2-D Numerical Wave Tank by Boundary Element Method Using Different Numerical Techniques

The traditional Boundary Element Method (BEM) is a collection of numerical techniques for solving some partial differential equations. The classical BEM produces a fully populated coefficients matrix. With Galerkin Boundary Element Method (GBEM) is possible to produce a symmetric coefficients matrix. The Fourier BEM is a more general numerical approach. To calculate the final matrix coefficients it is necessary to find the improper integrals. The article presents the method for calculation of such integrals.

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Application of Boundary Element Method for Determination of the Wavemaker Driving Signal

Volume 7B: Ocean Engineering ◽

10.1115/omae2018-77069 ◽

2018 ◽

Author(s):

Anatoliy Khait ◽

Lev Shemer

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Wave Train ◽

Amplitude Spectrum ◽

Surface Elevation ◽

Wave Tank ◽

Amplitude Spectra ◽

Wave Trains ◽

Driving Signal ◽

Element Method

Excitation of steep unidirectional broad-banded wave trains is studied numerically and experimentally. Iterative method is developed to adjust the driving signal of a paddle-type wavemaker to generate wave train with a prescribed free waves’ spectrum. Analytical post-processing procedure based on the Zakharov equation is applied to separate complex amplitude spectrum of the surface elevation into free and bound components, as required for the proposed method of the adjustment of the wavemaker driving signal. Numerical wave tank in the simulations was based on application of the Boundary Element Method. The results of numerical simulations were supported by measurements in a wave tank. The measured and the designed shapes of the surface elevation variation with time, as well as of the corresponding amplitude spectra were found to be in a good agreement.

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Application of Boundary Element Method for Determination of the Wavemaker Driving Signal

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.4042942 ◽

2019 ◽

Vol 141 (6) ◽

Cited By ~ 2

Author(s):

Anatoliy Khait ◽

Lev Shemer

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Wave Train ◽

Amplitude Spectrum ◽

Second Order ◽

Surface Elevation ◽

Frequency Spectra ◽

Wave Tank ◽

Driving Signal ◽

Element Method

A method for the generation of steep nonlinear broad-banded wave trains having an arbitrary prescribed shape is developed. It is shown that the second-order contributions to the velocity field are negligible in deep water, while the second-order bound components of the surface elevation are significant. This fact allows improvement of an iterative method of the wavemaker driving signal adjustment that increases the accuracy of excitation of wave train with the prescribed free waves’ spectrum. The decomposition of the complex amplitude spectrum of the surface elevation into free and bound components is based on the approach adopted in the derivation of the Zakharov model. The iterative adjustment of the driving signal is carried out using the numerical wave tank based on the boundary element method. It is demonstrated that accurate wave train excitation is attained for different values of the wave steepness. The method allows decreasing the number of iterations needed for the driving signal adjustment. The surface elevation values measured in the laboratory wave tank agree closely with those obtained in the numerical simulations. The measured and the simulated frequency spectra are in agreement as well.

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