A note on the application of a time exponential integrator to fully nonlinear numerical wave tanks for engineering applications

Abstract To improve the cost-effectiveness of modelling of wave interactions, a “numerical wavetank” is presented whose distinctive novel feature is its ability to couple both deep-water potential-flow and shallow-water models to controllable, prespecified wavemaker motion and beach topography. The coupling is in part obtained via a variational principle approach that guarantees important conservation properties and numerical stability. The model presented is the first fully nonlinear model to couple deep-water (discretised as finite elements) and shallow-water equations (discretised as finite volumes). Resulting simulations of wave generation, propagation and absorption by shallow-water-wave breaking are presented and analysed. A discussion is given on the efficacy of the novel approach.

The foldable quadcopter unmanned aerial vehicle (UAV), transported by an autonomous underwater vehicle (AUV) and launched subaquatically, represents cutting-edge technology for expanding ocean-sensing capabilities. However, its launch stability is severely challenged by complex cross-media flow fields. To address this, this paper employs a high-fidelity CFD method validated by experimental data, combined with dynamic overlapping mesh technology. Within a high-precision numerical wave tank, it systematically investigates the evolution of unsteady hydrodynamic characteristics throughout the entire launch process—from the drone’s emergence from the launch tube to its crossing of the water-air interface. Findings reveal that elevated initial launch velocities substantially alter surface flow patterns, inducing shear stress imbalances and complex flow separation on the trailing surface. This significantly amplifies lateral disturbance forces and yawing moments, constituting primary sources of motion instability. More critically, this study first uncovers and quantifies the hydrodynamic interference mechanism during the synchronous launch of dual vehicles: the wake field generated by the lead vehicle imposes a significant flow-shielding effect on the trailing vehicle. This effect alters its longitudinal forces while introducing an asymmetric pressure distribution, thereby generating substantial lateral interference. This study’s profound elucidation of these core hydrodynamic mechanisms provides crucial theoretical foundations for developing safe launch strategies, trajectory prediction, and anti-interference controller design for future AUV-UAV cooperative systems.

ABSTRACT In recent years, there has been an increasing interest in understanding the properties of wave energy, including its propagation and dissipation. This study established a numerical wave tank using VOF method to simulate real‐time wave‐making motion under rocking plate mode and investigated wave energy characteristics and dissipation in the wave propagation. The waveform data and wave spectrum model were obtained and verified with experimental data. Results indicated that the numerical results were good in agreement with the experimental data. The speed, amplitude, circular frequency, and water depth of the shake plate motion significantly affect wave propagation and wave energy characteristics; different wavelengths have different effects on wave energy attenuation, and wave nonlinear characteristics affect the characteristics and dissipation of wave energy. The results of this study can provide reference for marine engineering design and marine environmental protection.

This study analyzes the hydrodynamic performance of a V-type wave dissipation system and amphibious landing equipment under different combined fields using the Reynolds-averaged Navier–Stokes (RANS) method. A three-dimensional numerical wave tank is established to simulate regular waves and validate the performance of an airbag-type floating breakwater. This study evaluates the optimal hydrodynamic performance of a V-type wave dissipation system under various configurations in a wave-only field and subsequently compares the efficacy of the better-performing system across multiple environmental conditions. The results show that the V-type wave dissipation system in the configurations of 30° and 45° angles is more favorable for the flow field and the amphibious landing equipment behind it. Compared to the wave-only condition, the time histories of wave heights under both wave-current and wind-wave conditions present an obvious phase advancement. In the wave-current field, a following current reduces the wave height and shortens the wave period. Conversely, in the wind-wave field, a following wind velocity leads to a certain increase in wave height while exerting minimal impact on the wave period. Compared to the wave-only condition, the peak and trough values of the wave height monitoring points in the combined wind-wave-current field show an increasing trend, with a significant increase in resistance and a shorter resistance period for the amphibious landing equipment behind the V-type wave dissipation system. This study shows that the selected V-type wave dissipation system proves to be more effective in wave-only and wave-current conditions, providing valuable references for the engineering application of this system.

To address the lack of efficient flexible protection measures for ocean engineering equipment operating in complex coupled wind–wave–current environments, this study develops a coupled “flexible wave-dissipating system” numerical model based on a validated three-dimensional numerical wave tank. The model is used to investigate, under both regular and irregular wave conditions, the influence of different wind and current incidence angles and the presence or absence of the breakwater on wave propagation and hydrodynamic responses. By comparing the significant wave height, transmission coefficient and wave dissipation efficiency in the sheltered region along with the drag force and free-surface pressure, the wave-attenuation and load-reduction performance of the flexible breakwater is quantitatively evaluated. The results demonstrate that deploying a flexible breakwater can significantly attenuate wave energy in the sheltered region, enhance wave dissipation efficiency, and reduce the transmission coefficient, thereby concurrently decreasing both the drag force and free-surface pressure. Under both wind and current conditions, the maximum loads occur at 0° head-on incidence. However, under 30° oblique wind–wave action, the flexible breakwater yields the most pronounced increase in dissipation efficiency compared to the case without a breakwater. A stable correlation is observed between dissipation efficiency and hydrodynamic loads, which can serve as a unified evaluation metric for assessing the protective performance of flexible breakwaters in ocean engineering applications.

This paper analyzes the influence of moonpools on the hydrodynamic performance of drillships using the Reynolds-averaged Navier–Stokes (RANS) method. A three-dimensional numerical wave tank is established to realize regular waves and to perform prediction and validation of the KCS ship’s performance in calm water and head seas. After selecting optimal moonpool configurations under calm conditions, seakeeping analyses for a rectangular-moonpool drillship in waves and drag-reduction optimization in calm water and head seas are conducted. The comparative analysis shows that in calm-water navigation, different moonpool shapes lead to different added-resistance effects, and the drillship with a rectangular moonpool shows overall better performance in resistance and running attitude; the added resistance due to the moonpool mainly originates from the additional residual resistance. The sustained energy supply to the clockwise vortex within the moonpool is maintained by the continuous mass exchange between the water flow beneath the ship’s bottom and the water inside the moonpool. Under regular waves, the presence of a moonpool leads to an increase in the total resistance experienced by the drillship. A flange device can effectively reduce the mean amplitude of waves inside the moonpool, and when the flange is installed 10 mm above the still water level with a length of 120 mm, its drag-reduction effect is better. The flange structure can effectively improve the hydrodynamic characteristics of the drillship in waves. The numerical conclusions provide a reference value for the engineering application of drillships with moonpool structures.

A new integrated numerical wave tank in OpenFOAM for hydrodynamic modelling of offshore renewables

In naval and ocean engineering, accurate simulation of incident waves is essential for predicting the motion response of offshore structures. Traditional wave generation methods, such as piston- and flap-type wave makers, often face challenges in accurately replicating the orbital motion of water particles beneath the free surface, which can limit their applicability in high-fidelity simulations. In this study, a numerical investigation is conducted to compare the performance of piston-type, flap-type, and double-flap-type wave makers using STAR-CCM+2310(18.06.006-R8). The influence of water depth on wave height accuracy is evaluated across different measurement locations within a numerical wave tank. Theoretical analysis of wave generation mechanisms is incorporated to clarify the applicability limits of linear theory and to better interpret the numerical results. Results indicate that, under the tested two-dimensional CFD conditions, the double-flap-type wave maker tended to provide closer agreement with theoretical predictions, particularly at greater depths, compared with conventional methods. These findings suggest potential advantages of the double-flap configuration and provide insights for refining wave generation techniques in numerical and experimental wave tanks, thereby supporting more reliable hydrodynamic analyses of floating structures.

In the complex marine environment, the water entry process of air-droppable underwater gliders (ADUGs) faces numerous challenges. In particular, wave loads significantly affect the water entry characteristics and reduce the deployment success rate. This research builds a scaled-down ADUG model and a numerical wave tank through smoothed particle hydrodynamics - finite element method (SPH-FEM) to explore the water entry characteristics of ADUGs in waves. An improved recursive digital filtering algorithm is employed to calculate the shock response spectrum of the ADUG under wave conditions. The results show that the water entry impact acceleration varies with multiple parameters, including water entry point, wave height, water entry speed, and water entry angle. When the wave phase angle is π, the ADUG is more prone to exhibit the ‘ricochet’ behavior, which is most likely to happen when the wave height is 0.3 m. The inflection point in the impact response spectrum for water entry of the ADUG is mainly in the frequency band of 200 - 400 Hz. Under the same conditions, the angle of attack has little influence on the impact response spectrum. Tank experiments are performed based on a scaled-down model to investigate the water entry impact of ADUGs in waves. The experimental results show good consistency with the simulation results, with a maximum error of 13.58%. The research findings can guide the structural design and deployment planning of ADUGs and also offer theoretical references for the water entry research of other air-droppable equipment with complex geometries.

ABSTRACT This study presents an experimental and numerical investigation of uni-directional non-breaking focused waves generated using the NewWave model and transient wave packets. Model tests in the Deep Ocean Engineering Basin examine the spatial evolution and nonlinear characteristics of focused waves, applying amplitude and phase corrections from linear theory to improve target focusing. The experiments reveal nonlinear energy transfer near the focal point due to wave–wave interactions, leading to crest elevation increases, and quantify viscous energy dissipation during downstream propagation. Numerical simulations are performed in a Higher-Order Spectral (HOS) method-based numerical wave tank(NWT) with cosine bases and influx source generation to treat non-periodic boundaries. The simulations capture third- and higher-order nonlinear interactions, reproducing measured wave elevations and frequency spectra. The results clarify the dependence of wave propagation on the energy band and demonstrate the capability of HOS-based NWT as reliable tools for focused-wave design and analysis in offshore engineering.

Parametric roll is a critical nonlinear phenomenon that may induce large amplitude roll motions and pose significant risks to the safety of ships, especially when triggered by longitudinal waves. However, parametric roll in cross wave conditions remains insufficiently investigated. This study investigates the parametric roll behavior of a C11 class container ship encountering cross waves in head seas, using computational fluid dynamics simulations. A numerical wave tank is established based on the computational fluid dynamics software STAR-CCM+, and the ship's dynamic motion responses are simulated. A systematic sensitivity analysis of ship parametric roll with respect to cross wave amplitude, wavelength, ship forward speed, and wave encounter frequency is conducted, using a controlled variable approach to ensure the independent assessment of each factor. Furthermore, the influence of water depth on the parametric roll behavior is explored. The results indicate that, under identical wave conditions, cross waves induce significantly more intense parametric roll motion than regular unidirectional waves. Under varying water depths and speeds, when the cross wave amplitude reaches a certain threshold and the wave encounter frequency approaches approximately twice the natural roll frequency of the ship, the parametric roll becomes most pronounced, with roll amplitudes increasing progressively with wave height. When the incident wavelength is comparable to the ship length, the periodic variation of the restoring moment becomes most prominent, which tends to trigger a sharp increase in roll amplitude. Since the wave encounter frequency is determined by both wave frequency and ship speed, adjusting the ship speed and direction provides an effective strategy to suppress the occurrence of parametric roll.

Internal solitary waves (ISWs) are ubiquitous in the ocean and can impose substantial operational risks on submersibles. Rapid prediction of the hydrodynamic response of submersibles is essential for safe navigation. A numerical wave tank incorporating the density transport equation was established and validated against observational data. A submersible is modeled using overlapping grids. Simulations covered five wave amplitudes and five submersion depths, resulting in 25 cases. Increases in submersion depth and wave amplitude produce significant changes in the longitudinal force, vertical force, and pitching moment acting on the submersible. Gaussian basis function (longitudinal force) and Gaussian wavelet basis function (vertical force and pitching moment) underpinned regression models for rapid prediction. Subsequently, polynomial fits established quantitative relationships between the model parameters, ISW amplitude, and submergence depth. Finally, the rapid prediction model was validated against independent data.

An enhanced numerical wave tank for wave-structure interaction based on DualSPHysics+

This study examines the evolution characteristics of ship waves generated by large vessels in shallow waters. A CFD-based numerical wave tank, incorporating Torsvik’s ship wave theory, was developed using the VOF multiphase approach and the RNG k-ε turbulence model to capture free-surface evolution and turbulence effects. Results indicate that wave heights vary significantly near the critical depth-based Froude number (Fh). Comparative analyses between CFD results for a Wigley hull and proposed empirical correction formulas show strong agreement in predicting maximum wave heights in transcritical and supercritical regimes, accurately capturing the nonlinear surge of wave amplitude in the transcritical range. Simulations of 2000-ton and 6000-ton class vessels further reveal that wave heights increase with Fh, peak in the transcritical regime, and subsequently decay. Lateral wave attenuation was also observed with increasing transverse distance, highlighting the role of vessel dimensions and bulbous bow structures in modulating wave propagation. These findings provide theoretical and practical references for risk assessment and navigational safety in shallow waterways.

ABSTRACT Wave-in-deck events in extreme South China Sea conditions threaten offshore platform superstructures.To address this issue, a numerical wave tank was developed to simulate wave–structure interactions and validated against theoretical predictions and OTRC experiments.The model was applied to a deep-water jacket platform in the South China Sea to reproduce flow processes and characterize deck wave-load distributions.Time histories of horizontal deck loads were checked against API provisions, and vertical loads were compared with Kaplan's formula.Both analytical methods underestimated peak horizontal and vertical loads and lacked sensitivity to load variations during wave-in-deck events.Consequently, where feasible, numerical simulation or model testing is recommended for accurate assessment of deck wave loads.

Simulation and analysis of wave load on offshore wind turbines based on numerical wave tanks

Jack-up offshore platforms, supported by truss legs, are integral to the development of marine energy resources, including oil, gas, and offshore wind. Due to the structural complexity of truss legs, accurately quantifying wave loads is crucial for ensuring the safety and efficiency of energy extraction operations. In this work, a numerical wave tank approach combined with theoretical analysis is employed comprehensively to investigate wave loads on truss legs, with a particular emphasis on the effects of component forces and inflow angle. The results demonstrate that wave loads are not solely dependent on member dimensions. The influencing factors affecting component forces include water depth and phase differences between structural units, which amplify the contribution of the component forces of members near the free surface and without phase difference to the total force. Furthermore, the total force varies periodically with the inflow angle in cycles of 60°. Notably, the influence of inflow angle on the total force becomes negligible when the wavelength substantially exceeds the pile spacing. This framework fundamentally provides a theoretical basis for the structural optimization of Jack-up offshore platform support systems, thereby enhancing the safety and reliability of energy infrastructure.

The utilization of ocean wave energy through environmentally sustainable technologies plays a pivotal role in the transition toward renewable energy sources. Among such technologies, the Submerged Horizontal Plate (SHP) stands out as a viable option for clean power production. This study focuses on the system’s application in a region on the southern coast of Brazil, identified as a potential site for future installation. To investigate this system, a three-dimensional numerical wave tank was developed to simulate wave behavior and hydrodynamic loads using the Navier–Stokes framework in the computational fluid dynamics software ANSYS FLUENT 2022 R2. The volume of fluid approach was adopted to track the free surface. The setup for wave generation in the numerical wave tank was verified against analytical solutions to ensure precision and validated under the SHP’s non-oscillating condition. To represent the oscillating condition, boundary conditions constrained motion along the x- and y-axes, allowing movement exclusively along the z-axis. A parametric analysis of 54 cases, with varying geometric configurations, wave characteristics, and submersion depths, indicated that the oscillating SHP configuration elongated perpendicular to wave propagation, combined with specific wave conditions, achieved a theoretical mean efficiency of 76.61%.

The energy capture efficiency of oscillating water column (OWC) wave energy converters can be enhanced through the focusing effects of waves by a parabolic breakwater. Additionally, a shared mooring system for positioning the floating device arrays is considered an effective approach to reduce mooring costs. In this paper, a numerical wave tank was established to simulate the hydrodynamic performance of the OWC arrays based on the computational fluid dynamics methods. A mooring numerical model was developed to simulate mooring lines' behavior subject to axial elasticity, hydrodynamic forces, and vertical contact forces with the seabed based on the discrete element method. The numerical model and setup have been validated against experimental results. The motion responses, energy capture performances, and mooring lines' tensions of the floating OWC array under a shared mooring system with and without the parabolic breakwater were compared and analyzed. Results show that the parabolic breakwater significantly enhances the heave and surge motions of the OWC arrays. The central OWC deployed at the theoretical focal point of the parabolic breakwater demonstrates a substantial enhancement in energy capture capacity. Parabolic breakwater leads to an increase in the average mooring force on the leeward side of the OWC arrays system, while reducing the fluctuation in mooring force of the shared polyester ropes. This article can provide favorable reference data for the placement of floating OWC arrays under parabolic breakwater and the design and simulation of the shared mooring system in the future.