Numerical Computations and Integrations of the Wave Resistance Green's Function

Ponizy, Barbara; Guilbaud, M.; Ba, M.

doi:10.1007/s001620050105

Cited by 3 publications

(8 citation statements)

References 7 publications

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“…2 shows the wave resistance coefficient on the ellipsoid versus the Froude number with 2b/f = 0.8. Our results, in good agreement with those of [2] (steady), show that linear methods [16] overestimate the wave resistance in the high Froude number range. For the same calculations with finite water height (h/f = 2) but with the same value of the submersion depth of the ellipsoid, the coefficient is greatly increased.…”

Section: Abridged English Versionsupporting

confidence: 91%

“…In [14,15], preliminary calculations on a source-sink set with strength ±µ 0 (submersion f = 1; separated by 0.1f ) have been carried out in order to optimize the calculation parameters. We have checked that the results are in good agreement with those of [16] (steady linear), [17] (unsteady linear) and [12] (unsteady non linear). To avoid generating excessive velocity gradients, it is necessary to use starting functions given by Eq.…”

Section: Abridged English Versionsupporting

confidence: 63%

“…The agreement is excellent. In order to emphasize the non linear effects, linear results [16] corresponding to the same conditions are also plotted on this figure. Non linear effects are important (for weak submersion depth f ), the wave amplitude being larger than for the linear method.…”

Section: Abridged English Versionmentioning

confidence: 99%

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Prise en compte des effets non linéaires de surface libre en écoulement instationnaire

Rebeyrotte¹,

Ba²,

Guilbaud³

2004

Comptes Rendus. Mécanique

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On présente une méthode de calculs de l'écoulement tridimensionnel instationnaire autour d'un obstacle immergé avec vitesse d'avance par une méthode de singularités. Les deux conditions de surface libre sont utilisées sous leurs formes non-linéaires. On utilise une modélisation dans le domaine temporel par une méthode mixte Euler-Lagrange reposant sur la connaissance, à chaque pas de temps, du potentiel sur la surface libre et de sa position. On résout alors un problème mixte, avec une condition de Neumann sur le corps et de Dirichlet sur la surface libre. On utilise une technique des sources désingularisées. La méthode est validée sur des exemples stationnaires.

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Section: Abridged English Versionsupporting

confidence: 91%

Section: Abridged English Versionsupporting

confidence: 63%

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Prise en compte des effets non linéaires de surface libre en écoulement instationnaire

Rebeyrotte¹,

Ba²,

Guilbaud³

2004

Comptes Rendus. Mécanique

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“…This allows realization of fast and effective schemes for numerical evaluation of the 'double integral term'. A practical numerical implementation can be found in [42]; further development for the efficacy and accuracy in computation of the near-field term is described in [50].…”

Section: Introductionmentioning

confidence: 99%

“…However, the summation of such series is not a trivial computational task, it leads to poor accuracy when the source and the field points are close to the free-surface, the method is vulnerable to severe numerical problems because of the presence of very large in magnitude alternating terms and the criteria to choose one of the expansions is difficult to determine. Details of numerical algorithms using the expansions, discussion of their applicability and heuristic criteria of choice between the algorithms can be found in [2,3,38,50]. Another approach in [61] to calculation of the wavelike term is also based on the Green's function representation [5] but the work is in terms of integrals as opposed to the use of the series.…”

Section: Introductionmentioning

confidence: 99%

On computation of oscillating integrals of ship-wave theory

Motygin

2014

Preprint

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Green's function of the problem describing steady forward motion of bodies in an open ocean in the framework of the linear surface wave theory (the function is often referred to as Kelvin's wave source potential) is considered. Methods for numerical evaluation of the so-called 'single integral' (or, in other words, 'wavelike') term, dominating in the representation of Green's function in the far field, are developed. The difficulty in the numerical evaluation is due to integration over infinite interval of the function containing two differently oscillating factors and the presence of stationary points. This work suggests two methods to approximate the integral and its derivatives. First of the methods is based on the idea suggested by D. Levin in 1982 -evaluation of the integral is converted to finding a particular slowly oscillating solution of an ordinary differential equation. To overcome well-known numerical instability of Levin's collocation method, an alternative type of collocation is used; it is based on a barycentric Lagrange interpolation with a clustered set of nodes. The second method for evaluation of the wavelike term involves application of the steepest descent method and Clenshaw-Curtis quadrature. The methods are numerically tested and compared for a wide variety of parameters.

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Numerical approximation of oscillatory integrals of the linear ship wave theory

Motygin

2017

Applied Numerical Mathematics

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Numerical Computations and Integrations of the Wave Resistance Green's Function

Cited by 3 publications

References 7 publications

Prise en compte des effets non linéaires de surface libre en écoulement instationnaire

Prise en compte des effets non linéaires de surface libre en écoulement instationnaire

On computation of oscillating integrals of ship-wave theory

Numerical approximation of oscillatory integrals of the linear ship wave theory

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