Search results for: dispersive wave equations

Authors: H. Triki, Y. Hamaizi, A. El-Akrmi

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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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Authors: A. Errasti, F. Doffagne, O. Foucrier, S. Kao, A. Meigne, H. Pellae, T. Rouland

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Renewable energy recovery is an important domain of research in past few years in view of protection of our ecosystem. Several industrial companies are setting up widespread recovery systems to exploit wave energy. Most of them have a large size, are implanted near the shores and exploit current flows. However, as oceans represent 70% of Earth surface, a huge space is still unexploited to produce energy. Present analysis focuses on surface small scale wave energy recovery. The principle is exactly the opposite of wheel damper for a car on a road. Instead of maintaining the car body as non-oscillatory as possible by adapted control, a system is designed so that its oscillation amplitude under wave action will be maximized with respect to a boat carrying it in view of differential potential energy recuperation. From parametric analysis of system equations, interesting domains have been selected and expected energy output has been evaluated.

Keywords: small scale wave, potential energy, optimized energy recovery, auto-adaptive system

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Authors: Lev Idels, Arcady Ponosov

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Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.

Keywords: delay equations, operator methods, stochastic noise, weak solutions

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Authors: Abdel-Maksoud Abdel-Kader Soliman

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The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

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Authors: Chao-Qing Dai

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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: Bing Li, Tong Lu, Lei Qiang

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Stoneley waves are interface waves that propagate at the interface between two solid media. In this study, the dispersion characteristics and wave structures of Stoneley waves in elastic multilayered plates are displayed and investigated. With a perspective of bulk wave, a reasonable assumption of the potential function forms of the expansion wave and shear wave in nth layer medium is adopted, and the characteristic equation of Stoneley waves in a three-layered plate is given in a determinant form. The dispersion curves and wave structures are solved and presented in both numerical and simulation results. It is observed that two Stoneley wave modes exist in a three-layered plate, that conspicuous dispersion occurs on low frequency band, that the velocity of each Stoneley wave mode approaches the corresponding Stoneley wave velocity at interface between two half infinite spaces. The wave structures reveal that the in-plane displacement of Stoneley waves are relatively high at interfaces, which shows great potential for interface defects detection.

Keywords: characteristic equation, interface waves, potential function, Stoneley waves, wave structure

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Authors: Yingchen Yang

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Ocean waves are a rich renewable energy source that is nearly untapped to date, even though many wave energy conversion (WEC) technologies are currently under development. The present work discusses a vertical-axis WEC rotor for power generation. The rotor was specially designed to allow easy rearrangement of the same blades to achieve different rotor configurations and result in different wave-rotor interaction behaviors. These rotor configurations were tested in a wave tank under various wave conditions. The testing results indicate that all the rotor configurations perform unidirectional rotation about the vertical axis in waves, but the response characteristics are somewhat different. The rotor's unidirectional rotation about its vertical axis is essential in wave energy harvesting since it makes the rotor respond well in a wide range of the wave frequency and in any wave propagation directions. Result comparison among different configurations leads to a preferred rotor design for further hydrodynamic optimization.

Keywords: unidirectional rotation, vertical axis rotor, wave energy conversion, wave-rotor interaction

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Authors: Gulgassyl Nugmanova, Zhanat Zhunussova, Kuralay Yesmakhanova, Galya Mamyrbekova, Ratbay Myrzakulov

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In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr\"odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields.

Keywords: Heisenberg Ferromagnet equations, soliton equations, equivalence, Lax representation

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Authors: Hassan Youssef Mohamed

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In this paper, we show new wave equations, and by using the equations, we concluded that the strong force and the weak force are not fundamental, but they are quantum effects for electromagnetism. This result is different from the current scientific understanding about strong and weak interactions at all. So, we introduce three evidences for our theory. First, we prove the asymptotic freedom phenomenon in the strong force by using our model. Second, we derive the nuclear shell model as an approximation of our model. Third, we prove that the leptons do not participate in the strong interactions, and we prove the short ranges of weak and strong interactions. So, our model is consistent with the current understanding of physics. Finally, we introduce the electron-positron model as the basic ingredients for protons, neutrons, and all matters, so we can study all particles interactions and nuclear interaction as many-body problems of electrons and positrons. Also, we prove the violation of parity conservation in weak interaction as evidence of our theory in the weak interaction. Also, we calculate the average of the binding energy per nucleon.

Keywords: new wave equations, the strong force, the grand unification theory, hydrogen atom, weak force, the nuclear shell model, the asymptotic freedom, electron-positron model, the violation of parity conservation, the binding energy

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Authors: Amit Sharma, J. N. Sharma

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This paper deals with the study of reflection and transmission characteristics of acoustic waves at the interface of a semiconductor halfspace and elastic solid. The amplitude ratios (reflection and transmission coefficients) of reflected and transmitted waves to that of incident wave varying with the incident angles have been examined for the case of quasi-longitudinal wave. The special cases of normal and grazing incidence have also been derived with the help of Gauss elimination method. The mathematical model consisting of governing partial differential equations of motion and charge carriers diffusion of n-type semiconductors and elastic solid has been solved both analytically and numerically in the study. The numerical computations of reflection and transmission coefficients has been carried out by using MATLAB programming software for silicon (Si) semiconductor and copper elastic solid. The computer simulated results have been plotted graphically for Si semiconductors. The study may be useful in semiconductors, geology, and seismology in addition to surface acoustic wave (SAW) devices.

Keywords: quasilongitudinal, reflection and transmission, semiconductors, acoustics

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: R. K. Apalowo, D. Chronopoulos

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A Finite Element (FE) based scheme is presented for quantifying guided wave interaction with Localised Nonlinear Structural Damage (LNSD) within structures of arbitrary layering and geometric complexity. The through-thickness mode-shape of the structure is obtained through a wave and finite element method. This is applied in a time domain FE simulation in order to generate time harmonic excitation for a specific wave mode. Interaction of the wave with LNSD within the system is computed through an element activation and deactivation iteration. The scheme is validated against experimental measurements and a WFE-FE methodology for calculating wave interaction with damage. Case studies for guided wave interaction with crack and delamination are presented to verify the robustness of the proposed method in classifying and identifying damage.

Keywords: layered structures, nonlinear ultrasound, wave interaction with nonlinear damage, wave finite element, finite element

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: Md. Moniruzzaman

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The energy of ocean waves across a large part of the earth is inexhaustible. The whole world will benefit if this endless energy can be used in an easy way. The coastal countries will easily be able to meet their own energy needs. The purpose of this article is to use the infinite energy of the ocean wave in a simple way. i.e. a method of efficient use of wave energy. The paper starts by discussing various forces acting on a floating object and, afterward, about the method. And then a calculation for a 73.39MW hydropower from the tidal wave. Used some sketches/pictures. Finally, the conclusion states the possibilities and advantages.

Keywords: anchor, electricity, floating object, pump, ship city, wave energy

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Authors: Jin Song Gui, Han Li, Rui Jin Zhang, Heng Jiang Cai

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There is a large deviation between the measured wave power at the vertical breast wall and the calculated one according to current specification in the case of overtopping. In order to investigate the reasons for the deviation, the wave forces of vertical breast wall under overtopping conditions have been measured through physical model experiment and compared with the calculated results. The effect of water depth, period and the wave height on the wave forces of the vertical breast wall have been also investigated. The distribution of wave pressure under different wave actions was tested based on the force sensor which is installed in the vertical breakwater. By comparing and analyzing the measured values and norms calculated values, the applicability of the existing norms recommended method were discussed and a reference for the design of vertical breakwater was provided. Experiment results show that with the decrease of the water depth, the gap is growing between the actual wave forces and the specification values, and there are no obvious regulations between these two values with the variation of period while wave force greatly reduces with the overtopping reducing. The amount of water depth and wave overtopping has a significant impact on the wave force of overtopping section while the period has no obvious influence on the wave force. Finally, some favorable recommendations for the overtopping wave force design of the vertical breakwater according to the model experiment results are provided.

Keywords: overtopping wave, physical model experiment, vertical breakwater, wave forces

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Authors: Ramakrishna Rao Mamidi

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It is essential for Surface Mounted Permanent Magnet (SMPM) generators to determine the performance prediction and analyze the magnet’s air gap flux density wave shape. The flux density wave shape is neither a pure sine wave or square wave nor a combination. This is due to the variation of air gap reluctance between the stator and permanent magnets. The stator slot openings and the number of slots make the wave shape highly complicated. To reduce the complexity of analysis, approximations are made to the wave shape using Fourier analysis. In contrast to the traditional integration method, the Fourier coefficients, an and bn, are obtained by direct search method optimization. The wave shape with optimized coefficients gives a wave shape close to the desired wave shape. Harmonics amplitudes are worked out and compared with initial values. It can be concluded that the direct search method can be used for estimating Fourier coefficients for irregular wave shapes.

Keywords: direct search, flux plot, fourier analysis, permanent magnets

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Authors: Zuodong Liang, Dong-Sheng Jeng

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Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation.

Keywords: pore pressure, 3D wave model, seabed liquefaction, pipeline

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Authors: Roger Yu

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A numerical scheme has been developed to solve wave equations for chaotic systems such as stadium-shaped cavity. The same numerical method can also be used for finding wave properties of rectangle cavities with randomly placed obstacles. About 30k eigenvalues have been obtained accurately on a normal circumstance. For comparison, we also initiated an experimental study which determines both eigenfrequencies and eigenfunctions of a stadium-shaped cavity using pulse and normal mode analyzing techniques. The acoustic cavity was made adjustable so that the transition from nonchaotic (circle) to chaotic (stadium) waves can be investigated.

Keywords: quantum dot, chaos, numerical method, eigenvalues

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Authors: Suba Periyal Subramaniam, Babette Scheres, Altomare Corrado, Holger Schuttrumpf

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Due to the climatic change and the usage of coastal areas, there is an increasing risk of dike failures along the coast worldwide. Wave run-up plays a key role in planning and design of a coastal structure. The coastal dike lines are bent either due to geological characteristics or due to influence of anthropogenic activities. The effect of the curvature of coastal dikes on wave run-up and overtopping is not yet investigated. The scope of this research is to find the effects of the dike curvature on wave run-up by employing numerical model studies for various dike opening angles. Numerical simulation is carried out using DualSPHysics, a meshless method, and OpenFOAM, a mesh-based method. The numerical results of the wave run-up on a curved dike and the wave transformation process for various opening angles, wave attacks, and wave parameters will be compared and discussed. This research aims to contribute a more precise analysis and understanding the influence of the curvature in the dike line and thus ensuring a higher level of protection in the future development of coastal structures.

Keywords: curved dikes, DualSPHysics, OpenFOAM, wave run-up

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Authors: Ákos Wolf, Richard P. Ray

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Due to the introduction of Eurocode 8, the structural design for seismic and dynamic effects has become more significant in Hungary. This has emphasized the need for more effort to describe the behavior of structures under these conditions. Soil conditions have a significant effect on the response of structures by modifying the stiffness and damping of the soil-structural system and by modifying the seismic action as it reaches the ground surface. Shear modulus (G) and shear wave velocity (v_s), which are often measured in the field, are the fundamental dynamic soil properties for foundation vibration problems, liquefaction potential and earthquake site response analysis. There are several laboratory and in-situ measurement techniques to evaluate dynamic soil properties, but unfortunately, they are often too expensive for general design practice. However, a significant number of correlations have been proposed to determine shear wave velocity or shear modulus from Cone Penetration Tests (CPT), which are used more and more in geotechnical design practice in Hungary. This allows the designer to analyze and compare CPT and seismic test result in order to select the best correlation equations for Hungarian soils and to improve the recommendations for the Hungarian geologic conditions. Based on a literature review, as well as research experience in Hungary, the influence of various parameters on the accuracy of results will be shown. This study can serve as a basis for selecting and modifying correlation equations for Hungarian soils. Test data are taken from seven locations in Hungary with similar geologic conditions. The shear wave velocity values were measured by seismic CPT. Several factors are analyzed including soil type, behavior index, measurement depth, geologic age etc. for their effect on the accuracy of predictions. The final results show an improved prediction method for Hungarian soils

Keywords: CPT correlation, dynamic soil properties, seismic CPT, shear wave velocity

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Authors: Rawhy Ismail

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Applying fractional calculus in the field of electromagnetics shows significant results. The fractionalization of the conventional curl operator leads to having additional solutions to an electromagnetic problem. This work restudies the concept of the fractional curl operator considering fractional time derivatives in Maxwell’s curl equations. In that sense, a general scheme for the wave loss term is introduced and the degree of freedom of the system is affected through imposing the new fractional parameters. The conventional case is recovered by setting all fractional derivatives to unity.

Keywords: curl operator, fractional calculus, fractional curl operators, Maxwell equations

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Authors: K. D. R. Jagath-Kumara, D. D. Dias

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The sea waves carry thousands of GWs of power globally. Although there are a number of different approaches to harness offshore energy, they are likely to be expensive, practically challenging and vulnerable to storms. Therefore, this paper considers using the near shore waves for generating mechanical and electrical power. It introduces two new approaches, the wave manipulation and using a variable duct turbine, for intercepting very wide wave fronts and coping with the fluctuations of the wave height and the sea level, respectively. The first approach effectively allows capturing much more energy yet with a much narrower turbine rotor. The second approach allows using a rotor with a smaller radius but captures energy of higher wave fronts at higher sea levels yet preventing it from totally submerging. To illustrate the effectiveness of the approach, the paper contains a description and the simulation results of a scale model of a wave manipulator. Then, it includes the results of testing a physical model of the manipulator and a single duct, axial flow turbine, in a wave flume in the laboratory. The paper also includes comparisons of theoretical predictions, simulation results and wave flume tests with respect to the incident energy, loss in wave manipulation, minimal loss, brake torque and the angular velocity.

Keywords: near-shore sea waves, renewable energy, wave energy conversion, wave manipulation

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Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.

Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental

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Authors: E. I. Ugwu

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Theoretical analysis of the optical and Solid State properties of ZnS thin film using beam propagation technique in which a scalar wave is propagated through the material thin film deposited on a substrate with the assumption that the dielectric medium is section into a homogenous reference dielectric constant term, and a perturbed dielectric term, representing the deposited thin film medium is presented in this work. These two terms, constitute arbitrary complex dielectric function that describes dielectric perturbation imposed by the medium of for the system. This is substituted into a defined scalar wave equation in which the appropriate Green’s Function was defined on it and solved using series technique. The green’s value obtained from Green’s Function was used in Dyson’s and Lippmann Schwinger equations in conjunction with Born approximation method in computing the propagated field for different input regions of field wavelength during which the influence of the dielectric constants and mesh size of the thin film on the propagating field were depicted. The results obtained from the computed field were used in turn to generate the data that were used to compute the band gaps, solid state and optical properties of the thin film such as reflectance, Transmittance and reflectance with which the band gap obtained was found to be in close approximate to that of experimental value.

Keywords: scalar wave, optical and solid state properties, thin film, dielectric medium, perturbation, Lippmann Schwinger equations, Green’s Function, propagation

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Authors: Julien Deborde, Thomas Milcent, Stéphane Glockner, Pierre Lubin

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A fully Eulerian method is developed to solve the problem of fluid-elastic structure interactions based on a 1-fluid method. The interface between the fluid and the elastic structure is captured by a level set function, advected by the fluid velocity and solved with a WENO 5 scheme. The elastic deformations are computed in an Eulerian framework thanks to the backward characteristics. We use the Neo Hookean or Mooney Rivlin hyperelastic models and the elastic forces are incorporated as a source term in the incompressible Navier-Stokes equations. The velocity/pressure coupling is solved with a pressure-correction method and the equations are discretized by finite volume schemes on a Cartesian grid. The main difficulty resides in that large deformations in the fluid cause numerical instabilities. In order to avoid these problems, we use a re-initialization process for the level set and linear extrapolation of the backward characteristics. First, we verify and validate our approach on several test cases, including the benchmark of FSI proposed by Turek. Next, we apply this method to study the wave damping phenomenon which is a mean to reduce the waves impact on the coastline. So far, to our knowledge, only simulations with rigid or one dimensional elastic structure has been studied in the literature. We propose to place elastic structures on the seabed and we present results where 50 % of waves energy is absorbed.

Keywords: damping wave, Eulerian formulation, finite volume, fluid structure interaction, hyperelastic material

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Authors: Chih-Hua Chang

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This study uses a three-dimensional (3D) fully nonlinear model to simulate the wave generation problem caused by the movement of the seabed. The numerical model is first simplified into two dimensions and then compared with the existing two-dimensional (2D) experimental data and the 2D numerical results of other shallow-water wave models. Results show that this model is different from the earlier shallow-water wave models, with the phase being closer to the experimental results of wave propagation. The results of this study are also compared with those of the 3D experimental results of other researchers. Satisfactory results can be obtained in both the waveform and the flow field. This study assesses the application of the model to simulate the wave caused by the circular (radius r0) terrain rising or falling (moving distance bm). The influence of wave-making parameters r0 and bm are discussed. This study determines that small-range (e.g., r0 = 2, normalized by the static water depth), rising, or sinking terrain will produce significant wave groups in the far field. For large-scale moving terrain (e.g., r0 = 10), uplift and deformation will potentially generate the leading solitary-like waves in the far field.

Keywords: seismic wave, wave generation, far-field waves, seabed deformation

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Authors: A. C. Bennis, F. Dumas, F. Ardhuin, B. Blanke

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The mechanics of rip currents are complex, involving interactions between waves, currents, water levels and the bathymetry, that present particular challenges for numerical models. Here, the effects of a grid-spacing dependent horizontal mixing on the wave-current interactions are studied. Near the shore, wave rays diverge from channels towards bar crests because of refraction by topography and currents, in a way that depends on the rip current intensity which is itself modulated by the horizontal mixing. At low resolution with the grid-spacing dependent horizontal mixing, the wave motion is the same for both coupling modes because the wave deviation by the currents is weak. In high-resolution case, however, classical results are found with the stabilizing effect of the flow by feedback of waves on currents. Lastly, wave-current interactions and the horizontal mixing strongly affect the intensity of the three-dimensional rip velocity.

Keywords: numerical modeling, wave-current interactions, turbulence modeling, rip currents

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Authors: Yingchen Yang

Abstract:

In the present work, development of a new vertical-axis unidirectional wave rotor is reported. The wave rotor is a key component of a wave energy converter (WEC), which harvests energy from ocean waves. Differing from the huge majority of WEC designs that perform reciprocating motions (heaving up and down, swaying back and forth, etc.), our wave rotor performs unidirectional rotation about a vertical axis when directly exposed in waves. The unidirectional feature of the rotor makes the rotor respond well in a wide range of the wave frequency. The vertical axis arrangement of the rotor makes the rotor insensitive to the wave propagation direction. The rotor employs blades with a cross-section in an airfoil shape and a span curled into a semi-oval shape. Two sets of blades, with one nested inside the other, constitute the rotor. In waves, water particles perform an omnidirectional motion that constantly changes in both spatial and temporal domains. The blade nesting permits a compact rotor configuration that ‘sees’ a relatively uniform local flow in the spatial domain. The rotor was experimentally tested in simulated waves in a wave flume under various conditions. The testing results show a promising unidirectional rotor that is capable of extracting energy from waves at a capture width ratio of 0.08 to 0.15, depending on detailed wave conditions.

Keywords: unidirectional, vertical axis, wave energy converter, wave rotor

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Authors: Mustapha Kamel Mihoubi, Hocine Dahmani

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The purpose of work is to study the phenomenon of agitation of storm waves at basin caused by different directions of waves relative to the current provision thrown numerical model based on the equation in shallow water using Boussinesq model MIKE 21 BW. According to the diminishing effect of penetration of a wave optimal solution will be available to be reproduced in reduced model. Another alternative arrangement throws will be proposed to reduce the agitation and the effects of the swell reflection caused by the penetration of waves in the harbor.

Keywords: agitation, Boussinesq equations, combination, harbor

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Authors: Mahdi Hamzehei, Seyyed Amin Hakim, Nahid Taherian

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Fins play an important role in increasing the efficiency of compact shell and tube heat exchangers by increasing heat transfer. The objective of this paper is to determine the optimum fin wave angle, as one of the geometric parameters affecting the efficiency of the heat exchangers. To this end, finite volume method is used to model and simulate the flow in heat exchanger. In this study, computational fluid dynamics simulations of wave channel are done. The results show that the wave angle affects the temperature output of the heat exchanger.

Keywords: fin wave angle, tube, intercooler, optimum, performance

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