Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

Amini-Afshar, Mostafa; Bingham, Harry B.

doi:10.1016/j.apor.2017.11.001

Cited by 11 publications

(20 citation statements)

References 16 publications

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“…Numerical stability also requires special treatment of the ghost points at the boundaries of the free surface. More details about the developed numerical methodology can be found in [26], and [36].…”

Section: Methodsmentioning

confidence: 99%

“…In this section, we include a brief review of the theory and illustrate the details of our solution. The focus here is on the diffraction problem, while the details of our solution to the radiation problem can be found in [26].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…where L t is length-scale of the computational domain. Then, following [16] and as discussed in more detail by [26], we make a least-squares fit of the signal to the function…”

Section: Treatment Of the Critical Frequencymentioning

confidence: 99%

“…Motivated by the difficulties faced by BEM methods in obtaining a linear scaling of the solution effort with increasing resolution, we have been developing a high-order finite difference framework for nonlinear water wave simulation and wave-structure interaction, see for example [23,24,25,26,27,28,29] and [30]. While the total number of unknowns required here is typically an order of magnitude larger than that required by BEM methods, the resulting system matrix is sparse, leading to a linear scaling of the solution effort, as demonstrated for example by [26]. This is especially attractive for computing second-and higher-order wave forces (for example added resistance [31]), where convergence of the solution typically requires high resolution.…”

Section: Introductionmentioning

confidence: 99%

“…A method of lines approach [32] is applied to obtain the discrete solution, with the explicit fourthorder Runge-Kutta scheme chosen for the time-integration. For the Laplace problem, fourth-order spatial finite difference schemes are developed on overlapping, boundary-fitted grids, resulting in a consistently fourth-order accurate solution, as demonstrated by [26]. Frequency-domain quantities are obtained by taking the Fourier transform of the time-domain results, and forces are computed by integrating the pressure over the surface of the body (using at least fourth-order accurate integration schemes).…”

Section: Introductionmentioning

confidence: 99%

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Pseudo-impulsive solutions of the forward-speed diffraction problem using a high-order finite-difference method

Amini-Afshar

Bingham

2018

Applied Ocean Research

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This paper considers pseudo-impulsive numerical solutions to the forward-speed diffraction problem, as derived from classical linearized potential flow theory. Both head-and following-seas cases are treated. Fourth-order finite-difference approximations are applied on overlapping, boundary-fitted grids to obtain solutions using both the Neumann-Kelvin and the double-body flow linearizations of the problem. A method for computing the pseudo-impulsive incident wave forcing in finite water depth using the Fast Fourier Transform (FFT) is presented. The pseudo-impulsive scattering solution is then Fourier transformed into the frequency domain to obtain the wave excitation forces and the body motion response. The calculations are validated against reference solutions for a submerged circular cylinder and a submerged sphere. Calculations are also made for a modern bulk carrier, showing good agreement with experimental measurements.

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Section: Methodsmentioning

confidence: 99%

Section: Formulation Of the Problemmentioning

confidence: 99%

“…where L t is length-scale of the computational domain. Then, following [16] and as discussed in more detail by [26], we make a least-squares fit of the signal to the function…”

Section: Treatment Of the Critical Frequencymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Pseudo-impulsive solutions of the forward-speed diffraction problem using a high-order finite-difference method

Amini-Afshar

Bingham

2018

Applied Ocean Research

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A spectral element solution of the two‐dimensional linearized potential flow radiation problem

Visbech

Engsig-Karup

Bingham

2022

Numerical Methods in Fluids

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We present a scalable two‐dimensional Galerkin spectral element method solution to the linearized potential flow radiation problem for wave induced forcing of a floating offshore structure. The pseudo‐impulsive formulation of the problem is solved in the time domain using a Gaussian displacement signal tailored to the discrete resolution. The added mass and damping coefficients are then obtained via Fourier transformation. The spectral element method is used to discretize the spatial fluid domain, whereas the classical explicit 4‐stage fourth‐order Runge–Kutta scheme is employed for the temporal integration. Spectral convergence of the proposed model is established for both affine and curvilinear elements, and the computational effort is shown to scale with 𝒪false(Npfalse), with N$$ N $$ being the total number of grid points and pprefix≈1.12$$ p\approx 1.12 $$. The solver is used to compute the hydrodynamic coefficients for several floating bodies and compared against known public benchmark results. The results show excellent agreement, ultimately validating the solver and emphasizing the geometrical flexibility and high accuracy and efficiency of the proposed solution strategy. Lastly, an extensive investigation of nonresolved energy from the pseudo‐impulse is carried out to characterize the induced spurious oscillations of the free surface quantities leading to a robust strategy for tuning the pseudo‐impulsive motion to the spatial discretization.

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An innovative EFD using FBG pressure sensors for ship seakeeping

Suzuki,

Iwashita,

Kashiwagi

et al. 2024

J Mar Sci Technol

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This paper examines the acquisition of the measurement data of the spatial distribution of unsteady pressure on a ship advancing in waves. The purpose of the study is to investigate the reliability of the pressure data obtained by the unprecedented experiment and to provide experimental data of unsteady pressure which can be used for validation of arbitrary computation methods. The optical fiber sensing technology, so-called FBG (fiber Bragg gratings) sensing, is employed as the pressure sensors. In the experiment, 379 FBG pressure sensors (version 7; the latest version) in total are attached to the port side surface of ship model and also ordinary strain-type pressure sensors are embedded in the starboard side for validating reliability of FBG pressure sensors by comparing both results. In addition to the pressure distribution, measurement is made for unsteady hydrodynamic forces such as added mass, damping coefficients, and wave exciting forces, and also for ship motions and added resistance. Most of the measurement is repeated at least five times for each condition, and results of measured pressures are evaluated with mean value and standard deviation. Regarding the added resistance, the distribution for estimating added resistance is also extracted from obtained pressure distribution and its pressure contour is illustrated to show visually which hull region affects the added resistance significantly. Validation of the measured pressure with FBG pressure sensors is carried out also by integrating measured pressures over the ship model surface and comparing it with forces directly measured with load cells. The measured pressure distribution is compared with typical calculation results with the Rankine panel method in frequency domain to demonstrate usefulness of the spatial pressure data for validating the calculation method. Through these studies, it is confirmed that the measured unsteady pressures with FBG pressure sensors are accurate enough and valuable as the validation data for any calculation method.

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Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

Cited by 11 publications

References 16 publications

Pseudo-impulsive solutions of the forward-speed diffraction problem using a high-order finite-difference method

Pseudo-impulsive solutions of the forward-speed diffraction problem using a high-order finite-difference method

A spectral element solution of the two‐dimensional linearized potential flow radiation problem

An innovative EFD using FBG pressure sensors for ship seakeeping

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