Computation of Second-Order Wave Forces With a Panel-Free Method

2008 ◽  
Author(s):  
Hongxuan Peng ◽  
Wei Qiu
Keyword(s):  
Integral Equation ◽  
Body Surface ◽  
Near Field ◽  
Gaussian Quadrature ◽  
Boundary Integral ◽  
The Body ◽  
Computational Method ◽  
Wave Forces ◽  
Surface Green Function ◽  
Wave Drift Forces

Wave drift forces on floating structures have been computed based on the near-field formulation and a panel-free method. The singular-free boundary integral equation is developed by removing the singularity in the free-surface Green function. The desingularized integral equation is then discretized by Gaussian quadrature over the exact geometry. The Gaussian points coincide with the collocation points. NURBS surfaces are employed to represent the exact body surface. No panelization of the body surface is required. Accuracy of the solution can be enhanced by changing the number of Gaussian points. For illustration, the computational method was applied to a floating hemisphere and a floating box in waves.

Computation of Wave-Body Interactions Using the Panel-Free Method and Exact Geometry

2006 ◽  
Vol 128 (1) ◽  
pp. 31-38 ◽  
Author(s):  
W. Qiu ◽  
H. Peng ◽  
J. M. Chuang
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Body Surface ◽  
Analytical Description ◽  
Finite Depth ◽  
Boundary Integral ◽  
The Body ◽  
Floating Bodies ◽  
Wigley Hull ◽  
The Time Domain

A panel-free method was developed earlier to solve the radiation and the diffraction problems of floating bodies in waves in the time domain. This method has been extended to compute wave interactions with bodies in water of infinite depth and finite depth in the frequency domain. After removing the singularities in the boundary integral equation and representing the body surface exactly by either analytical description or NURBS surfaces, the boundary integral equation can be discretized over the exact body surface by Gaussian quadratures. Accuracy of the method is demonstrated by its application to the radiation and the diffraction problems of a floating hemisphere, a vertically floating axisymmetric cylinder, and a Wigley hull. Computed added-mass, damping coefficients, and wave exciting forces agree well with published results.

Computations of Arbitrary Thin-Shell Vertical Cylinders in a Wave Field by a Hypersingular Integral-Equation Method

2014 ◽  
Author(s):  
Mohamed Hariri Nokob ◽  
Ronald W. Yeung
Keyword(s):  
Integral Equation ◽  
Thin Shell ◽  
Boundary Integral ◽  
The Body ◽  
Boundary Integral Method ◽  
Hypersingular Integral Equation ◽  
Wave Load ◽  
Hypersingular Integral ◽  
Method Of Solution ◽  
Vertical Cylinders

We present a numerical formulation and computational results for the hydrodynamic loads on bottom-mounted thin-shell vertical cylinders of arbitrary cross-sectional shapes, including open bodies. Such cylinders may undergo prescribed or free motion or may be subjected to a wave load. The formulation is based on linear theory and a hypersingular integral-equation results from sectional contours of zero thickness. The method reduces the fully three-dimensional problem into a number of two-dimensional ones in the horizontal plane and is therefore much faster than the usual boundary integral method used for water wave problems. This traditional method of solution is also known to become ill-conditioned as the body thickness decreases. As an example of the current method, radiation and diffraction loads are presented for the cases of a circular and square closed and opened cylinders with the effect of the increased opening size discussed at different frequencies. The free-surface elevation associated with this method of solution is presented for some cases as well.

Scattering in a Shallow Ocean with an Elastic Seabed

1997 ◽  
Vol 05 (04) ◽  
pp. 403-431 ◽  
Author(s):  
R. P. Gilbert ◽  
Zhongyan Lin
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Near Field ◽  
Scattering Problem ◽  
Sufficient Conditions ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Parallel Computer ◽  
Hankel Transformation ◽  
Necessary And Sufficient

In this paper the boundary integral equation method is used to solve a scattering problem in a shallow ocean with an elastic seabed. The Hankel transformation and Mittag–Leffler decomposition were used to construct the propagating solution for both far-field and near-field. In particular, necessary and sufficient conditions are found for the existence of the propagating solution. Using the propagating solution, the scattering problem is recast as a boundary integral equation. A numerical algorithm is developed for solving this boundary integral equation and its implementation on a T3D parallel computer is used to compute an illustrative example.

Hydrodynamic Analysis of Floating Bodies in General Bathymetry

2005 ◽  
Author(s):  
K. A. Belibassakis
Keyword(s):  
Near Field ◽  
Boundary Integral ◽  
The Body ◽  
Hydrodynamic Characteristics ◽  
Hybrid Technique ◽  
Floating Bodies ◽  
Hydrodynamic Analysis ◽  
Coupled Mode ◽  
Simple Geometry ◽  
Boundary Integral Representation

A hybrid technique, based on the coupled-mode theory developed by Athanassoulis & Belibassakis (1999) and extended to 3D by Belibassakis et al (2001) and Belibassakis & Athanassoulis (2004), which is free of any mild-slope assumption, is used, in conjunction with a boundary integral representation of the near field in the vicinity of the body, to treat the problem of hydrodynamic analysis of floating bodies in the presence of variable bathymetry. Numerical results are presented concerning floating bodies of simple geometry lying over sloping seabeds. With the aid of systematic comparisons, the effects of bottom slope on the hydrodynamic characteristics (hydrodynamic coefficients and responses) are illustrated and discussed.

Wave Drift Forces in Directional Seas in Shallow Water

2009 ◽  
Author(s):  
J. A. Pinkster
Keyword(s):  
Shallow Water ◽  
Near Field ◽  
Low Frequency ◽  
Computational Method ◽  
Direct Evaluation ◽  
Beam Seas ◽  
Wave Drift ◽  
Wave Effects ◽  
Wave Drift Forces ◽  
Drift Forces

Wave drift forces in shallow water are dominated by low frequency bound wave effects. The effect of short-crestedness of the waves on the wave drift forces is investigated based on direct evaluation of the near field pressure equations in irregular directional seas. The background to the method is treated and examples of results showing some of the details of the computational method are given. Some trends found for the effect of the short-crestedness on the second order wave drift forces on a typical LNG carrier moored in shallow water are presented. Finally, results are given of low-frequency horizontal motions of the LNG carrier in directionally spread head, bow-quartering and beam seas for a range of directional spreading values.

Geometric Modeling for Fully Nonlinear Ship-Wave Interactions

1997 ◽  
Vol 41 (01) ◽  
pp. 17-25
Author(s):  
M.S. Celebi ◽  
R.F. Beck
Keyword(s):  
Body Surface ◽  
Geometric Modeling ◽  
Mixed Boundary ◽  
Boundary Integral ◽  
The Body ◽  
Boundary Integral Method ◽  
Lagrange Equations ◽  
Time Step ◽  
Fully Nonlinear ◽  
Node Placement

Using the desingularized boundary integral method to solve transient nonlinear water-wave problems requires the solution of a mixed boundary value problem at each time step. The problem is solved at nodes (or collocation points) distributed on an ever-changing body surface. In this paper, a dynamic node allocation technique is developed to distribute efficiently nodes on the body surface. A B-spline surface representation is employed to generate an arbitrary ship hull form in parametric space. A variational adaptive curve grid generation method is then applied on the hull station curves to generate effective node placement. The numerical algorithm uses a conservative form of the parametric variational Euler-Lagrange equations to perform adaptive gridding on each station. Numerical examples of node placement on typical hull cross sections and for fully nonlinear wave resistance computations are presented.

Near Field Expression of Ship Wave Resistance by Green’s Theorem

2016 ◽  
Author(s):  
Takashi Tsubogo
Keyword(s):  
Integral Equation ◽  
Near Field ◽  
Field Method ◽  
Momentum Conservation ◽  
Wave Resistance ◽  
Boundary Integral ◽  
Far Field ◽  
Ship Wave ◽  
Direct Pressure ◽  
Run Up

The ship wave resistance can be estimated by two alternative methods after solving the boundary integral equation. One is the far field method e.g. Havelock’s formula based on momentum conservation in fluid domain, and another is the near field method based on direct pressure integration over the wetted body surface. Nakos and Sclavounos (1994) had shown a new near field expression of ship wave resistance from the momentum conservation law in the fluid domain with linearized free surface condition. Their new expression differs slightly from the traditional near field form. This problem of near field expression is reconsidered in terms of Green’s second identity. After linearization of the free suface condition and some transformation of equations, the present paper will agree with the Nakos and Sclavounos’ near field expression for the ship wave resistance. Some numerical calculations of wave resistance from the far field method and from the near field method are shown using the classical Kelvin sources distributed on the centerplane of thin ship but solving the different boundary integral equation. Numerical results suggest that the problematic run-up square integration along the waterline is to be omitted as a higher order small quantity. If this run-up term is omitted in each method except for far field, the traditional direct pressure integrtaion is equal to the Nakos and Sclavounos’ near field expression.

The Role of Computer Modeling in Electrocardiography

1990 ◽  
Vol 29 (04) ◽  
pp. 282-288 ◽  
Author(s):  
A. van Oosterom
Keyword(s):  
Electrical Activity ◽  
Computer Modeling ◽  
Body Surface ◽  
Electrical Current ◽  
The Body ◽  
Volume Conductor ◽  
Current Generator ◽  
Cardiac Electrical Activity ◽  
Source Models

AbstractThis paper introduces some levels at which the computer has been incorporated in the research into the basis of electrocardiography. The emphasis lies on the modeling of the heart as an electrical current generator and of the properties of the body as a volume conductor, both playing a major role in the shaping of the electrocardiographic waveforms recorded at the body surface. It is claimed that the Forward-Problem of electrocardiography is no longer a problem. Several source models of cardiac electrical activity are considered, one of which can be directly interpreted in terms of the underlying electrophysiology (the depolarization sequence of the ventricles). The importance of using tailored rather than textbook geometry in inverse procedures is stressed.

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