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Solitary Waves (solitary + wave)

Distribution by Scientific Domains

Mathematics and Statistics	47%
Engineering	41%
Physics and Astronomy	11%

Selected Abstracts

Numerical simulation of free-surface flow using the level-set method with global mass correction

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010
Yali Zhang
Abstract A new numerical method that couples the incompressible Navier,Stokes equations with the global mass correction level-set method for simulating fluid problems with free surfaces and interfaces is presented in this paper. The finite volume method is used to discretize Navier,Stokes equations with the two-step projection method on a staggered Cartesian grid. The free-surface flow problem is solved on a fixed grid in which the free surface is captured by the zero level set. Mass conservation is improved significantly by applying a global mass correction scheme, in a novel combination with third-order essentially non-oscillatory schemes and a five stage Runge,Kutta method, to accomplish advection and re-distancing of the level-set function. The coupled solver is applied to simulate interface change and flow field in four benchmark test cases: (1) shear flow; (2) dam break; (3) travelling and reflection of solitary wave and (4) solitary wave over a submerged object. The computational results are in excellent agreement with theoretical predictions, experimental data and previous numerical simulations using a RANS-VOF method. The simulations reveal some interesting free-surface phenomena such as the free-surface vortices, air entrapment and wave deformation over a submerged object. Copyright © 2009 John Wiley & Sons, Ltd. [source]

A level set characteristic Galerkin finite element method for free surface flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2005
Ching-Long Lin
Abstract This paper presents a numerical method for free surface flows that couples the incompressible Navier,Stokes equations with the level set method in the finite element framework. The implicit characteristic-Galerkin approximation together with the fractional four-step algorithm is employed to discretize the governing equations. The schemes for solving the level set evolution and reinitialization equations are verified with several benchmark cases, including stationary circle, rotation of a slotted disk and stretching of a circular fluid element. The results are compared with those calculated from the level set finite volume method of Yue et al. (Int. J. Numer. Methods Fluids 2003; 42:853,884), which employed the third-order essentially non-oscillatory (ENO) schemes for advection of the level set function in a generalized curvilinear coordinate system. The comparison indicates that the characteristic Galerkin approximation of the level set equations yields more accurate solutions. The second-order accuracy of the Navier,Stokes solver is confirmed by simulation of decay vortex. The coupled system of the Navier,Stokes and level set equations then is validated by solitary wave and broken dam problems. The simulation results are in excellent agreement with experimental data. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A meshless method using the radial basis functions for numerical solution of the regularized long wave equation

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2010
Ali Shokri
Abstract This article discusses on the solution of the regularized long wave (RLW) equation, which is introduced to describe the development of the undular bore, has been used for modeling in many branches of science and engineering. A numerical method is presented to solve the RLW equation. The main idea behind this numerical simulation is to use the collocation and approximating the solution by radial basis functions (RBFs). To avoid solving the nonlinear system, a predictor-corrector scheme is proposed. Several test problems are given to validate the new technique. The numerical simulation, includes the propagation of a solitary wave, interaction of two positive solitary waves, interaction of a positive and a negative solitary wave, the evaluation of Maxwellian pulse into stable solitary waves and the development of an undular bore. The three invariants of the motion are calculated to determine the conservation properties of the algorithm. The results of numerical experiments are compared with analytical solution and with those of other recently published methods to confirm the accuracy and efficiency of the presented scheme.© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source]

Cosine expansion-based differential quadrature algorithm for numerical solution of the RLW equation

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2010
dris Da
Abstract The differential quadrature method based on cosine expansion is applied to obtain numerical solutions of the RLW equation. The propagation of single solitary wave is studied to validate the efficiency of the algorithm. Then, test problems including interaction of two and three solitary waves, undulation, and evolution of solitary waves are implemented. Solutions are compared with earlier results. Discrete conservation quantities are computed for test experiments. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source]

Long-time dynamics of KdV solitary waves over a variable bottom

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 6 2006
Steven I. Dejak
We study the variable-bottom, generalized Korteweg,de Vries (bKdV) equation ,tu = ,,x(,u + f(u) , b(t,x)u), where f is a nonlinearity and b is a small, bounded, and slowly varying function related to the varying depth of a channel of water. Many variable-coefficient KdV-type equations, including the variable-coefficient, variable-bottom KdV equation, can be rescaled into the bKdV. We study the long-time behavior of solutions with initial conditions close to a stable, b = 0 solitary wave. We prove that for long time intervals, such solutions have the form of the solitary wave whose center and scale evolve according to a certain dynamical law involving the function b(t,x) plus an H1(,)-small fluctuation. © 2005 Wiley Periodicals, Inc. [source]

A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2003
K. Djidjeli
Abstract An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW). The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time. =10pt An important advantage to be gained from the use of this method, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized stability analysis, it is shown that the proposed method is unconditionally stable. The method is second order in time and all-order in space. The method presented here is for the RLW equation and its generalized form, but it can be implemented to a broad class of non-linear long wave equations (Equation (2)), with obvious changes in the various formulae. Test problems, including the simulation of a single soliton and interaction of solitary waves, are used to validate the method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Note on non-orthogonality of local curvilinear co-ordinates in a three-dimensional boundary element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2005
C. Fochesato
Abstract We give a more general derivation of the particle velocity and acceleration used in the numerical wave model of Grilli et al. (Int. J. Numer. Meth. Fluids 2001; 35:829,867), by expressing these quantities in a local orthogonal co-ordinate system. Computations of solitary waves propagating and breaking over a sloping bottom show that the new formulation gives better results than the former one in the latest stages of overturning. Nevertheless, both formulations are found to be as suitable for the simulation of non-overturning waves. Results on wave profiles as well as on surface and internal kinematics are presented. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Experimental and numerical analysis of solitary waves generated by bed and boundary movements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2004
L. Cea
Abstract This paper is an experimental and numerical study about propagation and reflection of waves originated by natural hazards such as sea bottom movements, hill slope sliding and avalanches. One-dimensional flume experiments were conducted to study the characteristics of such waves. The results of the experimental study can be used by other researchers to verify their numerical models. A finite volume numerical model, which solves the shallow water equations, was also verified using our own experimental results. In order to deal with reflection on sloping surfaces and overtopping walls, a new condition for the treatment of the coastline is suggested. The numerical simulation of wave generation is also studied considering the bed movement. A boundary condition is proposed for this case. Those situations when the shallow water equations are valid to simulate this type of phenomena have been studied, as well as their limitations. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Modelling solitons under the hydrostatic and Boussinesq approximations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003
Chris Daily
Abstract An examination of solitary waves in 3D, time-dependant hydrostatic and Boussinesq numerical models is presented. It is shown that waves in these models will deform and that only the acceleration term in the vertical momentum equation need be included to correct the wave propagation. Modelling of solitary waves propagating near the surface of a small to medium body of water, such as a lake, are used to illustrate the results. The results are also compared with experiments performed by other authors. Then as an improvement, an alternative numerical scheme is used which includes only the vertical acceleration term. Effects of horizontal and vertical diffusion on soliton wave structure is also discussed. Copyright © 2003 John Wiley & Sons, Ltd. [source]

A ,-coordinate three-dimensional numerical model for surface wave propagation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002
Pengzhi Lin
Abstract A three-dimensional numerical model based on the full Navier,Stokes equations (NSE) in , -coordinate is developed in this study. The , -coordinate transformation is first introduced to map the irregular physical domain with the wavy free surface and uneven bottom to the regular computational domain with the shape of a rectangular prism. Using the chain rule of partial differentiation, a new set of governing equations is derived in the , -coordinate from the original NSE defined in the Cartesian coordinate. The operator splitting method (Li and Yu, Int. J. Num. Meth. Fluids 1996; 23: 485,501), which splits the solution procedure into the advection, diffusion, and propagation steps, is used to solve the modified NSE. The model is first tested for mass and energy conservation as well as mesh convergence by using an example of water sloshing in a confined tank. Excellent agreements between numerical results and analytical solutions are obtained. The model is then used to simulate two- and three-dimensional solitary waves propagating in constant depth. Very good agreements between numerical results and analytical solutions are obtained for both free surface displacements and velocities. Finally, a more realistic case of periodic wave train passing through a submerged breakwater is simulated. Comparisons between numerical results and experimental data are promising. The model is proven to be an accurate tool for consequent studies of wave-structure interaction. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Tsunami generation and propagation from the Mjølnir asteroid impact

METEORITICS & PLANETARY SCIENCE, Issue 9 2007
S. Glimsdal
The geological structure resulting from the impact is today known as the Mjølnir crater. The present work attempts to model the generation and the propagation of the tsunami from the Mjølnir impact. A multi-material hydrocode SOVA is used to model the impact and the early stages of tsunami generation, while models based on shallow-water theories are used to study the subsequent wave propagation in the paleo-Barents Sea. We apply several wave models of varying computational complexity. This includes both three-dimensional and radially symmetric weakly dispersive and nonlinear Boussinesq equations, as well as equations based on nonlinear ray theory. These tsunami models require a reconstruction of the bathymetry of the paleo-Barents Sea. The Mjølnir tsunami is characteristic of large bolides impacting in shallow sea; in this case the asteroid was about 1.6 km in diameter and the water depth was around 400 m. Contrary to earthquake- and slide-generated tsunamis, this tsunami featured crucial dispersive and nonlinear effects: a few minutes after the impact, the ocean surface was formed into an undular bore, which developed further into a train of solitary waves. Our simulations indicate wave amplitudes above 200 m, and during shoaling the waves break far from the coastlines in rather deep water. The tsunami induced strong bottom currents, in the range of 30,90 km/h, which presumably caused a strong reworking of bottom sediments with dramatic consequences for the marine environment. [source]

Non-linear bending waves in Keplerian accretion discs

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2006
G. I. Ogilvie
ABSTRACT The non-linear dynamics of a warped accretion disc is investigated in the important case of a thin Keplerian disc with negligible viscosity and self-gravity. A one-dimensional evolutionary equation is formally derived that describes the primary non-linear and dispersive effects on propagating bending waves other than parametric instabilities. It has the form of a derivative non-linear Schrödinger (DNLS) equation with coefficients that are obtained explicitly for a particular model of a disc. The properties of this equation are analysed in some detail and illustrative numerical solutions are presented. The non-linear and dispersive effects both depend on the compressibility of the gas through its adiabatic index ,. In the physically realistic case , < 3, non-linearity does not lead to the steepening of bending waves but instead enhances their linear dispersion. In the opposite case , > 3, non-linearity leads to wave steepening and solitary waves are supported. The effects of a small effective viscosity, which may suppress parametric instabilities, are also considered. This analysis may provide a useful point of comparison between theory and numerical simulations of warped accretion discs. [source]

A meshless method using the radial basis functions for numerical solution of the regularized long wave equation

Cosine expansion-based differential quadrature algorithm for numerical solution of the RLW equation

Blowup for nonlinear wave equations describing boson stars

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2007
Jürg Fröhlich
We consider the nonlinear wave equation modeling the dynamics of (pseudorelativistic) boson stars. For spherically symmetric initial data, u0(x) , C (,3), with negative energy, we prove blowup of u(t, x) in the H1/2 -norm within a finite time. Physically this phenomenon describes the onset of "gravitational collapse" of a boson star. We also study blowup in external, spherically symmetric potentials, and we consider more general Hartree-type nonlinearities. As an application, we exhibit instability of ground state solitary waves at rest if m = 0. © 2007 Wiley Periodicals, Inc. [source]