Wave-structure Interaction Problems Research Articles

Pathologies in the Asymptotics of low-Froude Free-surface Waves Over Smooth Bodies

In the study of low-speed or low-Froude flows of a potential gravity-driven fluid past a wave-generating object, the traditional asymptotic expansion in powers of the Froude number predicts a waveless free-surface at every order. This is due to the fact that the waves are, in fact, exponentially small and beyond-all-orders of the naive expansion. The theory of exponential asymptotics indicates that such exponentially-small water waves are switched-on across so-called Stokes lines—these curves partition the fluid-domain into wave-free regions and regions with waves. In prior studies, Stokes lines are associated with singularities in the flow field, such as stagnation points, or corners of submerged objects or rough beds. In this work, we present a smoothed geometry that was recently highlighted by Pethiyagoda et al. [Int. J. Numer. Meth. Fluids. 2018; 86:607–624] as capable of producing waves, yet paradoxically exhibiting no obvious Stokes line according to conventional exponential asymptotics theory. In this work, we demonstrate that the Stokes line for this smooth geometry originates from an essential singularity at infinity in the analytic continuation of free-surface quantities. We discuss some of the difficulties in extending the typical methodology of exponential asymptotics to general wave-structure interaction problems with smooth geometries.

A Comparative Study of LSTM and Temporal Convolutional Network Models for Semisubmersible Platform Wave Runup Prediction

Abstract Wave runup prediction is necessary for offshore structure designs and early warnings. Data-driven methods based on machine learning have inspired reduced-order solutions for wave–structure interaction problems. This study provides the quantification of deep learning algorithms’ potential for wave runup prediction. Two prominent deep learning models were utilized to predict the wave runups along the fore column of semisubmersible under head seas. The long short-term memory (LSTM) and the temporal convolutional networks (TCNs) were comprehensively compared based on the datasets from a model test carried out in the deep ocean basin. The LSTM and TCN model structures were optimized to compare prediction accuracy and computational complexity reasonably. The results reveal that (1) both developed TCN and LSTM models had a satisfied prediction accuracy of over 90%. Their predictions were extended to 10 s into the future with accuracies over 80% and 45%, respectively. (2) With the noise-extended datasets, the LSTM model was robust to noises, while the TCN model showed better prediction performance on the extreme wave runup events. (3) The incident wave and dominant rotation provided the major information for wave runup prediction. TCN and LSTM models’ prediction accuracies were 91.5% and 89.3% based on the simplified input tensors composed of incident wave and pitch. The comparison showed the great potential of the TCN model to predict the nonlinear wave runup with less time and memory costs. The input tensors’ design and optimization based on physical understanding also play a significant role in the prediction performance.

An adaptive harmonic polynomial cell method for three-dimensional fully nonlinear wave-structure interaction with immersed boundaries

To accurately simulate wave-structure interaction based on fully nonlinear potential flow theory, a three-dimensional (3 D) high-order immersed-boundary adaptive harmonic polynomial cell (IB-AHPC) method is proposed. Both the free surface and body surface are immersed in background octree cells that are adaptively refined near the boundaries of interest, thereby dramatically reducing computational costs without loss of accuracy. We also propose an easy-to-implement IB strategy to deal with possible instabilities in the time-domain solution arising from the intersection of Dirichlet–Neumann boundaries. For a linearized problem of wave-wall interaction, a matrix-based stability analysis is performed, providing mathematical support for the robustness of the proposed IB strategy. In contrast to the two-dimensional HPC method, compressed cells are found to offer superior stability compared to stretched cells in the vertical direction, while equal mesh aspect ratio in the horizontal plane is superior. Cubic octree cells are, however, still preferred in practice. The free surface is primarily described by a set of massless background wave markers; however, to address the challenges of IB methods in tracking the free surface evolution near the structure, additional body-fitted wave markers are introduced close to the waterline. The information exchange between these two sets of wave markers is realized by radial basis function (RBF) interpolation. While standard RBF schemes have grid-size-dependent filtering performance, we propose a normalized RBF scheme, which is then optimized in terms of the number of neighboring nodes, a smoothing coefficient and the basis functions. Excellent accuracy properties of the proposed 3 D IB-AHPC method are demonstrated by studying fully nonlinear wave propagation. The method is further applied to study relevant fully nonlinear wave-structure interaction problems, including sloshing in 3 D rectangular tanks and wave diffraction of a bottom-mounted cylinder in regular waves. Satisfactory agreement is demonstrated with existing experimental and numerical results, suggesting that the proposed 3 D IB-AHPC method is a promising potential-flow method in marine hydrodynamics.

On the Cauchy problem for a wave-structure interaction problem

On the Cauchy problem for a wave-structure interaction problem

Scattering of Long Waves by Freely Oscillating Submerged Plates

Abstract We consider a horizontal, submerged plate in shallow water that is allowed to oscillate in the vertical direction due to the wave loads. The plate is attached to a linear spring and damper to control the oscillations. The focus of the study is on the transformation of the wave field by the submerged oscillating plate. To estimate energy scattering, wave reflection and transmission coefficients are determined from four wave gauges: two placed upwave and two placed downwave of the oscillating plate. The flow is governed by the nonlinear level I Green–Naghdi (GN) equations, coupled with the equations of the vertical oscillations of the plate. Time series of water surface elevation recorded at gauges upwave and downwave of the plate obtained by the GN model are compared with the available laboratory experiments and other data, and very good agreement is observed. Wave reflection and transmission coefficients are then determined for a range of involved parameters, including wave conditions (wavelength and wave height), initial submergence depth of the plate, plate length, and the spring-damper system attached to the plate. It is found that a submerged oscillating plate can have a remarkable effect on the wave field and that nonlinearity plays an important role in this wave–structure interaction problem. Discussion is provided on how the wave reflection and transmission coefficients vary with the wave conditions, plate characteristics, initial submergence depth, and spring-damper system properties.

Development of a two-dimensional coupled smoothed particle hydrodynamics model and its application to nonlinear wave simulations

This paper presents a two dimensional two-way coupled model combining Smoothed Particle Hydrodynamics (SPH) based on the Navier–Stokes equations (NSE) and OceanWave3D based on the fully nonlinear potential flow theory (FNPT) in order to efficiently simulate non-linear waves and wave–structure interaction problems. The two models are strongly coupled in space and time domains using a fixed overlapping zone, wherein the information from both solvers is exchanged by relaxation functions. In the SPH model, an open relaxation boundary, which is implemented as open and relaxation zones, is used in the coupling region. Horizontal velocity and free surface elevation in the open and relaxation zones are obtained from OceanWave3D, while vertical velocity and density in the open zones are interpolated from the relaxation region. OceanWave3D requires the free surface elevation and vertical velocity at the free surface from SPH in the coupled region. The coupled model is tested by modelling a regular wave, irregular wave and wave over a submerged bar and an oscillating water column (OWC) device. The results demonstrate that the coupled model can produce satisfactory results with less computational time than the SPH-only model.

Hydrodynamic characteristics of a 15 MW semi-submersible floating offshore wind turbine in freak waves

Dynamics of the floating offshore wind turbines (FOWTs) in harsh ocean environments gains increasing attention due to the high maintenance costs in case of structural damage. The freak wave occurring more frequently than believed poses a threat to FOWTs, but mechanism and influencing factors of the wave-structure interaction problem have not been fully explained. In this paper, dynamics of the VolturnUS-S semi-submersible platform designed for the IEA 15 MW wind turbine under freak waves is studied using a coupled computational fluid dynamics and finite element mooring line model. First, the hydrodynamic model is validated using the DeepCwind semi-submersible platform. Then, the validated model is employed for the analysis of the VolturnUS-S semi-submersible platform under freak waves described as a focused group of waves. Hydrodynamic behaviors of the semi-submersible FOWT are described in detail, and parametric analysis of the problem including the effects of focusing crest amplitude, focusing location, incident angle, gravity center location is conducted. Important results include the dramatic surge motion of the platform and fairlead tension of the upstream mooring line, and alleviation of these responses by varying the wave angle to 30° and moving the gravity center to the centroid of the platform geometry.

Efficiency and accuracy of the domain and functional decomposition strategies for the wave-structure interaction problem

Extreme waves can be modelled in a numerical wave tank (NWT) as a focusing wave in order to generate events that are crucial for designing any offshore structures. The focused wave generation implemented in the completely nonlinear potential solver Higher Order Spectral method (HOS-NWT) with the time-reversal technique was used in the present work. The OpenFOAM based solvers foamStar and foamStarSWENSE which use the domain decomposition and the functional decomposition approach, respectively, were used to couple with a HOS-NWT to perform the focusing wave interaction with the structure (in this case, a cylinder). The incident waves from HOS-NWT are blended into a foamStar and foamStarSWENSE subdomain, where the waves will propagate and interact with the structure within their domain. In the SWENSE methodology, the total field in the computational domain is divided into the incident field and a complementary field. foamStar solves for the total flow fields, and foamStarSWENSE solves for the complementary (total minus incident) flow fields. The Volume of Fluid (VoF) method was selected to capture the interface. 2D parametric studies for focused wave generation were carried out with both solvers, and 3D wave interactions for different mesh types (coarse, medium, and fine) were investigated to understand the convergence for such transient type problems. For verification, the case’s uncertainty was quantified using the Richardson extrapolation approach, and validation was then done by comparing the results to the experiment. The computational efficiency of the two coupling techniques was also compared, and recommendations for solver improvements are made. In general, when solving the problem of wave generation and propagation in 2D and 3D conditions, foamStarSWENSE surpassed foamStar in accuracy. On the other hand, when the simulation included a structure in the domain, the accuracy of the solution in foamStar and foamStarSWENSE was nearly the same, but the foamStar performed better in terms of computational cost. Overall, both coupling approaches generate a realistic depiction of focused wave interaction and force over the cylinder at a minimum computational cost.

Linear analysis on the non-hydrostatic pressure field of depth-integrated models

In the development of depth-integrated models, certain assumptions are made on the vertical profile of the horizontal velocity, and the pressure field is eliminated through vertical integration of the vertical momentum equation. In this study, analytical forms of the approximated non-hydrostatic pressure field are derived from five most representative depth-integrated models, which include three Boussinesq-type models, a weighted residual type model and a non-hydrostatic model. A Stokes wave-type Fourier analysis is then conducted to examine their capability in reproducing the vertical profile of the non-hydrostatic pressure field, which is compared with linear wave theory. We found the Boussinesq-type models are able to reproduce the non-hydrostatic pressure field from shallower water up to the kd values similar to that of concerning linear wave phase velocity. Specifically, the two-layer Boussinesq model generally outperforms the higher-order (μ4) Boussinesq model, especially for higher kd values. The weighted residual type model can reasonably capture the non-hydrostatic pressure near to the free surface even at high kd values, but undulations appear in the lower part of the water column where non-hydrostatic pressure is close to zero. The non-hydrostatic model shows rapid convergence of linear wave phase velocity by using few vertical layers, however, its capability in reproducing the non-hydrostatic pressure field is limited, especially at the highest layer interface, where nonphysical phenomena of reversed pressure could appear. This suggests that it is necessary to employ more layers when detailed information on the pressure field is needed, e.g. wave–structure interaction problems.

A generalized weak-scatterer approximation for nonlinear wave–structure interaction in marine hydrodynamics

In this paper, a generalized weak-scatterer (GWS) approximation is proposed for solving nonlinear wave–structure interaction problems. In contrast to the original weak-scatterer (OWS) theory, where the approximated free surface boundary conditions (FSBCs) are Taylor-expanded in the vertical direction from the incident wave surface, we apply Taylor series expansion in an arbitrary direction which, in particular, is tangential to the boundary of the floating structure close to the waterline. This leads to generalized kinematic and dynamic FSBCs for the radiated and scattered waves, along with corresponding expressions of the wave loads. Accordingly, an Arbitrary Lagrangian–Eulerian (ALE) approach is adopted to track the free-surface properties. The new GWS method is more consistent than the OWS model in that the wave markers do not separate from the body surface at the waterline for structures with flare. An Immersed-Boundary Adaptive Harmonic Polynomial Cell (IB-AHPC) method is implemented to solve the corresponding boundary value problems (BVPs) for both the velocity potential and the Lagrangian acceleration potential at each time step. The new formulation introduces additional convective terms in the FSBCs, making them similar to the seakeeping problems for ships with forward speed, and this requires special treatment to avoid instability in the time-domain simulations. Based on a matrix-based eigenvalue stability analysis, we illustrate that stable solutions can be achieved by introducing an upwind-biased scheme to discretize the convective terms in the kinematic FSBC. The proposed model is verified by three wave diffraction problems in regular waves, including a submerged circular cylinder, a rounded-corner rectangular ship section, and a trapezoidal section with a large flare angle.

A Review on the Modelling of Wave-Structure Interactions Based on OpenFOAM

The modelling of wave-structure interaction (WSI) has significant applications in understanding natural processes as well as securing the safety and efficiency of marine engineering. Based on the technique of Computational Fluid Dynamics (CFD) and the open-source simulation framework - OpenFOAM, this paper provides a state-of-the-art review of WSI modelling methods. The review categorises WSI scenarios and suggests their suitable computational approaches, concerning a rigid, deformable or porous structure in regular, irregular, non-breaking or breaking waves. Extensions of WSI modelling for wave-structure-seabed interactions and various wave energy converters are also introduced. As a result, the present review aims to help understand the CFD modelling of WSI and guide the use of OpenFOAM for target WSI problems.

On the energy conversion characteristics of a top-mounted pitching absorber by using smoothed particle hydrodynamics

The top-mounted pitching point absorber is one of the most promising wave energy converters in that it can be easily attached to an existing offshore structure. However, it is difficult to predict accurately its energy conversion performance because of the strongly nonlinear hydrodynamic behaviour. Herein, smoothed particle hydrodynamics (SPH) is used to solve this wave-structure interaction problem. The SPH method is first validated against free surface deformation measurements obtained from a wedge water entry experiment. SPH simulations of regular wave interaction with fixed and freely pitching devices agree well with measured data, providing confidence in the prediction of power conversion performance. Absorbed power and capture width ratio exhibit uni-modal behaviour with wave period. The wave period of peak power within this distribution increases with PTO damping. According to the observed scaling behaviour with device scale, an optimally damped larger scale device is effective at absorbing energy from incident waves of longer wavelength. In finite deep water, the larger device achieves higher efficiency compared with the smaller ones, and its peak efficiency at 2πh/λ=1.1 provides reference for siting.

Simulation of random wave overtopping by a WCSPH model

In this work the Weakly Compressible SPH-based (WCSPH) model DualSPHysics has been validated and applied to study the random wave overtopping of dike-promenade layout in shallow water conditions. Data from physical model tests carried out in a small-scale wave flume have been used for model validation. The results have been compared in terms of water surface elevation, mean discharges and individual overtopping volumes distribution. The selected geometrical layout is representative of the coastal area of Premià de Mar, in Catalonia (Spain). This stretch of the coast presents both railways and a bike path very close to the shore and therefore exposed to possible sea storms. For the first time an SPH-based model has been employed to reproduce long-lasting wave overtopping tests, made of time series of 1000 irregular waves, which are representative of real sea states. The density diffusion scheme and the modified Dynamic Boundary Conditions have been applied in the present simulations. By employing standard setup for SPH modelling of wave-structure interaction problems of a very long duration, stable simulations and accurate results have been attained.

Waves interacting with a partially immersed obstacle in the Boussinesq regime

This paper is devoted to the derivation and mathematical analysis of a wave-structure interaction problem which can be reduced to a transmission problem for a Boussinesq system. Initial boundary value problems and transmission problems in dimension d= 1 for $2\times2$ hyperbolic systems are well understood. However, for many applications, and especially for the description of surface water waves, dispersive perturbations of hyperbolic systems must be considered. We consider here a configuration where the motion of the waves is governed by a Boussinesq system (a dispersive perturbation of the hyperbolic nonlinear shallow water equations), and in the presence of a fixed partially immersed obstacle. We shall insist on the differences and similarities with respect to the standard hyperbolic case, and focus our attention on a new phenomenon, namely, the apparition of a dispersive boundary layer. In order to obtain existence and uniform bounds on the solutions over the relevant time scale, a control of this dispersive boundary layer and of the oscillations in time it generates is necessary. This analysis leads to a new notion of compatibility condition that is shown to coincide with the standard hyperbolic compatibility conditions when the dispersive parameter is set to zero. To the authors' knowledge, this is the first time that these phenomena (likely to play a central role in the analysis of initial boundary value problems for dispersive perturbations of hyperbolic systems) are exhibited.

Nondimensionalized semi-empirical equation to predict secondary load cycles on vertical cylinders of different diameters

Theoretical solutions including the Morison equation have been widely used to estimate the wave forces exerted on offshore structures of vertical cylindrical configuration. However, none of those methods can accurately predict the wave force of the secondary load cycle induced by a steep wave acting on the cylinder. In this study, regular waves of different wave steepness are generated using an experimental wave flume with a piston-type wavemaker, and the forces exerted on the cylinders of three different diameters are investigated. Using the data-fitting method, the difference between the experimentally measured wave force and that calculated by the Morison equation is empirically formulated, and the effects of key non-dimensional parameters on the force difference function are analyzed. The results show that the amplitude and phase of the force difference function are mainly governed by the incident wave condition including the relative depth, relative amplitude, and relative elevation. On the other hand, the effect of the relative radius is negligible when the diameter-to-wavelength ratio satisfies the small-scale structure condition. The proposed equation is valid for predicting the non-breaking regular wave forces exerted on a vertical cylinder when the secondary load cycle occurs and can be utilized in wave-structure interaction problems.

NEW DEVELOPMENTS FOR CFD HYBRID MODELING FOR NUMERICAL WAVE TANKS

The use of CFD for numerical representation of laboratory wave flume and basins, commonly known as numerical wave tanks (NWT), has become more popular in recent years with the aim of improving knowledge in the field of wave-structure interaction (WSI), both fixed and floating, due to advances that have been made in numerical modelling, mainly with the reproduction of three dimensional problems. The use of this technique is displacing even traditional approaches based on the use of potential flow equations, due to the versatility provided by the CFD approach, which allows considering nonlinear interactions between structures and waves, and above all, extreme events such as wave breaking. However, implementation of these models as a complementary tool to physical modeling facilities is not yet standardized and requires further development to hybridize these two techniques, numerical and experimental, in order to obtain a better knowledge of physical processes. Implementation still requires overcoming existing modeling limitations and the additional steps to be taken focus on the following areas are: a) numerically mirror wave generation and active/passive absorption in physical installations; b) numerical resolution of WSI problems, which to date depends on each WSI case; c) computational cost, which may be the bottleneck for NWT implementation; and, finally, the most important feature that is where the added value of the hybrid approach lies, d) the exchange of information between the laboratory measurements and the results of the numerical simulations in order to obtain a better understanding of WSI problems. This paper will present an analysis of the main aspects described above for the implementation of hybrid techniques for the study of WSI problems (floating and fixed). The latest advances in modeling developed with IHFOAM solver (ihfoam.ihcantabria.com), and physical modeling procedures to link laboratory and numerical tools will be presented. The main objective is establishing a standard procedure to implement this technique in any physical installation.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/6mAQccSrREM

A Cartesian cut-cell based multiphase flow model for large-eddy simulation of three-dimensional wave-structure interaction

A multiphase flow numerical approach for performing large-eddy simulations of three-dimensional (3D) wave-structure interaction is presented in this study. The approach combines a volume-of-fluid method to capture the air-water interface and a Cartesian cut-cell method to deal with complex geometries. The filtered Navier–Stokes equations are discretised by the finite volume method with the PISO algorithm for velocity-pressure coupling and the dynamic Smagorinsky subgrid-scale model is used to compute the unresolved (subgrid) scales of turbulence. The versatility and robustness of the presented numerical approach are illustrated by applying it to solve various three-dimensional wave-structure interaction problems featuring complex geometries, such as a 3D travelling wave in a closed channel, a 3D solitary wave interacting with a vertical circular cylinder, a 3D solitary wave interacting with a horizontal thin plate, and a 3D focusing wave impacting on an FPSO-like structure. For all cases, convincing agreement between the numerical predictions and the corresponding experimental data and/or analytical or numerical solutions is obtained. In addition, for all cases, water surface profiles and turbulent vortical structures are presented and discussed.

Performance of different techniques of generation and absorption of free-surface waves in Computational Fluid Dynamics

In wave-structure interaction problems, the minimization of wave reflection at boundaries is important for achieving accurate results and limiting the disturbances on the air/water interface. The present study compares a set of existing wave outlet techniques which are commonly applied in free surface simulations using a viscous flow solver. These techniques are stretched mesh, linear damping source, increased viscosity, and relaxation schemes. The comparisons are performed for test conditions which include propagation of regular incident waves and damping of radiation waves.

Water wave scattering by floating flexible porous plate over variable bathymetry regions

The study deals with the scattering of obliquely incident gravity waves by a horizontal floating flexible porous plate in the water of finite depth having a variable bottom bed. The problem when a vertical rigid wall is placed in the downstream of the plate is also considered. The problem is analyzed under the assumptions of small amplitude water wave theory and structural responses. The undulated bottom bed is finitely extended and lies beneath the floating plate regions. A coupled eigenfunction expansion - boundary element method is used for the solution purpose. Energy balance relations for wave scattering in the presence of the flexible plate and when the vertical rigid wall is placed in the downstream are derived and used to check the accuracy of the numerical results. The effect of sinusoidally varying bottom topography, plate porosity and heading angle of the incident wave on the Bragg resonance is analyzed. Moreover, various results are computed and analyzed to study the role of the wave parameters, bottom undulation and floating porous flexible plate on wave scattering. The proposed solution methodology can be easily extended to deal with wave-structure interaction problems of varied structural configurations and bottom bed.

Broadband cloaking of multiple truncated cylinders in water waves using the arrangement defects

Cloaking based on scattering cancellation is investigated for a surface-piercing truncated cylinder surrounded by several annularly arranged small truncated cylinders in water waves. The cloaking condition of a body in water waves corresponds to the absence of scattered waves radiating to infinity; that is, the cloaked structure appears invisible to a far-field observer. The effects of three kinds of defects of the outer cylinders on cloaking are considered: a radial location defect, a circumferential location defect, and a size defect. The higher-order boundary element method is combined with the wave interaction theory to accurately study this wave–structure interaction problem. Both the scattered wave energy of the entire structure and the wave drift force on the inner cylinder are calculated and analyzed for the different defects. The symmetry of the defect effects and the cloaking-wavenumber offset caused by a radial position defect of the entire outer cylinder array are first identified. The radial location defect is successfully adopted to control the cloaking frequencies over a wide band.