Numerical Wave Maker Research Articles

Numerical simulation of bichromatic wave propagation based on the paddle- and modified mass source wave-maker methods

A second-order numerical wave-maker is realized by combining the paddle wave-maker theory proposed by Schäffer for physical experiments with the Fluent software. The numerical results from the paddle wave-maker method are compared with the results from the modified mass source wave-maker method, the theoretical solutions, and the physical experimental data. The numerical model based on the paddle wave-maker method is verified, and the applicable scopes of the two wave-maker methods are discussed. The paddle wave-maker method is not suitable for bichromatic wave combinations that include shallow-water waves. However, within their common applicable range, the numerical results from the paddle wave-maker method are better than those from the modified mass source wave-maker method, at least for the grid divisions adopted in this study. The effects of the incident wave parameters on the nonlinear wave-wave interaction are also analyzed.

RANS Computation of the Mean Forces and Moments, and Wave-Induced Six Degrees of Freedom Motions for a Ship Moving Obliquely in Regular Head and Beam Waves

Ship maneuvering performance in waves has attracted much attention in recent years. One of main research efforts for this problem has been devoted to the high-accuracy computation of hydrodynamic forces and moments, as well as wave-induced motions, for ships performing maneuvering motions in waves. The objective of this article is to present a numerical study on the computation of the mean forces and moments, and wave-induced six degrees of freedom motions for a ship moving obliquely in regular head and beam waves. The RANS (Reynolds-Averaged Navier-Stokes) solver based on OpenFOAM is used for this purpose. The RANS computations herein are carried out in a horizontal coordinate system. The numerical wave maker with prescribing values of flow variables on the domain boundaries is applied for the wave generation in the computational domain. However, in order to prevent wave reflection, relaxed zones adjacent to the wave maker boundaries are set up. A new program module is inserted into OpenFOAM to update the flow velocity and wave evaluation on the wave-maker boundaries and in the relaxed zones during the RANS computation. The mesh deformation method is employed to allow the ship to perform motions in space. However, a virtual spring system is attached to the ship so as to restrain the surge, sway and yaw, while heave, pitch and roll are completely free, so that the ship is able to oscillate periodically around a certain position in space. The computed mean forces and moments with the inertia effects agree fairly well with the experimental data, and the computed wave-induced motions are also in quite reasonable agreement with the experimental data. This study shows a very successful computation, as well as the procedure of the RANS results processing.

The Efficient Application of an Impulse Source Wavemaker to CFD Simulations

Computational Fluid Dynamics (CFD) simulations, based on Reynolds-Averaged Navier–Stokes (RANS) models, are a useful tool for a wide range of coastal and offshore applications, providing a high fidelity representation of the underlying hydrodynamic processes. Generating input waves in the CFD simulation is performed by a Numerical Wavemaker (NWM), with a variety of different NWM methods existing for this task. While NWMs, based on impulse source methods, have been widely applied for wave generation in depth averaged, shallow water models, they have not seen the same level of adoption in the more general RANS-based CFD simulations, due to difficulties in relating the required impulse source function to the resulting free surface elevation for non-shallow water cases. This paper presents an implementation of an impulse source wavemaker, which is able to self-calibrate the impulse source function to produce a desired wave series in deep or shallow water at a specific point in time and space. Example applications are presented, for a Numerical Wave Tank (NWT), based on the open-source CFD software OpenFOAM, for wave packets in deep and shallow water, highlighting the correct calibration of phase and amplitude. Furthermore, the suitability for cases requiring very low reflection from NWT boundaries is demonstrated. Possible issues in the use of the method are discussed, and guidance for accurate application is given.

On the Assessment of Numerical Wave Makers in CFD Simulations

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.

A numerical wave-maker for internal solitary waves with timely updated mass source/sink terms

On the basis of the two-dimensional Navier–Stokes equations, a new numerical method is proposed to generate internal solitary waves (ISWs) of expected parameters by adding a source term above the interface and a sink term below the interface into the continuity equation. Fluxes between the source and the sink are balanced to assure mass conservation, and the source/sink regions (the spatial windows over which the sink/source terms are placed) are adjusted as functions of time with the interface motion. Thus, the nonphysical trailing waves can be eliminated, which makes it easy to assure the prescribed ISW parameters. Moreover, a new layout is presented to avoid the difficulty of sizing and positioning the source/sink region, which has been proved to be an intrinsic drawback of the traditional mass source method. Numerical experiments are performed to validate the proposed method by analyzing the wave displacements and vertical profiles of velocity fields. It is shown that the numerical waveform remains stable with much less trailing waves than previous methods, and the numerical results are in good agreement with theoretical and experimental results. In addition, through sensitivity analysis, a reasonable method to determine the width of source/sink region is recommended.

Extreme run-up events on a vertical wall due to nonlinear evolution of incident wave groups

Nonlinear evolution of long-crested wave groups can lead to extreme interactions with coastal and marine structures. In the present study the role of nonlinear evolution in the formation of extreme run-up events on a vertical wall is investigated. To this end, the fundamental problem of interaction between non-breaking water waves and a vertical wall over constant water depth is considered. In order to simulate nonlinear wave–wall interactions, the high-order spectral method is applied to a computational domain which aims to represent a two-dimensional wave flume. Wave generation is simulated at the flume entrance by means of the additional potential concept. Through this concept, the implementation of a numerical wavemaker is applicable. In addition to computational efficiency, the adopted numerical approach enables one to consider the evolution of nonlinear waves while preserving full dispersivity. Utilizing these properties, the influence of the nonlinear wave evolution on the wave run-up can be examined for a wide range of water depths. In shallow water, it is known that nonlinear evolution of incident waves may result in extreme run-up events due to the formation of an undular bore. The present study reveals the influence of the nonlinear evolution on the wave run-up in deep-water conditions. The results suggest that extreme run-up events in deep water may occur as a result of the disintegration of incident wave groups into envelope solitons.

Numerical simulation of wave and current interaction with a fixed offshore substructure

Offshore substructures have been developed to support structures against complex offshore environments. The load at offshore substructures is dominated by waves, and deformation of waves caused by interactions with the current is an important phenomena. Wave load simulation of fixed offshore substructures in waves with the presence of uniform current was carried out by numerical wave tank technique using the commercial software, FLUENT. The continuity and Navier–Stokes equations were applied as the governing equations for incompressible fluid motion, and numerical wavemaker was employed to reproduce offshore wave environment. Convergence test against grids number was carried out to investigate grid dependency and optimized conditions for numerical wave generation were derived including investigation of the damping effect against length of the damping domain. Numerical simulation of wave and current interactions with fixed offshore substructure was carried out by computational fluid dynamics, and comparison with other experiments and simulations results was conducted.

Simulating Hull Dynamics in Waves using a RANSE Code

The paper presents an example of the application of RANSE method for the simulation of ship motion in waves. A finite-volume flow solver extended with the rigid body motion module and the numerical wavemaker was used for the simulation. Presented results for the free drop of a prism show good accuracy and robustness of the model. Results for the motion of a ship in regular waves agree satisfactorily with the strip theory.

Finite-Element Computation of Wave-Structure Interaction between Steep Stokes Waves and Vertical Cylinders

The diffraction of highly nonlinear Stokes waves by vertical cylinders of circular cross section is numerically simulated in the time domain. A finite-element method, based on Hamilton’s principle, is used to discretize the fluid domain. The Stokes waves, input at the numerical wave maker, are obtained numerically from the two-dimensional steady solution of the finite element model. A new matching scheme is developed to match the two-dimensional wave at the far field and the three-dimensional diffracted wave in the near field. The method developed here can easily be extended to the diffraction of irregular, nonlinear waves. Numerical examples are presented for the diffraction of Stokes waves with various steepnesses by single and multiple circular cylinders. The wave elevation and runup on the cylinder are calculated and compared with the available theoretical and experimental results.

Emerging Trends in Numerical Predictive Technologies in Offshore and Marine Engineering

Emerging Trends in Numerical Predictive Technologies in Offshore and Marine Engineering

중첩 격자계를 이용한 물체운동의 수치 시뮬레이션

A CFD simulation technique has been developed to handle the unsteady body motion with large amplitude by use of overlapping multi-block grid system. The three-dimensional, viscous and incompressible flow around body is investigated by solving the Navier-Stokes equations, and the motion of body is represented by moving effect of the grid system. Composite grid system is employed in order to deal with both the body motion with large amplitude and the condition of numerical wave maker in convenience at the same time. The governing equations, Navier-Stokes (N-S) and continuity equations, are discretized by a finite volume method, in the framework of an O-H type boundary-fitted grid system (inner grid system including test model) and a rectangular grid system (outer grid system including simulation equipments for generation of wave environments). If this study, several flow configurations, such as an oscillating cylinder with large KC number, are studied in order to predict and evaluate the hydrodynamic forces. Furthermore, the motion simulation of a Series 60 model advancing in a uniform flow under the condition of enforced roll motion of angle 20<TEX>$^{\circ}$</TEX> is performed in the developed numerical wave tank.

Numerical Simulation of the 2D and 3D Breaking Waves by Finite-Difference Method

A new finite-difference method which can cope with strong interface motions is developed. The air and water flows are simultaneously solved in the time-marching solution procedure for the Navier-Stokes equation. The marker-density technique and the porosity techinique are devised for the implementation of the interface and the body-boundary conditions, respectively. Two test computations are performed, one is a 2D breaking flow of regular periodic wave generated by a numerical wave maker, the other is a 3D breaking flow about a ship-like body. The accuracy is examined and improvement of the method is described by the comparison with the records of physical experiments.

A Numerical Modeling of Ship Bow Waves

A two-dimensional numerical wavemaker model is used to predict the three-dimensional bow wave pattern caused by a wedge-shaped model moving at constant velocity. Solutions with linear and nonlinear free-surface conditions agree well with the experimental result. A formula derived from dimensional analysis is proved to be a good approximation of the numerical solution based on the linear formulation. A wave splashing phenomenon is predicted at high velocity by the nonlinear theory. The numerical results are compared with the analytic and experimental results reported by Ogilvie [1].2 The improvements given by the nonlinear formulations are observed to be in the correct direction.