A numerical study of nonlinear wave interaction in regular and irregular seas: irrotational Green–Naghdi model

Kim, Jang Whan; Ertekin, R. Cengiz

doi:10.1016/s0951-8339(00)00015-0

Cited by 33 publications

(13 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The main difficulty which arises in the dispersive case is handling of high order (possibly mixed) derivatives. The SGN system is an archetype of such systems with sufficient degree of nonlinearity and practically important applications in Coastal Engineering [96].…”

Section: Methodsmentioning

confidence: 99%

Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space

Khakimzyanov¹,

Dutykh²,

Gusev³

et al. 2018

CICP

View full text Add to dashboard Cite

In this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE-GREEN-NAGHDI (SGN) celebrated model. Namely, our scheme is based on reliable finite volume methods, proven to be very efficient for the hyperbolic part of equations. The particularity of our study is that we develop an adaptive numerical model using moving grids. Moreover, we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a linear elliptic equation. Moreover, this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed (numerical) problem.

show abstract

Section: Methodsmentioning

confidence: 99%

Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space

Khakimzyanov¹,

Dutykh²,

Gusev³

et al. 2018

CICP

View full text Add to dashboard Cite

show abstract

“…In this theory, the fluid is assumed to be incompressible and inviscid, although viscosity of the fluid is not a constraint in the general form of the theory. No assumption of irrotationality of the flow is made, even though such assumption may be made to develop a specialized form of the equations, known as Irrotational Green-Naghdi equations, see Kim and Ertekin (2000) and Kim et al (2001).…”

Section: The Level I Green-naghdi Equationsmentioning

confidence: 99%

Vulnerability assessment of coastal bridges on Oahu impacted by storm surge and waves

et al. 2015

View full text Add to dashboard Cite

Vulnerability assessment of four selected prototype coastal bridges on the island of Oahu, Hawaii, to the combination of storm surge and waves is presented. The maximum storm surge condition is estimated by considering an extensive series of simulated hurricanes making landfall on the island of Oahu, where the bridges are located. For the given extreme environmental conditions, wave loads on the deck of the selected bridges are calculated by use of several theoretical and computational approaches, including Euler's equations (OpenFOAM), the Green-Naghdi nonlinear equations, linear long-wave approximation and existing simplified, design-type force equations. Multiple scenarios of the relative location of the bridge deck and the still-water level are studied to determine the maximum possible wave loads on the bridge decks. Vulnerability of the coastal bridges to storm wave loads is determined by comparing the capacity of the bridge to the wave-induced loads on the structure.

show abstract

“…However, they are still computationally expensive, thus barely applied so far to model waves in a scale of hundred wave lengths and thousand wave periods. Another category of the fully nonlinear potential methods is based on or associated with the Fast Fourier Transform (FFT), e.g., FFT mixed method [14][15][16], Irrotational Green-Naghdi model [17], Higher-Order Spectral (HOS) method [18,19], Spectral Continuation method [20], Spectral Boundary Integral method [21][22][23][24] and Enhanced Spectral Boundary Integral (ESBI) method [25]. This class of models is relatively faster but still needs significant amount of time.…”

Section: Introductionmentioning

confidence: 99%

Numerical study on the quantitative error of the Korteweg–de Vries equation for modelling random waves on large scale in shallow water

Wang

Yan

et al. 2018

European Journal of Mechanics - B/Fluids

View full text Add to dashboard Cite

The Korteweg-de Vries (KdV) equation is often adopted to simulate phase-resolved random waves on large scale in shallow water. It shows that the KdV equation is computationally efficient and can give sufficiently accurate results, but it is not always suitable and the error by using it cannot be predicted. This paper attempts to give the quantitative formulas for estimating the error of the statistics when simulating random waves in shallow water by using it. The formulas are obtained by fitting the errors of the KdV equation in comparison with the fully nonlinear model using the same initial condition based on the Wallops spectrum with a wide range of parameters. This paper also demonstrates how the formulas would be used, e.g., to estimate the error of the results by using the KdV model, or to justify its suitability for modelling random waves on large scale in shallow water.

show abstract

A numerical study of nonlinear wave interaction in regular and irregular seas: irrotational Green–Naghdi model

Cited by 33 publications

References 10 publications

Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space

Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space

Vulnerability assessment of coastal bridges on Oahu impacted by storm surge and waves

Numerical study on the quantitative error of the Korteweg–de Vries equation for modelling random waves on large scale in shallow water

Contact Info

Product

Resources

About