidden layer inputs to significantly enhance the network's nonlinear mapping capability. To validate the method's effectiveness, systematic studies are conducted on four typical shell structures - flat plate, cylindrical shell, stiffened plate, and stiffened cylindrical shell - under body force, surface pressure, and concentrated loads. Additionally, the static response of a simplified submarine pressure hull subjected to complex loading scenarios was predicted. The results demonstrate that the proposed FEM-PIKAN method accurately predicts the static responses of various complex shell structures, providing a new paradigm for efficient and high-precision analysis of such structures. The source code is available at https://github.com/ whatuphmz/FEM-PIKAN.

Violent sloshing flows under various conditions including wave traveling, entrapped air bubbles/pockets and high-frequency tank motions are investigated through comparative simulations using single-phase and multi-phase consistent δ+-SPH models. To enhance numerical robustness in violent sloshing simulations, a boundary shield technique (BST) is proposed to prevent unphysical penetration at solid walls. The consistent δ+-SPH results are validated against analytical solutions and experimental data. Numerical results show that the multi-phase consistent δ+-SPH simulations accurately capture pressure evolution and complex liquid–gas interface dynamics, particularly in cases involving entrapped air bubbles. For sloshing cases without significant air entrainment, the single-phase model achieves comparable accuracy with much lower computational cost. Moreover, for cases where air bubbles are entrapped but rapidly breaking up, such as the sloshing under high-frequency tank motions, both single-phase and multi-phase simulations provide similar predictions of global sloshing behavior and impact forces on the tank wall. This study clarifies the applicability of both single-phase and multi-phase SPH models, providing practical guidelines for efficient and accurate simulation of violent sloshing in marine and aeronautical engineering applications.

This paper proposes a novel consistent δ+- Updated Lagrangian Particle Hydrodynamics (ULPH) model. Although the Smoothed Particle Hydrodynamics (SPH) model has gained recognized achievements, it is afflicted by excessive numerical dissipation when the neighboring particles are insufficient. The present proposed consistent δ+-ULPH model has advantages in overcoming this problem. To improve the accuracy, efficiency, stability, and energy conservation, several new techniques are introduced to the consistent δ+-ULPH model. A novel extended support domain technique is proposed to achieve higher accuracy with fewer neighboring particles. An optimal matrix for the velocity divergence is proposed to improve the free-surface stability. A consistent particle shifting technique for the ULPH scheme is proposed to maintain a uniform and regular particle distribution and obtain superior conservation. In addition, an acoustic damper term for the ULPH scheme is introduced to improve the pressure field stability. Five benchmark tests were carried out to validate the consistent δ+-ULPH model. The conventional ULPH and the consistent δ+-SPH results are presented for comparison. Results indicate that the proposed consistent δ+-ULPH model can accurately simulate both gentle waves and violent sloshing flows and shows higher accuracy and lower numerical dissipation when using fewer neighboring particles, even in long-term and long-distance wave propagation simulations. Additionally, the computational efficiency of the consistent δ+-ULPH model is enhanced visibly because of fewer neighboring particles.