Comparisons of Computational and Experimental Results of Solitary Wave Breaking

In this paper, the solitary wave deformation along a gentle slope and the impact pressure, on the wall are investigated experimentally and the results are compared with numerical results obtained based on the volume of fluid (VOF) method. The topography used in the experiment consists of three segments. The left segment is a 1:4 slope, the middle segment 1 :SO slope and the right segment a horizontal bed. Both the wave heights and breaking points obtained from numerical simulation and experiments are in good agreement. Numerical results give reasonable pressure distributions of breaking waves on the wall.

Numerical simulation of solitary and random wave propagation through vegetation based on VOF method

A vertical two-dimensional numerical model has been applied to solving the Reynolds Averaged Navier- Stokes （RANS} equations in the simulation of current and wave propagation through vegetated and non- vegetated waters. The k-e model is used for turbulence closure of RANS equations. The effect of vegeta- tion is simulated by adding the drag force of vegetation in the flow momentum equations and turbulence model. To solve the modified N-S equations, the finite difference method is used with the staggered grid system to solver equations. The Youngs＇ fractional volume of fluid （VOF） is applied tracking the free sur- face with second-order accuracy. The model has been tested by simulating dam break wave, pure current with vegetation, solitary wave runup on vegetated and non-vegetated channel, regular and random waves over a vegetated field. The model reasonably well reproduces these experimental observations, the model- ing approach presented herein should be useful in simulating nearshore processes in coastal domains with vegetation effects.

Shoaling Internal Solitary Waves and the Formation of Boluses

An internal solitary wave of elevation in a two-layer density stratified system of an incompressible, viscous and homogeneous fluid was studied. The run-up of a wave of elevation encountering different slopes was investigated numerically based on solving the continuity, Navier-Stokes and convective-diffusion equations within the Boussinesq approximation. The commercial software COMSOL Multiphysics was used to conduct the numerical simulations. For gradual shoals, a bolus formed that transported dense fluid up the shoal. The bolus disappeared when it reached its maximum height on the slope due to the draining of the dense fluid. Various shoal angles were simulated to detect the critical angle above which a bolus does not form. An angle of 30 or less resulted in the formation of a bolus. In addition, the simulations demonstrated that the size of the bolus induced by shallower slopes was larger and that the vertical height traveled by the bolus was insensitive to the slope of the shoal.

RANS-VOF Solver for Solitary Wave Run-up on A Circular Cylinder

Simulation of solitary wave run-up on a vertical circular cylinder is carried out in a viscous numerical wave tank developed based on the open source codes Open FOAM. An incompressible two-phase flow solver naoe-FOAM-SJTU is used to solve the Reynolds-Averaged Navier–Stokes（RANS） equations with the SST k ？？ turbulence model. The PISO algorithm is utilized for the pressure-velocity coupling. The air-water interface is captured via Volume of Fluid（VOF） technique. The present numerical model is validated by simulating the solitary wave run-up and reflected against a vertical wall, and solitary wave run-up on a vertical circular cylinder. Comparisons between numerical results and available experimental data show satisfactory agreement. Furthermore, simulations are carried out to study the solitary wave run-up on the cylinder with different incident wave height H and different cylinder radius a. The relationships of the wave run-up height with the incident wave height H, cylinder radius a are analyzed. The evolutions of the scattering free surface and vortex shedding are also presented to give a better understanding of the process of nonlinear wave-cylinder interaction.

Numerical simulation of solitary wave propagation based on MPS method

The concept of candidate particle set is introduced in the MPS gridless numerical method to generate neighboring particle set ma- trix, which can reduce the CPU time to 1/11 of that before introduction. The Bi-CGSTAB （bi-conjugate gradient stabilized） algorithm is applied to solving the Poisson pressure equation, by which the solving speed is significantly accelerated. The process of solitary waves propagating over a numerical flume and interacting with a vertical wall is simulated. The simulated results of water surface elevation are in good agreement with the analytical solution as well as the measured data. The predicted maximum values of the run-up of solitary waves with various relative incident wave heights agree well with the measured results.

MPS Method for Interaction Between Solitary Waves and Submerged Horizontal Plate

The interaction between structure and wave is a typical phenomenon in naval architecture and ocean engineering.In this paper,numerical simulation is carried out to study the interaction between a two-dimensional submerged,fixed,horizontal rigid plate and solitary wave with our in-house meshless particle CFD solver MLParticle-SJTU.First,the in-house CFD solver is verified by experimental results conducted at the State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology.During the verification,the plate is submerged under water and the solitary wave with a given amplitude is generated by a piston-type wave maker.Free surface elevation of the wave and the pressure impacting on the plate is recorded and compared with experimental data respectively.The predicted pressure and surface elevation agree well with the experimental results.Then in order to further investigate factors affecting wave-structure interaction,wave height,submerged depth and plate length are analyzed.

A polynomial Expansion Method and New General Solitary Wave Solutions to KS Equation

Using a polynomial expansion method, the general exact solitary wave solution and singular one areconstructed for the non-linear KS equation. This approach is obviously applicable to a large variety of nonlinear evolution equation.

Numerical Study on Breaking Criteria for Solitary Waves

Studies of the breaking criteria for solitary waves on a slope are presented in this paper. The boundary element method is used to model the processes of shoaling and breaking of solitary waves on various slopes. Empirical formulae that can be used to characterize the breaking of solitary waves are presented. These include the breaking index, the wave height, the water depth, and the maximum particle velocity at the point of breaking. Comparisons with the results of other researches are given.

Solitary Wave Solutions of Discrete Complex Ginzburg-Landau Equation by Modified Adomian Decomposition Method

In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method （mADM）, which is an efficient method and does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions are also compared with their corresponding analytical solutions. It is shown that a very good approximation is achieved with the analytical solutions. Finally, the modulational instability is investigated and the corresponding condition is given.

Breaking of Solitary Waves on Uniform Slopes

The propagation, shoaling and breaking of solitary waves on mild slopes are simulated by boundary element method. In this paper, the criterion of breaking solitary waves on mild slopes is discussed. The criterion is that the ratio of horizontal velocity of water particles on the wave crest to wave celerity equals one. However, the case that the ratio of horizontal velocity of water particles on the wave crest to wave celerity is below one but the front face of wave profile becomes vertical is also considered as a breaking criterion. According to the above criteria, the breaking index for slopes 1:10 to 1:25 is studied. The result is compared to other researchers'. The deformation of solitary waves on slopes is discussed and the distribution of fluid velocities at breaking is shown.

Simulations of solitary waves of RLW equation by exponential B-spline Galerkin method

In this paper, an approximate function for the Galerkin method is composed using the combination of the exponential B-spline functions. Regularized long wave equation （RLW） is integrated fully by using an exponential B-spline Galerkin method in space together with Crank-Nicolson method in time. Three numerical examples related to propagation of sin- gle solitary wave, interaction of two solitary waves and wave generation are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.

INTERACTION OF A SOLITARY WAVE AND A FRONT STEP SIMULATED BY LEVEL SET METHOD

As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been investigated. By using the Level Set method, the transformation of a solitary wave over a front step was simulated. The results were in good agreement with laboratory experiments.

Dispersive propagation of optical solitions and solitary wave solutions of Kundu-Eckhaus dynamical equation via modified mathematical method

In this research work,we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus(KE)equation with the help of modified mathematical method.We obtained the solutions in the form of dark solitons,bright solitons and combined dark-bright solitons,travelling wave and periodic wave solutions with general coefficients.In our knowledge earlier reported results of the KE equation with specific coefficients.These obtained solutions are more useful in the development of optical fibers,dynamics of solitons,dynamics of adiabatic parameters,dynamics of fluid,problems of biomedical,industrial phenomena and many other branches.All calculations show that this technique is more powerful,effective,straightforward,and fruitfulness to study analytically other higher-order nonlinear complex PDEs involves in mathematical physics,quantum physics,Geo physics,fluid mechanics,hydrodynamics,mathematical biology,field of engineering and many other physical sciences.

An Irregular Wave Maker of Active Absorption with VOF Method

A numerical irregular wave flume with active absorption of re-reflected waves is simulated by use of volume of fluid （VOF） method. An active ＇absorbing wave-maker based on linear wave theory is set on the left boundary of the wave flume. The progressive waves and the absorbing waves are generated simultaneously at the active wave generating-absorbing boundary. The absorbing waves are generated to eliminate the waves coming back to the generating boundary due to reflection from the outflow boundary and the structures. SIRW method proposed by Frigaard and Brorsen （1995） is used to separate the incident waves and reflected waves. The digital filters are designed based on the surface elevation signals of the two wave gauges. The corrected velocity of the wave-maker paddle is the output from the digital filter in real time. The numerical results of regular and irregular waves by the active absorbing-generating boundary are compared with the numerical results by the ordinary generating boundary to verify the performance of the active absorbing-generator boundary. The differences between the initial incident waves and the estimated incident waves are analyzed.

Numerical Simulation of the Solitary Wave Interacting with an Elastic Structure Using MPS-FEM Coupled Method

Fluid-Structure Interaction(FSI) caused by fluid impacting onto a flexible structure commonly occurs in naval architecture and ocean engineering. Research on the problem of wave-structure interaction is important to ensure the safety of offshore structures. This paper presents the Moving Particle Semi-implicit and Finite Element Coupled Method(MPS-FEM) to simulate FSI problems. The Moving Particle Semi-implicit(MPS) method is used to calculate the fluid domain, while the Finite Element Method(FEM) is used to address the structure domain. The scheme for the coupling of MPS and FEM is introduced first. Then, numerical validation and convergent study are performed to verify the accuracy of the solver for solitary wave generation and FSI problems. The interaction between the solitary wave and an elastic structure is investigated by using the MPS-FEM coupled method.

Generation and Deformation of Solitary Waves

Base on the Lagrangian description and finite differencing of the time step, the generation, propagation and deformation of solitary waves are simulated numerically by means of boundary element method. An algorithm to generate waves with any prescribed form is also implanted in the scheme, but in this research, solitary waves are studied. The numerical model is first verified by studying the case of a solitary wave impinging against a vertical wall. Time histories of evolution of a soliton running up on a sloping beach, as well as over a submerged obstacle are then presented. Applications to scattering problems due to solitary waves progressing over a slope onto a shelf are also shown.

Numerical investigation of solitary wave action on tworectangular boxes with a narrow gap

Based on the time-domain higher-order boundary element method(HOBEM), a two-dimensional numerical wave flume is developed to investigate solitary wave interaction with two rectangular boxes with a narrow gap.In the numerical model, the fully nonlinear boundary conditions are satisfied on the free surface, the mixed Eulerian-Lagrangian method is adopted to track the transient water surface and the fourth-order Runga-Kutta method is used to predict the velocity potential and wave elevation on the free surface. The acceleration potential technique is used to compute the transient wave forces along the wetted object surface. A piston-type wavemaker is used to generate solitary waves. The proposed model is validated by comparing the simulated wave run-up and the wave loads with the published experimental and numerical results of the reflection of a solitary wave from a vertical wall. Then, numerical experiments are performed to study the effects of the narrow gap and the size of each box on the wave run-ups at the two sides of the two-box system and in the narrow gap between two boxes, and the wave loads on the two boxes. The interaction between double solitary waves with a time interval between them with a two-box system is also investigated.

Modeling the interaction of an internal solitary wave with a sill

A nonhydrostatic numerical model was developed and numerical experiments performed on the interaction of an internal solitary wave （ISW） with a sill, for a two-layer fluid with a diffusive interface. Based on the blocking parameter （Br）, the flow was classified into three cases： （1） when bottom topography has little influence on the propagation and spatial structure of the ISW （Br〈0.5）, （2） where the ISW is distorted significantly by the blocking effect of the topography （though no wave breaking occurs, （0.5〈Br〈0.7）, and （3） where the ISW is broken as it encounters and passes over the bottom topography （0.7〈Br）. The numerical results obtained here are consistent with those obtained in laboratory experiments. The breaking process of the incident ISW when Br=0.7 was completely reproduced. Dissipation rate was linearly related to the blocking parameter when B,〈0.7, and the maximum dissipation rate could reach about 34% as Br raised to about 1.0. After that, instead of breaking, more reflection happened. Similarly, breaking induced mixing was also most effective during Br around 1.0, and can be up to 0.16.

THE DIFFRACTION OF A SOLITARY WAVE BY A CIRCULAR CYLINDER

This paper contributes to the diffraction of a solitary Wave by a cylinder, governed by the Boussinesq eq. The Spectrum Method is used to transform 2-D eqs. into a set of 1-D eqs., which is solved by F. D. M. The example given in the paper shows that this method is both accurate and cost ef- fective.

Developing Serpent-Type Wave Generators to Create Solitary Wave Simulations with BEM

Developing serpent-type wave generators to generate solitary waves in a 3D-basin was investigated in this study. Based on the Lagrangian description with time-marching procedures and finite differences of the time derivative, a 3D multiple directional wave basin with multidirectional piston wave generators was developed to simulate ocean waves by using BEM with quadrilateral elements, and to simulate wave-caused problems with fully nonlinear water surface conditions. The simulations of perpendicular solitary waves were conducted in the first instance to verify this scheme. Furthermore, the comparison of the waveform variations confirms that the estimation of 3D solitary waves is a feasible scheme.