Search Results (9)

This study developed a two-dimensional fully nonlinear numerical wave tank (FN-NWT) to examine the nonlinear interaction between waves and dual submerged porous structures. Using the FN-NWT, not only reflection and transmission coefficients, but also wave deformation/force depending on porosity were investigated. The FN-NWT was developed using the boundary element method (BEM), and consisted of a fluid domain and a porous medium domain. Darcy’s law or the non-Darcy (Forchheimer) flow equation were applied to the flow passing through the porous domain. The wave reflection coefficient of the porous submerged structures agreed well with the given experimental data when using Forchheimer flow boundary conditions. Excessive attenuation of the transmitted wave occurred when Darcy’s condition was employed. The difference in each coefficient due to the spacing of the submerged structure was reduced in the porous structure compared with the non-porous structure. The difference according to the incident wave height was clearly revealed in the transmission coefficient. The developed dual-domain FN-NWT can be applied to investigate the nonlinear interaction between waves and porous structures as a first-cut design tool. Full article

The Akhmediev breather (AB) solution of the nonlinear Schrödinger equation (NLSE) shows that the maximum crest height of modulated wave trains reaches triple the initial amplitude as a consequence of nonlinear long-term evolution. Several fully nonlinear numerical studies have indicated that the amplification can exceed 3, but its physical mechanism has not been clarified. This study shows that spectral broadening, bound-wave production, and phase convergence are essential to crest enhancement beyond the AB solution. The free-wave spectrum of modulated wave trains broadens owing to nonlinear quasi-resonant interaction. This enhances bound-wave production at high wavenumbers. The phases of all the wave components nearly coincide at peak modulation and enhance amplification. This study found that the phase convergence observed in linear-focusing waves can also occur due to nonlinear wave evolution. These findings are obtained by numerically investigating the modulated wave trains using the higher-order spectral method (HOSM) up to the fifth order, which allows investigations of nonlinearity and spectral bandwidth beyond the NLSE framework. Moreover, the crest enhancement is confirmed through a tank experiment wherein waves are generated in the transition region from non-breaking to breaking. Owing to strong nonlinearity, the maximum crest height observed in the tank begins to exceed the HOSM prediction at an initial wave steepness of 0.10. Full article

This paper presents a combined analytical and numerical (CAN) model to simulate the scattering of cnoidal waves by a fixed and partially immersed box-type breakwater. A set of Boussinesq equations are solved in the outer region using the finite-difference method to model the propagation of cnoidal waves and their subsequent reflection and transmission after encountering the breakwater. The two-dimensional (2D) velocity potential in the inner region beneath the body is derived analytically by solving the equations formulated from the orthogonality of eigenfunctions and the interfacial matching conditions. Experimental measurements on the wave profiles were carried out in a wave tank to verify the model solutions. Reflected and transmitted wave elevations obtained from the present CAN model match closely with the measured data. Additionally, the calculated horizontal and vertical forces on the body using the developed CAN model are in reasonable agreement with those from a potential 2D flow-based fully nonlinear wave model (FNWM). The method and proposed CAN model, if applied to a simple parametric investigation, can provide the expected trends in terms of applied forces, wave reflection, and transmission. Full article

Accurate and efficient numerical wave generation and absorption of two-dimensional nonlinear periodic waves traveling on a steady, uniform current were carried out in a potential, fully nonlinear numerical wave tank. The solver is based on the Βoundary Εlement Μethod (ΒΕΜ) with linear singularity distributions and plane elements and on the mixed Eulerian–Lagrangian formulation of the free surface equations. Wave generation is implemented along the inflow boundary by imposing the stream function wave solution, while wave absorption at both end-boundaries is effectively treated by introducing absorbing layers. On the absorbing beach side, the outflow boundary condition is modified to ensure that the solution accurately satisfies the dispersion relation of the generated waves. The modification involves a free-parameter that depends on the mass flux through the domain and is determined through a feedback error-correction loop. The developed method provides accurate time domain wave solutions for shallow, intermediate, and deep water depths of high wave steepness (wave heights up to 80% of the maximum value) that remain stable for 150 wave periods. This also holds in case a coplanar or opposing uniform current of velocity up to 20% of the wave celerity interacts with the wave. Full article

Modern design for marine and coastal activities places increasing focus on numerical simulations. Several numerical wave models have been developed in the past few decades with various techniques and assumptions. Those numerical models have their own advantages and disadvantages. The proper choice of the most useful numerical tool depends on the understanding of the validity and limitations of each model. In the past years, REEF3D has been developed into an open-source hydrodynamic numerical toolbox that consists of several modules based on the Navier–Stokes equations, the shallow water equations and the fully nonlinear potential theory. All modules share a common numerical basis which consists of rectilinear grids with an immersed boundary method, high-order finite differences and high-performance computing capabilities. The numerical wave tank of REEF3D utilises a relaxation method to generate waves at the inlet and dissipate them at the numerical beach. In combination with the choice of the numerical grid and discretisation methods, high accuracy and stability can be achieved for the calculation of free surface wave propagation and transformation. The comparison among those models provide an objective overview of the different wave modelling techniques in terms of their numerical performance as well as validity. The performance of the different modules is validated and compared using several benchmark cases. They range from simple propagations of regular waves to three-dimensional wave breaking over a changing bathymetry. The diversity of the test cases help with an educated choice of wave models for different scenarios. Full article

The International Energy Agency Technology Collaboration Programme for Ocean Energy Systems (OES) initiated the OES Wave Energy Conversion Modelling Task, which focused on the verification and validation of numerical models for simulating wave energy converters (WECs). The long-term goal is to assess the accuracy of and establish confidence in the use of numerical models used in design as well as power performance assessment of WECs. To establish this confidence, the authors used different existing computational modelling tools to simulate given tasks to identify uncertainties related to simulation methodologies: (i) linear potential flow methods; (ii) weakly nonlinear Froude–Krylov methods; and (iii) fully nonlinear methods (fully nonlinear potential flow and Navier–Stokes models). This article summarizes the code-to-code task and code-to-experiment task that have been performed so far in this project, with a focus on investigating the impact of different levels of nonlinearities in the numerical models. Two different WECs were studied and simulated. The first was a heaving semi-submerged sphere, where free-decay tests and both regular and irregular wave cases were investigated in a code-to-code comparison. The second case was a heaving float corresponding to a physical model tested in a wave tank. We considered radiation, diffraction, and regular wave cases and compared quantities, such as the WEC motion, power output and hydrodynamic loading. Full article

Nonlinear wave interactions and superpositions among the different wave components and wave groups in a random sea sometimes produce rogue waves with extremely large wave heights that appear unexpectedly. A good understanding of the generation and evolution of such extreme wave events is of great importance for the analysis of wave forces on marine structures. A fully nonlinear potential flow (FNPF) model is proposed in the presented paper to investigate the different factors that influence the wave focusing location, focusing time and focusing wave height in a numerical wave tank. Those factors include wave steepness, spectrum bandwidth, wave generation method, focused wave spectrum, and wave spreading functions. The proposed model solves the Laplace equation together with the boundary conditions on a $\sigma$ -coordinate grid using high-order discretisation schemes on a fully parallel computational framework. The model is validated against the focused wave experiments and thereafter used to obtain insights into the effects of the different factors. It is found that the wave steepness contributes to changing the location and time of focus significantly. Spectrum bandwidth and directional spreading affect the focusing wave height and profile, for example, a wider bandwidth and a wider directional spread lead to a lower focusing wave height. A Neumann boundary condition represents the nonlinearity of the wave groups better than a relaxation method for wave generation. Full article

A fully non-linear numerical wave tank (NWT), based on Computational Fluid Dynamics (CFD), provides a useful tool for the analysis of coastal and offshore engineering problems. To generate and absorb free surface waves within a NWT, a variety of numerical wave maker (NWM) methodologies have been suggested in the literature. Therefore, when setting up a CFD-based NWT, the user is faced with the task of selecting the most appropriate NWM, which should be driven by a rigorous assessment of the available methods. To provide a consistent framework for the quantitative assessment of different NWMs, this paper presents a suite of metrics and methodologies, considering three key performance parameters: accuracy, computational requirements and available features. An illustrative example is presented to exemplify the proposed evaluation metrics, applied to the main NWMs available for the open source CFD software, OpenFOAM. The considered NWMs are found to reproduce waves with an accuracy comparable to real wave makers in physical wave tank experiments. However, the paper shows that significant differences are found between the various NWMs, and no single method performed best in all aspects of the assessment across the different test cases. Full article

The hydroelastic vibrational responses of a large ship sailing in regular and irregular head waves are investigated numerically and experimentally. A 3D time-domain nonlinear hydroelastic mathematical model is established in which the hydrostatic restoring forces and incident wave forces are calculated on the instantaneous wetted hull surface to consider nonlinear effects of the rigid motion and elastic deformation of the hull in harsh waves. Radiation and diffraction wave forces are computed on the mean wetted surface based on the 3D frequency-domain potential flow theory. The slamming loads are calculated by momentum theory and integrated into the hydrodynamic forces. The 1D Timoshenko beam theory is adopted to model the vibrational structural response and is fully coupled with the presented hydrodynamic theory in time-domain to generate the hydroelastic equation of motion. Moreover, self-propelled segmented model tests were conducted in a laboratory wave tank to experimentally investigate the hydroelastic responses of a target ship in regular and irregular head seas. The numerical and experimental results are systemically compared and analyzed, and the established hydroelastic analysis model turns out to be reliable and effective in the prediction of ship hydroelastic responses in waves. Full article