Application and Verification of Deepwater Green Function for Water Waves

2001 ◽  
Vol 45 (03) ◽  
pp. 187-196
Author(s):  
Subrata K. Chakrabarti
Keyword(s):  
Green Function ◽  
Water Waves ◽  
Near Field ◽  
Finite Depth ◽  
Offshore Structures ◽  
Accurate Analysis ◽  
Mathematical Functions ◽  
Infinite Depth ◽  
Analysis And Design ◽  
The Green Function

An efficient method for the numerical evaluation of the free-surface Green function for deep-water application was presented by Telste & Noblesse (1986) and again by Ponizy et al (1994). A FORTRAN code was include in their 1986 paper. The numerical method makes use of known mathematical functions. Numerical values of some of these mathematical functions were depicted, but no verification on the accuracy of the Green function routine in an application was given. The purpose of this paper is to compare their numerical values in the near-field and far-field regions with other similar computation for the infinite-depth Green function. The results of the infinite-depth Green function are also compared with the results from the finite-depth Green function that is more time consuming. Based on the accuracy of the various methods, the regions of application of the efficient deepwater Green function formulation and the effect of the water depth on the Green function are discussed. Any regions of inaccurate results are noted. Forces on submerged offshore structures and motions of the floating structures are determined using the lower-order panel method and these different Green function routines. The results on the motions of a semisubmersible in various water depths are compared and the accuracy of these routines in various regions is shown. The presented results will help the hydrodynamicist and designer to evaluate the suitable formulation and its regions of application for the accurate analysis and design of offshore structures.

Reflexion of water waves by a permeable barrier

1979 ◽  
Vol 95 (1) ◽  
pp. 141-157 ◽  
Author(s):  
C. Macaskill
Keyword(s):  
Water Waves ◽  
Water Wave ◽  
Finite Depth ◽  
Infinite Depth ◽  
Permeable Barrier ◽  
Impermeable Barrier ◽  
Linearized Problem ◽  
Special Case ◽  
Thin Barrier ◽  
Standard Techniques

The linearized problem of water-wave reflexion by a thin barrier of arbitrary permeability is considered with the restriction that the flow be two-dimensional. The formulation includes the special case of transmission through one or more gaps in an otherwise impermeable barrier. The general problem is reduced to a set of integral equations using standard techniques. These equations are then solved using a special decomposition of the finite depth source potential which allows accurate solutions to be obtained economically. A representative range of solutions is obtained numerically for both finite and infinite depth problems.

scholarly journals An Extremely Efficient Boundary Element Method for Wave Interaction with Long Cylindrical Structures Based on Free-Surface Green’s Function

2016 ◽  
Author(s):  
Yingyi Liu ◽  
Ying Gou ◽  
Bin Teng
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Water Waves ◽  
Chebyshev Approximation ◽  
Wave Interaction ◽  
Coefficient Matrix ◽  
Influence Coefficient ◽  
Cauchy Type ◽  
Cylindrical Structures ◽  
The Green Function

The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters. A higher-order scheme is used to discretize geometry of the structure as well as the relevant physical quantities. As the kernel of this method, Wehausen’s free-surface Green function is calculated by a newly-developed Gauss-Kronrod adaptive quadrature algorithm after elimination of its Cauchy-type singularities. To improve computational efficiency, a Chebyshev approximation approach is applied to a fast calculation of the Green function that needs evaluation thousands of times. In addition, OpenMP parallel technique is used to the formation of influence coefficient matrix, which significantly reduces CPU time. Finally, computations are performed on wave exciting forces and hydrodynamic coefficients for the long cylindrical structures, either floating or submerged. Comparison with other numerical and analytical methods demonstrates good performance of the present method.

Stokeslet arrays in a pipe and their application to ciliary transport

1984 ◽  
Vol 143 ◽  
pp. 173-195 ◽  
Author(s):  
N. Liron
Keyword(s):  
Green Function ◽  
Fluid Transport ◽  
Near Field ◽  
Plug Flow ◽  
Singular Integral Equations ◽  
Summation Formula ◽  
Poisson Summation Formula ◽  
Parabolic Profile ◽  
The Green Function ◽  
Local Results

The problem of fluid transport by cilia in a circular cylinder is investigated. The discrete-cilia approach is used in building the model, using the Green function due to an infinite periodic Stokeslet array in a pipe. Two different expressions are obtained for the Green function, one via a residue method and the other using the Poisson summation formula each amenable for computation in a different region. Interaction of the Stokeslets is investigated to see how, as distance decreases, interaction changes from initially separated closed vortices to a continuous flow. The singular integral equations for the forces in this model are now replaced by non-singular equations, thus overcoming the numerical difficulties in earlier works. It is found that in the pipe core the flow is time-independent and varies between a plug flow and a negative parabolic profile, in the pumping range. These results are seen to be local results due to the near field. Streamlines in the sublayer show eddies near the cilia bases blending into a uniform flow near the cilia tips.

Further developments in a nonlinear theory of water waves for finite and infinite depths

1987 ◽  
Vol 324 (1577) ◽  
pp. 47-72 ◽  
Keyword(s):  
General Theory ◽  
Nonlinear Theory ◽  
Water Waves ◽  
Finite Depth ◽  
Balance Laws ◽  
Jump Conditions ◽  
Infinite Depth ◽  
Inviscid Fluids ◽  
Special Cases ◽  
Special Case

This paper is a companion to an earlier one (Green & Naghdi 1986, Phil. Trans. R. Soc. Lond . A 320, 37-70 (1986)) and deals with certain aspects of a nonlinear waterwave theory and its applications to waters of infinite and finite depths. A new procedure is used to establish a 1-1 correspondence between the lagrangian and eulerian formulations of the integral balance laws of a general thermomechanical theory of directed fluid sheets, as well as their associated jump conditions in the presence of any number of directors. (Such a correspondence between lagrangian and eulerian formulations was previously possible in the special case of a single constrained director.) These results are valid for both compressible and incompressible (not necessarily inviscid) fluids. Applications are then made to special cases of the general theory (including the jump conditions) for incompressible inviscid fluids of infinite depth (with two directors) and of finite depth (with three directors) and the nature of the results are illustrated with particular reference to a wedge-like boat.

A global approximation to the Green function for diffraction radiation of water waves

2017 ◽  
Vol 65 ◽  
pp. 54-64 ◽  
Author(s):  
Huiyu Wu ◽  
Chenliang Zhang ◽  
Yi Zhu ◽  
Wei Li ◽  
Decheng Wan ◽  
...  
Keyword(s):  
Green Function ◽  
Water Waves ◽  
Diffraction Radiation ◽  
Global Approximation ◽  
The Green Function

Exponentially Convergent Approximation to the Elliptic Solution Operator

2006 ◽  
Vol 6 (4) ◽  
pp. 386-404 ◽  
Author(s):  
Ivan. P. Gavrilyuk ◽  
V.L. Makarov ◽  
V.B. Vasylyk
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Solution Operator ◽  
Hyperbolic Operator ◽  
Elliptic Solution ◽  
Elliptic Boundary Value ◽  
Sine Family ◽  
The Green Function

AbstractWe develop an accurate approximation of the normalized hyperbolic operator sine family generated by a strongly positive operator A in a Banach space X which represents the solution operator for the elliptic boundary value problem. The solution of the corresponding inhomogeneous boundary value problem is found through the solution operator and the Green function. Starting with the Dunford — Cauchy representation for the normalized hyperbolic operator sine family and for the Green function, we then discretize the integrals involved by the exponentially convergent Sinc quadratures involving a short sum of resolvents of A. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [0, 1].

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