Nonlinear Wave-body Interactions Research Articles

An accurate and efficient HOS-meshfree CFD coupling method for simulating strong nonlinear wave–body interactions

The study on strong nonlinear wave–structure interaction (WSI) is crucial in ocean engineering. The Smoothed Particle Hydrodynamics (SPH) method is popular in this field because of its advantages in simulating free surface flow. However, to predict the details of WSI, a high resolution of particles is usually required, which results in a huge computational cost. In this paper, a potential-meshfree CFD weak coupling method based on the High Order Spectral (HOS) and SPH method is developed, which combines the advantages of the former in generating nonlinear waves quickly and accurately and the latter in adapting to strong nonlinear free surface problems. The accuracy of the coupling method was verified through the simulations of regular and irregular waves compared with experiment data. It shows the coupling method can effectively improve computational efficiency and extensively reduce the numerical dissipation. Furthermore, a simulation of the interaction between the focus wave and the floating body was conducted by using the coupling method, the original SPH method and the Constrained Interpolation Profile (CIP) method. Among all numerical methods, the coupling method is the best one for predicting the impact pressure of the floating body and is the only one that can capture the second impacting peak.

Stabilized BEM-MEL for fully nonlinear wave-body interactions using a mesh adjustment velocity

Stabilized BEM-MEL for fully nonlinear wave-body interactions using a mesh adjustment velocity

Numerical Simulation of Green Water on Deck with a Hybrid Eulerian-Lagrangian Method

Green water on the ship deck in rough sea conditions may induce extreme impulsive wave impacts on superstructures and result in severe structural damage. It is of great importance to consider green water loads in ship structure design. However, there are many challenges in predicting green water loads due to the strongly nonlinear wave–ship interactions and the multiphase, multi-scale nature of the wave impact phenomena. In this article, a three-dimensional hybrid Eulerian–Lagrangian approach is proposed for simulating green water loads on the ship deck. It is extended from an efficient and accurate two-dimensional method developed for fluid–structure interaction problems. In this method, the flow field is solved on a fixed regular Cartesian grid system in an Eulerian framework, whereas the solid body motion is tracked with a set of markers immersed in the fluid and solved in a Lagrangian framework. Two benchmark cases, green water on a fixed simplified Floating Production Storage and Offloading (FPSO) model and green water on ship, are simulated. Comparison between experimental data and numerical results shows that our method is a viable choice for predicting green water loads. Introduction In rough sea conditions, ships may undergo large-amplitude motions and suffer green water impacts due to the strongly nonlinear wave–body interaction. Large waves run up to the ship deck and impact on superstructures with huge volume of water impulsively. It can induce extreme impulsive wave impact loads on superstructures and result in severe structural damage. Thus, it is important to predict wave impact loads for ship structure design. However, there are still great challenges in predicting green water impact loads accurately because it is a flow phenomenon of high complexity and randomness due to its multiphase, highly turbulent nature with wave breaking, air entrainment, etc (Temarel et al. 2016).

Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states.

Predicting motions of vessels in extreme sea states represents one of the most challenging problems in naval hydrodynamics. It involves computing complex nonlinear wave-body interactions, hence taxing heavily computational resources. Here, we put forward a new simulation paradigm by training recurrent type neural networks (RNNs) that take as input the stochastic wave elevation at a certain sea state and output the main vessel motions, e.g. pitch, heave and roll. We first compare the performance of standard RNNs versus GRU and LSTM neural networks (NNs) and show that LSTM NNs lead to the best performance. We then examine the testing error of two representative vessels, a catamaran in sea state 1 and a battleship in sea state 8. We demonstrate that good accuracy is achieved for both cases in predicting the vessel motions for unseen wave elevations. We train the NNs with expensive CFD simulations offline, but upon training, the prediction of the vessel dynamics online can be obtained at a fraction of a second. This work is motivated by the universal approximation theorem for functionals (Chen & Chen, 1993. IEEE Trans. Neural Netw. 4, 910-918 (doi:10.1109/72.286886)), and it is the first implementation of such theory to realistic engineering problems.

OpenMP parallelism in computations of three-dimensional potential numerical wave tank for fully nonlinear simulation of wave-body interaction using NURBS

The open multi-processing parallelism was implemented into a serial code to compute a high-order boundary integral equation based on the second Green's identity. on symmetric multiprocessing computer platforms. The parallel code is augmented to a three-dimensional potential numerical wave tank for fully nonlinear wave-body interaction problems in the time domain. The non-uniform rational B-Spline surface was manipulated to define the geometry of the computational boundaries and the distribution of boundary values either as a high-order iso-geometric formulation. The material node approach and fourth-order Runge-Kutta time integration method were compounded for time marching the fully nonlinear free surface boundary. The propagation of a fifth-order Stokes wave was simulated to examine the scalability of the parallel constructs implementation. Afterwards, the second-order Stokes wave interaction with a cylindrical pile was modeled as a practical case study to show the benefits of the parallel code. The results were compared with former experiments and numerical studies.

Influence of Viscosity and Non-Linearities in Predicting Motions of a Wind Energy Offshore Platform in Regular Waves

AbstractMotion predictions of floating bodies in extreme waves represent a challenging problem in naval hydrodynamics. The solution of the seakeeping problem involves the study of complex non-linear wave-body interactions that require large computational costs. For this reason, over the years, many seakeeping models have been formulated in order to predict ship motions using simplified flow theories, usually based on potential flow theories. Neglecting viscous effects in the wave-induced forces might largely underestimate the energy dissipated by the system. This problem is particularly relevant for unconventional floating bodies at resonance. In these operating conditions, the linear assumption is no longer valid, and conventional boundary element methods, based on potential flow, might predict unrealistic large responses if not corrected with empirical viscous damping coefficients. The application considered in this study is an offshore platform to be operated in a wind farm requiring operability even in extreme meteorological conditions. In this paper, we compare heave and pitch response amplitude operators predicted for an offshore platform using three different seakeeping models of increasing complexity, namely, a frequency-domain boundary element method (BEM), a partly nonlinear time domain BEM, and a non-linear viscous model based on the solution of the unsteady Reynolds-averaged Navier–Stokes (URANS) equations. Results are critically compared in terms of accuracy, applicability, and computational costs.

Numerical Study of the Influence of Fishnet Mesh Size on a Floating Platform

This study aims to investigate the influence of fishnet mesh size on a floating platform. A self-developed, time-domain numerical model was used for the evaluation. This model is based on potential flow theory, uses the boundary element method (BEM) to solve nonlinear wave-body interactions, and applies the Morison equation to calculate the hydrodynamic forces exerted on fishnets. The mooring system is treated as a linear and symmetric spring. The results near the resonant frequency of the platform indicate that the smaller the fishnet mesh size, the lower the heave, pitch, and sea-side tension response amplitude operators (RAOs), but the higher the reflection coefficient. The results in the lower frequency region reveal that the smaller the fishnet mesh size, the lower the surge and heave RAOs, but the higher the pitch and tension RAOs. Meanwhile, the time-domain results at the resonant frequency of heave motion are shown to indicate the influences of a platform with various fishnets mesh sizes on the rigid body motion, mooring line tension, and transmitted wave heights. In addition, a comparison of nonlinear effects indicates that, after reducing the fishnet mesh size, the second-order RAOs of heave, pitch, and sea-side tension decrease, but the changes are minor against the first-order results.

Instability of finite-amplitude gravity–capillary progressive ring waves by an oscillating surface-piercing body

We investigate the instability of finite-amplitude progressive ring waves in deep water, which are radiated by the time-periodic oscillation of a half-submerged sphere (with radius ), under the influence of gravity and surface tension. We use direct numerical simulations of fully nonlinear wave–body interactions to quantify the temporal–spatial evolution of the base and perturbed outgoing ring wave fields, from which the stability of ring waves is analysed. The numerical simulation is based on a mixed Euler–Lagrangian quadratic boundary-element method and accounts for fully nonlinear wave–wave and wave–body interactions in the context of potential flow. We find that the progressive gravity–capillary ring waves (with frequency ) become unstable to (small-amplitude) radial cross-wave disturbances when the body-motion parameter exceeds the threshold value , where is the amplitude of body oscillation and is the wavenumber of the ring wave at subharmonic frequency . The predicted from nonlinear simulations under the assumption of ideal fluid, which decreases with increasing , is generally smaller than the experimental measurement of Tatsuno et al. (Rep. Res. Inst. Appl. Mech. Kyushu University, vol. 17, 1969, pp. 195–215) by approximately 50 %. When the viscous effects in body-surface and free-surface boundary layers are taken into account, the predicted matches the experimental data excellently. The unstable modes are characterized as the progressive radial cross-waves at the subharmonic frequency ( ) with the growth rates generally increasing with . The maximum growth rate is achieved for the cross-wave mode with the azimuthal wavenumber . These distinctive features of instability obtained in numerical simulations are consistent with the experimental observations. From the comparison with the weakly nonlinear analysis of Shen & Liu (J. Fluid Mech., vol. 869, 2019, pp. 439–467), it is found that inclusion of finite-amplitude ring wave effects generally reduces the growth rate of unstable modes but has an insignificant influence on the shape of unstable modes and the value of . Moreover, for moderately steep ring waves, nonlinear interactions of a few unstable modes can excite broadbanded unstable subharmonic cross-wave modes, leading to the formation/observation of distinctive non-axisymmetric wave patterns during long-time evolutions.

A spectral/[formula omitted] element depth-integrated model for nonlinear wave–body interaction

We present a depth-integrated Boussinesq model for the efficient simulation of nonlinear wave–body interaction. The model exploits a ‘unified’ Boussinesq framework, i.e. the fluid under the body is also treated with the depth-integrated approach. The unified Boussinesq approach was initially proposed by Jiang (2001) and recently analyzed by Lannes (2017). The choice of Boussinesq-type equations removes the vertical dimension of the problem, resulting in a wave–body model with adequate precision for weakly nonlinear and dispersive waves expressed in horizontal dimensions only. The framework involves the coupling of two different domains with different flow characteristics. Inside each domain, the continuous spectral/hp element method is used to solve the appropriate flow model since it allows to achieve high-order, possibly exponential, convergence for non-breaking waves. Flux-based conditions for the domain coupling are used, following the recipes provided by the discontinuous Galerkin framework. The main contribution of this work is the inclusion of floating surface-piercing bodies in the conventional depth-integrated Boussinesq framework and the use of a spectral/hp element method for high-order accurate numerical discretization in space. The model is verified using manufactured solutions and validated against published results for wave–body interaction. The model is shown to have excellent accuracy and is relevant for applications of waves interacting with wave energy devices.

A 3D parallel boundary element method on unstructured triangular grids for fully nonlinear wave-body interactions

This paper presents the development and validation of a three-dimensional numerical wave tank devoted to studying wave-structure interaction problems. It is based on the fully nonlinear potential flow theory, here solved by a boundary element approach and using unstructured triangular meshes of the domain's boundaries. Time updating is based on a second-order explicit Taylor series expansion. The method is parallelized using the Message Passing Interface (MPI) in order to take advantage of multi-processor systems. For radiation problems, with cylindrical bodies moving in prescribed motion, the free-surface is updated with a fully Lagrangian scheme, and is able to reproduce reference results for nonlinear forces exerted on the moving body. For diffraction problems, semi-Lagrangian time-updating is used, and reproduces nonlinear effects for diffraction on monopiles. Finally, we study the nonlinear wave loads on a fixed semi-submersible structure, thereby illustrating the possibility to apply the proposed numerical model for the design of offshore structures and floaters.

Numerical Modelling of Interaction between Solitary Wave and Sloped Seawall

A numerical model for solving interaction between solitary wave and a sloped seawall is established. The CIP (Constrained Interpolation profile) scheme is employed to solve the flow field. THINC (Tangent of Hyperbola Interpolation for Interface Capturing) method is applied for capturing the free surface. Hydrodynamic forces is calculated by integrating the pressure and friction along the seawall surface. First, convergence tests with respect to mesh resolution and time step are examined, and the solitary wave profile is validated by experimental data from the published paper. Then, time series of the free surface elevation at specific location with different heights of incident solitary wave are presented. Finally, hydrodynamic forces acting on the weather side of the seawall are analyzed. The conclusion can be drawn that this numerical model has applicability for strongly nonlinear wave-body interaction problems.

Experimental study on motions of tunnel element during immersion standby stage in long wave regime

The motions of a small-freeboard tunnel element are prone to strongly nonlinear wave-body interaction as a result of significant water-on-deck occurrence. To obtain a better prediction for the accurate and safe handling of a tunnel element in severe weather, 3D physical model tests were conducted under regular and irregular waves with long period to estimate the motions of three floating bodies (single tunnel element, pontoon and the tunnel-pontoons assembly) and predict possible resonance. The experimental results demonstrate that, due to the green water loadings, the non-zero mean heave of the tunnel and tunnel-pontoons assembly is significantly affected by roll resonant motion and has a similar dependence on the wave period as the roll in long wave regime. For wave period smaller than the roll period, the mean drift forces have substantial influence on the mean sway of all the three floating bodies, provoking greater offshore mooring tensions. Wave excitation at periods close to resonance of the heave, roll and pitch results in large local peaks in RAOs of the three floating bodies.

Improved numerical solution of Dobrovol'skaya's boundary integral equations on similarity flow for uniform symmetrical entry of wedges

Dobrovol'skaya [1] presented a similarity solution for the water entry of symmetrical wedges with constant velocity. The solution involves an integral equation that becomes increasingly harder to numerically solve as the deadrise angle decreases. Zhao and Faltinsen [2] were able to present reliable results for deadrise angles down to 4°. In this paper, Zhao and Faltinsen's results are improved and reliable results for deadrise angles down to 1° are confirmed by comparing to the asymptotic solutions at small deadrise angles and the solutions by the traditional boundary element method at relatively large deadrise angles. The present similarity solution results provide a reference solution in theoretical studies of water entry problems and in developing accurate numerical solvers for simulating strongly nonlinear wave–body interactions, which flows are governed by Laplace equation or Euler equation.

On reduced models for gravity waves generated by moving bodies

In 1983, Tulin published a report proposing a framework for reducing the equations for gravity waves generated by moving bodies into a single nonlinear differential equation solvable in closed form (Proceedings of the 14th Symposium on Naval Hydrodynamics, 1983, pp. 19–51). Several new and puzzling issues were highlighted by Tulin, notably the existence of weak and strong wave-making regimes, and the paradoxical fact that the theory seemed to be applicable to flows at low speeds, ‘but not too low speeds’. These important issues were left unanswered, and despite the novelty of the ideas, Tulin’s report fell into relative obscurity. Now, 30 years later, we will revive Tulin’s observations, and explain how an asymptotically consistent framework allows us to address these concerns. Most notably, we demonstrate, using the asymptotic method of steepest descents, how the production of free-surface waves can be related to the arrangement of integration contours connected to the shape of the moving body. This approach provides a new and powerful methodology for the study of geometrically nonlinear wave–body interactions.

A desingularized Rankine source method for nonlinear wave–body interaction problems

A two-dimensional nonlinear wave–body interaction problem is solved by a desingularized integral method in combination with a mixed Euler–Lagrange method. A special treatment of the intersection point singularity is introduced by employing an optimal technique to smooth the wave elevation around the intersection point and the utilization of a free surface control point distribution. By this means the nonlinear boundary effects arising from body surface and free surface are taken into consideration in addition to the development of a free surface Rankine source distribution method. A Lagrangian formulation is applied to capture the time-dependent motion of the control points and source points to describe the body and free surface nonlinear boundary conditions. The validation of the proposed method is demonstrated by comparing findings with a selection of existing numerical and experimental data.

Wave-current impacts on surface-piercing structure based on a fully nonlinear numerical tank

Fully nonlinear wave-body interactions for a surface-piercing structure with combined wave-current flow in different water depths are studied by using a 2-D numerical tank. The model is based on Reynolds averaged Navier-Stokes (RANS) equations and renormalization group (RNG) k – ɛ model. The mean and maximum wave-current impacts, including forces in two directions and rotational moment, are calculated and discussed. The effects of U/C and water depth condition on forces and moment have been investigated and the results for combined irregular waves and currents are compared with those induced by combined regular waves and currents.

A CIP-based numerical simulation of freak wave impact on a floating body

The purpose of this work is to develop advanced numerical tools for modeling freak waves impact on a floating body undergoing large amplitude motions. An improved model governed by the Navier–Stokes equations with free surface boundary conditions is presented for nonlinear wave-body interactions, in which a more accurate Volume of Fluid (VOF)-type scheme, the Tangent of hyperbola for interface capturing/Slope weighting (THINC/SW) is adopted for interface capturing. The model is solved by a Constrained Interpolation Profile (CIP)-based high order finite-difference method on a fixed Cartesian grid system. A focusing wave theory is used for freak wave generation. Newly designed physical experiments in a two-dimensional glass-wall wave tank are performed for benchmark validation. Fairly good agreements are obtained from the qualitative and quantitative comparisons between numerical results and laboratory data regarding to distorted free surfaces and large amplitude body motions. Some discrepancies are found for the predicted peak pressure. The effects of grid resolution on body motions and impact pressure are performed for error analysis. The comparison of the numerical results and measured data reveals that the proposed model is capable of reproducing the nonlinear dynamics of the floating body for applications.

Time series prediction of nonlinear ship structural responses in irregular seaways using a third-order Volterra model

To predict the nonlinear structural responses of a ship traveling through irregular waves, a third-order Volterra model was applied based on the given irregular data. A nonlinear wave–body interaction system was identified using the nonlinear autoregressive with exogenous input (NARX) technique, which is one of the most commonly used nonlinear system identification schemes. The harmonic probing method was applied to extract the first-, second- and third-order frequency response functions of the system. To achieve this, a given set of time history data of both the irregular wave excitation and the corresponding midship vertical bending moment for a certain sea state was fed into the three-layer perceptron neural network. The network parameters are determined based on the supervised training. Next, the harmonic probing method was applied to the identified system to extract the frequency response function of each order. While applying the harmonic probing method, the nonlinear activation function (i.e., the hyperbolic tangent function) was expanded into a Taylor series for harmonic component matching. After the frequency response functions were obtained, the structural responses of the ship under an arbitrary random wave excitation were easily calculated with rapidity using a third-order Volterra series. Additionally, the methodology was validated through the in-depth analysis of a nonlinear oscillator model for a weak quadratic and cubic stiffness term, whose analytic solutions are known. It was confirmed that the current method effectively predicts the nonlinear structural response of a large container carrier under arbitrary random wave excitation.

직교격자 기반 수치기법을 이용한 선박의 대변위 운동해석

In this study, a Cartesian-grid method based on finite volume approach is applied to simulate the ship motions in large amplitude waves. Fractional step method is applied for pressure-velocity coupling and TVD limiter is used to interpolate the cell face value for the discretization of convective term. Water, air, and solid phases are identified by using the concept of volume-fraction function for each phase. In order to capture the interface between air and water, the tangent of hyperbola for interface capturing (THINC) scheme is used with weighed line interface calculation (WLIC) method which considers multidimensional information. The volume fraction of solid body embedded in the Cartesian grid system is calculated using a level-set based algorithm, and the body boundary condition is imposed by a volume weighted formula. Numerical simulations for the two-dimensional barge type model and Wigley hull in linear waves have been carried out to validate the newly developed code. To demonstrate the applicability for highly nonlinear wave-body interactions such as green water on the deck, numerical analysis on the large-amplitude motion of S175 containership is conducted and all computational results are compared with experimental data.

Numerical and experimental study on a 2-D floating body under extreme wave conditions

This paper presents further developments of a constrained interpolation profile (CIP)-based Cartesian grid method [29] to model nonlinear interactions between extreme waves and a floating body, which is validated against to a newly performed experiment. In the experiment, three kinds of waves (regular wave, focused wave and combined regular and focused wave) are generated and a box-shaped floating body with a superstructure is used. Validation computations on the experiment are performed by the improved CIP-based Cartesian grid method, in which the THINC/WLIC scheme (THINC: tangent of hyperbola for interface capturing; WLIC: weighed line interface calculation), is used for interface capturing. The highly nonlinear wave–body interactions, including large amplitude body motions and water-on-deck are numerically investigated through implementation of focused wave input to the CIP-based method. Computations are compared with experimental results and good agreement is achieved. The effects of the water-on-deck phenomena and different input focus positions on the body response are also dealt with in the research.