Abstract
Fast and accurate computation of the free-surface Green function is of key importance for the numerical solution of linear and second-order wave-structure interaction problems in three dimensions. Integral and series expressions for the Green function are derived for which the limiting values for zero and infinite frequency are consistent with the zero and infinite frequency Green function defined in terms of infinite series of Rankine image sources. The integral expressions presented here have the advantage that they are slowly varying with the non-dimensional wave frequency, making them more efficient to approximate compared with previous expressions.
Highlights
The boundary element method (BEM) is often used to solve linear and second-order wave-structure interaction problems in three dimensions [1]
We propose a simple modification to the expression, which improves the numerical accuracy for high values of K and makes the limiting value consistent with the series expression for the Green function at infinite frequency
In the mid- to far-field, when R/h > 1 the Green function is expressed using a modified form of the series defined by John [4]
Summary
The boundary element method (BEM) is often used to solve linear and second-order wave-structure interaction problems in three dimensions [1]. The integrals that are approximated in Newman and Chen’s methods are functions of three non-dimensional variables (R/h, |z ± ζ|/h, Kh), where K is the infinite-depth wavenumber. Following Newman [17] and Chen [18], triple Chebyshev polynomials are used to approximate the integrals that are derived in this work This provides an efficient means for calculating the Green function in the domain R/h ≤ 1 and has the advantage that the partial derivatives can be computed using the same approximation, with minimal additional computational cost.
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