Higher-order derivatives of the Green function in hyper-singular integral equations

Liang, Hui; Shao, Yanlin; Chen, Jikang

doi:10.1016/j.euromechflu.2020.12.006

Cited by 11 publications

(3 citation statements)

References 43 publications

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“…(8a), which requires special attention in the numerical implementation. This difficulty has been recently circumvented in Liang, Shao, and Chen (2021). The uniform dipole distribution can be transformed to a vortex ring comprising edge segments of the panel, and the induced velocity components are then obtained by the Biot-Savart law.…”

Section: Basic Equationsmentioning

confidence: 99%

Water wave scattering by impermeable and perforated plates

et al. 2021

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Section: Basic Equationsmentioning

confidence: 99%

Water wave scattering by impermeable and perforated plates

et al. 2021

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“…( 38), the computation of ∇φ (1) is required. This can alternatively be realized by a direct differentiation of the boundary integral equation (30) through which the second-order derivatives of the Rankine source function are needed [24]. However, this will increase the computational and storage burden as the setup of extra coefficient matrices and matrix multiplication are needed.…”

Section: Hydrodynamic Forces/momentsmentioning

confidence: 99%

An Implicit Time-Domain Rankine Panel Method for Ship Motions in a Non-Inertial Body-Fixed Frame of Reference

Liang

Shao

Chua

et al. 2022

Volume 5A: Ocean Engineering

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Evaluation of wave loads on a ship translating in water waves is of practical importance in ship hydrodynamics, because it is paramount to the design of ship hull structures and provides essential inputs for ship maneuvering analysis. The linear radiation and diffraction of water waves by a translating ship is studied in this paper. A time-domain Rankine panel method is developed in a non-inertial body-fixed coordinate system, which is able to consider large-amplitude horizontal motions consistently. The double-body flow is used as the basic steady flow model. To ensure numerical stability, an implicit Euler scheme is adopted for time marching, and horizontal derivatives on the free surface are calculated using an upwind-biased finite difference scheme. Numerical examples in comparison with experimental measurements are exhibited to demonstrate the validity of the developed solver.

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“…Compared with overdetermined integral equations (15a) and (15b), however, the implementation of enhanced overdetermined integral equations requires the evaluation of second derivatives of the free-surface Green function and thus is more complicated than that of overdetermined integral equations. The evaluation of the free-surface term of the Green function and the integration of Rankine terms over a flat panel are considered in Liang et al (2020). By enforcing stronger constraints, however, less points on the interior free surface are required in the enhanced overdetermined integral equations.…”

Section: Overdetermined Integral Equationsmentioning

confidence: 99%