A fully non-linear model for three-dimensional overturning waves over an arbitrary bottom

Grilli, Stéphan T.; Guyenne, Philippe; Dias, Frédéric

doi:10.1002/1097-0363(20010415)35:7<829::aid-fld115>3.0.co;2-2

Cited by 250 publications

(283 citation statements)

References 30 publications

(67 reference statements)

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“…Here, we use an auxiliary BIE to find a more accurate approach. As proposed by Dombre et al [3,33], an analogous BIE for ψ = ∂φ/∂t can be considered. This auxiliary BIE does not increase significantly the computational cost because the discretization is the same as in the main BIE.…”

Section: Hydrodynamic Pressurementioning

confidence: 99%

“…Therefore, to obtain the temporal evolution of the free surface, a temporal integration scheme is needed. In the context of strong non-linear gravity waves, several schemes has been proposed [3,29,71,90]. In this study, we use the the standard 4th order Runge Kutta method (RK4), which has been shown to be numerically stable and accurate.…”

Section: Time Marchingmentioning

confidence: 99%

“…For periodic wave problems the time step is usually chosen as a fraction of the wave period such that the physical phenomenon is represented accurately [71]. For a solitary wave, Grilli et al [3] proposed an adaptive time steeping method as a function of the spatial discretization and the Courant number, C (Eq. 40).…”

Section: Time Marchingmentioning

confidence: 99%

“…These models have been applied to simulated tsunami generation and [1] overturning waves [2][3][4], to design breakwaters [5,6], to predict the wave pressure impact on structures [7], or to study radiation and diffraction waves produced by a wave-maker [8][9][10][11]. Nowadays, because of the increasing interest on the ocean renewable energy, in which the generation systems are installed near-shore or off-shore, new applications of such models are being used to study the fluid-structure interaction considering the effect of the waves [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…It is worth to mention the studies reported by Grilli et al [2,24,25] who developed an advanced approach using 2D high order BEM. Later, Grilli et al [3] and Guyenne and Grilli [4] extended the model to three-dimensional (3D) geometries to analyse overturning waves over an arbitrary bottom.…”

Section: Introductionmentioning

confidence: 99%

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A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

Maestre¹,

Pallarès²,

Cuesta³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. In this paper we describe a three-dimensional Isogeometric BEM in the time domain based on the T-spline and Non Uniform Rational B-Splines (NURBS) basis to study the free surface behavior. Traditionally, the Lagrange polynomials have been used to discretize the geometry and the BEMs variables. The Lagrange basis are discontinues across the elements although the physical variables are continuous. In dynamics problems with high mesh distortions this approach can produce numerical instabilities that can be quickly propagated. This problem could be overcome using T-spline or NURB basis. The main advantages of this approach are: (1) the control of the continuity and smoothness of the T-spline and NURBS basis, which makes the model numerically stable without the need of artificial smooth techniques;(2) the high order geometrical approximation by non-rational splines;(3) the refinement capabilities without affecting the geometry and BEM's variables; and (4) the direct integration with computer aid geometrical design tools. We use the concept of the Bézier extraction operation which provides an element point of view of the T-Spline and NURBS similar to the traditional finite element. The boundary integral Equation is solved at each time step by the GMRES algorithm and the time marching scheme is performed with a fourth-order Runge-Kutta method to update the model. Additionally, the hydrodynamic force is calculated by an auxiliary boundary equation. Some numerical benchmark examples are analysed to show the accuracy and the stability of the method 7967 J. Maestre, J. Pallarés and I. Cuesta

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Section: Hydrodynamic Pressurementioning

confidence: 99%

Section: Time Marchingmentioning

confidence: 99%

Section: Time Marchingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

Maestre¹,

Pallarès²,

Cuesta³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Phase‐Resolving Wave Modeling

Chalikov

2017

Encyclopedia of Maritime and Offshore Engineering

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Phase‐resolving modeling of sea waves is the mathematical modeling of surface waves including explicit reproduction of the sea surface and velocity field evolution. The general approach is based on equation of potential motion with a free boundary. Conformal transformation of coordinates is the most effective method of solution of two‐dimensional ( x–z ) periodic problem. For three dimensional models, several different approaches have been developed: boundary integral equation method (BIEM), method based on expansion of velocity potential in a vicinity of surface [high order spectral method (HOSM)], and method based on direct solution of three‐dimensional equation for velocity potential. These methods do not compete with each other because all of them have their advantages. The brief descriptions of each method are given as well as the examples of theirs applications. The investigations of nonperiodic problems are based on a direct solution of equation for velocity potential. The methods of including in the models of algorithms for parameterization of energy input and dissipation are discussed.

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Meshless numerical simulation for fully nonlinear water waves

Tsay

Young

2005

Numerical Methods in Fluids

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SUMMARYA meshless numerical model for nonlinear free surface water wave is presented in this paper. An approach of handling the moving free surface boundary is proposed. Using the fundamental solution of the Laplace equation as the radial basis functions and locating the source points outside the computational domain, the problem is solved by collocation of only a few boundary points. Present model is ÿrst applied to simulate the generation of periodic ÿnite-amplitude waves with high wave-steepness and then is employed to simulate the modulation of monochromatic waves passing over a submerged obstacle. Good agreements are observed as compared with experimental data and other numerical models.

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A fully non-linear model for three-dimensional overturning waves over an arbitrary bottom

Cited by 250 publications

References 30 publications

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

Phase‐Resolving Wave Modeling

Meshless numerical simulation for fully nonlinear water waves

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