Home About us Contact
|
Home About us Contact | ||
|
|
||
Water Waves (water + wave)
Selected AbstractsBoundary Perturbation Methods for Water WavesGAMM - MITTEILUNGEN, Issue 1 2007David P. Nicholls Abstract The most successful equations for the modeling of ocean wave phenomena are the free,surface Euler equations. Their solutions accurately approximate a wide range of physical problems from open,ocean transport of pollutants, to the forces exerted upon oil platforms by rogue waves, to shoaling and breaking of waves in nearshore regions. These equations provide numerous challenges for theoreticians and practitioners alike as they couple the difficulties of a free boundary problem with the subtle balancing of nonlinearity and dispersion in the absence of dissipation. In this paper we give an overview of, what we term, "Boundary Perturbation" methods for the analysis and numerical simulation of this "water wave problem". Due to our own research interests this review is focused upon the numerical simulation of traveling water waves, however, the extensive literature on the initial value problem and additional theoretical developments are also briefly discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Three-dimensional travelling gravity-capillary water wavesGAMM - MITTEILUNGEN, Issue 1 2007M. D. Groves [source] Boundary Perturbation Methods for Water WavesGAMM - MITTEILUNGEN, Issue 1 2007David P. Nicholls Abstract The most successful equations for the modeling of ocean wave phenomena are the free,surface Euler equations. Their solutions accurately approximate a wide range of physical problems from open,ocean transport of pollutants, to the forces exerted upon oil platforms by rogue waves, to shoaling and breaking of waves in nearshore regions. These equations provide numerous challenges for theoreticians and practitioners alike as they couple the difficulties of a free boundary problem with the subtle balancing of nonlinearity and dispersion in the absence of dissipation. In this paper we give an overview of, what we term, "Boundary Perturbation" methods for the analysis and numerical simulation of this "water wave problem". Due to our own research interests this review is focused upon the numerical simulation of traveling water waves, however, the extensive literature on the initial value problem and additional theoretical developments are also briefly discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A viscoelastic model for the dynamic response of soils to periodical surface water disturbanceINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2006P. C. Hsieh Abstract In many instances soils can be assumed to behave like viscoelastic materials during loading/unloading cycles, and this study is aimed at setting up a viscoelastic model to investigate the dynamic response of a porous soil layer of finite thickness under the effect of periodically linear water waves. The waves and homogeneous water are described by potential theory and the porous material is described by a viscoelastic model, which is modified from Biot's poroelastic theory (1956). The distributions of pore water pressures and effective stresses of various soils such as silt, sand, and gravel are demonstrated by employing the proposed viscoelastic model. The discrepancies of the dynamic response between the simulations of viscoelastic model and elastic model are found to be strongly dependent on the wave frequency. Copyright © 2006 John Wiley & Sons, Ltd. [source] Transient deformation of a poroelastic channel bedINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2002P.C. Hsieh Abstract The coupled transient response of a poroelastic bed form due to stream flow and non-linear water waves is investigated numerically. The theory of potential flow is applied to channel flow while Biot's theory of poroelasticity (J. Appl. Phys. 1962; 33(4):1482) is adopted to deal with the deformable porous bed. A boundary-fitted co-ordinate system is used to calculate the variation in the bed form. The result of a simple periodic wave form over a soft poroelastic bed agrees well with the analytical solution of Hsieh et al. (J. Eng. Mech., ASCE 2000; 126(10):1064). However, due to the rapidly damping second dilatational wave inside the soft poroelastic bed, the solution for transient bed form near the interface is not easy to compute accurately. In order to overcome this difficulty, a simplified numerical model based on the boundary layer correction concept proposed by Hsieh et al. (2000) is established, which neglects Darcy's terms. The transient deformation of an irregular poroelastic bed that includes a trench and a downward step at the channel bed is simulated successfully. Copyright © 2002 John Wiley & Sons, Ltd. [source] Dynamic response of soft poroelastic bed to linear water waves,a boundary layer correction approachINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2001Ping-Cheng Hsieh Abstract According to Chen et al. (Journal of Engineering Mechanics, ASCE 1997; 123(10):1041,1049.) a boundary layer exists within the porous bed and near the homogeneous-water/porous-bed interface when oscillatory water waves propagate over a soft poroelastic bed. This boundary layer makes the evaluation of the second kind of longitudinal wave inside the soft poroelastic bed very inaccurate. In this study, the boundary layer correction approach for the poroelastic bed is applied to the boundary value problem of linear oscillatory water waves propagating over a soft poroelastic bed. After the analyses of length scale and order of magnitude of physical variables are done, a perturbation expansion for the boundary layer correction approach based on two small parameters is proposed and solved. The solutions are carried out for the first and third kind of waves throughout the entire domain. The second kind of wave which disappears outside the boundary layer is solved systematically inside the boundary layer. The results are compared with the linear wave solutions of Huang and Song (Journal of Engineering Mechanics, ASCE 1993; 119:1003,1020.) to confirm the validity. Moreover, a simplified boundary layer correction formulation which is expected to be very useful in numerical computation is also proposed. Copyright © 2001 John Wiley & Sons, Ltd. [source] Numerical simulation of pollutant transport acted by wave for a shallow water sea bayINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2006Sun Tao Abstract A numerical model of pollutant transport acted by water waves on a shallow-water mild-slope beach is established in this study. The numerical model is combined with a wave propagation model, a multiple wave-breaking model, a wave-induced current model and a pollutant convection,dispersion model. The wave propagation model is based on the higher-order approximation of parabolic mild-slope equation which can be used to simulate the wave refraction, diffraction and breaking in a large area of near-shore zone combined with the wave-breaking model. The wave-induced current model is established using the concept of the radiation stress and considering the effect of bottom resistance caused by waves. The numerical model is verified by laboratory experiment results of regular and irregular waves over two mild beaches with different slopes. The numerical results agree well with experimental results. The numerical model has been applied in the near-shore zone of Bohai bay in China. It is concluded that pollutant transport parallel to the shoreline due to the action of waves, which will induce serious pollution on the beach. Copyright © 2005 John Wiley & Sons, Ltd. [source] Further experiences with computing non-hydrostatic free-surface flows involving water wavesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2005Marcel Zijlema Abstract A semi-implicit, staggered finite volume technique for non-hydrostatic, free-surface flow governed by the incompressible Euler equations is presented that has a proper balance between accuracy, robustness and computing time. The procedure is intended to be used for predicting wave propagation in coastal areas. The splitting of the pressure into hydrostatic and non-hydrostatic components is utilized. To ease the task of discretization and to enhance the accuracy of the scheme, a vertical boundary-fitted co-ordinate system is employed, permitting more resolution near the bottom as well as near the free surface. The issue of the implementation of boundary conditions is addressed. As recently proposed by the present authors, the Keller-box scheme for accurate approximation of frequency wave dispersion requiring a limited vertical resolution is incorporated. The both locally and globally mass conserved solution is achieved with the aid of a projection method in the discrete sense. An efficient preconditioned Krylov subspace technique to solve the discretized Poisson equation for pressure correction with an unsymmetric matrix is treated. Some numerical experiments to show the accuracy, robustness and efficiency of the proposed method are presented. Copyright © 2004 John Wiley & Sons, Ltd. [source] Numerical solutions of fully non-linear and highly dispersive Boussinesq equations in two horizontal dimensionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2004David R. Fuhrman Abstract This paper investigates preconditioned iterative techniques for finite difference solutions of a high-order Boussinesq method for modelling water waves in two horizontal dimensions. The Boussinesq method solves simultaneously for all three components of velocity at an arbitrary z -level, removing any practical limitations based on the relative water depth. High-order finite difference approximations are shown to be more efficient than low-order approximations (for a given accuracy), despite the additional overhead. The resultant system of equations requires that a sparse, unsymmetric, and often ill-conditioned matrix be solved at each stage evaluation within a simulation. Various preconditioning strategies are investigated, including full factorizations of the linearized matrix, ILU factorizations, a matrix-free (Fourier space) method, and an approximate Schur complement approach. A detailed comparison of the methods is given for both rotational and irrotational formulations, and the strengths and limitations of each are discussed. Mesh-independent convergence is demonstrated with many of the preconditioners for solutions of the irrotational formulation, and solutions using the Fourier space and approximate Schur complement preconditioners are shown to require an overall computational effort that scales linearly with problem size (for large problems). Calculations on a variable depth problem are also compared to experimental data, highlighting the accuracy of the model. Through combined physical and mathematical insight effective preconditioned iterative solutions are achieved for the full physical application range of the model. Copyright © 2004 John Wiley & Sons, Ltd. [source] Absorbing boundary condition on elliptic boundary for finite element analysis of water wave diffraction by large elongated bodiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2001Subrata Kumar Bhattacharyya Abstract In a domain method of solution of exterior scalar wave equation, the radiation condition needs to be imposed on a truncation boundary of the modelling domain. The Bayliss, Gunzberger and Turkel (BGT) boundary dampers of first- and second-orders, which require a circular cylindrical truncation boundary in the diffraction-radiation problem of water waves, have been particularly successful in this task. However, for an elongated body, an elliptic cylindrical truncation boundary has the potential to reduce the modelling domain and hence the computational effort. Grote and Keller [On non-reflecting boundary conditions. Journal of Computational Physics 1995; 122: 231,243] proposed extension of the first- and second-order BGT dampers for the elliptic radiation boundary and used these conditions to the acoustic scattering by an elliptic scatterer using the finite difference method. In this paper, these conditions are implemented for the problem of diffraction of water waves using the finite element method. Also, it is shown that the proposed extension works well only for head-on wave incidence. To remedy this, two new elliptic dampers are proposed, one for beam-on incidence and the other for general wave incidence. The performance of all the three dampers is studied using a numerical example of diffraction by an elliptic cylinder. Copyright © 2001 John Wiley & Sons, Ltd. [source] Stability properties of steady water waves with vorticityCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 6 2007Adrian Constantin We present two stability analyses for exact periodic traveling water waves with vorticity. The first approach leads in particular to linear stability properties of water waves for which the vorticity decreases with depth. The second approach leads to a formal stability property for long water waves that have small vorticity and amplitude although we do not use a small-amplitude or long-wave approximation. © 2006 Wiley Periodicals, Inc. [source] Exact steady periodic water waves with vorticityCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 4 2004Adrian Constantin We consider the classical water wave problem described by the Euler equations with a free surface under the influence of gravity over a flat bottom. We construct two-dimensional inviscid periodic traveling waves with vorticity. They are symmetric waves whose profiles are monotone between each crest and trough. We use bifurcation and degree theory to construct a global connected set of such solutions. © 2003 Wiley Periodicals, Inc. [source] | |||||||||||||