Numerical Solution of Wave Diffraction Problem in the Time Domain With the Panel-Free Method

2004 ◽  
Vol 126 (1) ◽  
pp. 1-8 ◽  
Author(s):  
W. Qiu ◽  
J. M. Chuang ◽  
C. C. Hsiung
Keyword(s):  
Body Surface ◽  
Time Domain ◽  
Diffraction Problem ◽  
The Body ◽  
Floating Body ◽  
B Splines ◽  
Rankine Source ◽  
Diffracted Waves ◽  
The Green Function ◽  
The Time Domain

A panel-free method (PFM) was developed earlier to solve the radiation problem of a floating body in the time domain. In the further development of this method, the diffraction problem has been solved. After removing the singularity in the Rankine source of the Green function and representing the body surface mathematically by Non-Uniform Rational B-Splines (NURBS) surfaces, integral equations were globally discretized over the body surface by Gaussian quadratures. Computed response functions and forces due to diffracted waves for a hemisphere at zero speed were compared with published results.

Numerical Solution of Body-Exact Problem in the Time Domain

2013 ◽  
Vol 57 (01) ◽  
pp. 13-23
Author(s):  
Wei Qiu ◽  
Hongxuan (Heather) Peng
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
The Body ◽  
Floating Body ◽  
Entire Body ◽  
Surface Boundary ◽  
Time Step ◽  
Submerged Sphere ◽  
Wigley Hull ◽  
The Time Domain

Motions of a floating body in waves are computed in the time domain by solving the body-exact problem with the panel-free method and exact geometry. In the present study, the body boundary condition is imposed on the instantaneous wetted surface exactly at each time step. The free surface boundary is assumed linear so that the time-domain Green function can be applied. The body geometry is represented by NonUniform Rational B-Spline surfaces. At each time step, the instantaneous wetted surface is obtained by trimming the entire body surface. With the panel-free method, the body-exact problems are solved without involving repanelization of the wetted hull surface at each time step. Validation studies have been carried out for a submerged sphere, a flared body, and a Wigley hull. The hydrodynamic forces on the submerged sphere undergoing large-amplitude motion were computed and compared with analytical solutions. For the flared body oscillating in a free surface and the Wigley hull in waves, numerical results were compared with experimental data and solutions by other numerical methods.

scholarly journals Computation of Nonlinear Hydrodynamic Loads on Floating Wind Turbines Using Fluid-Impulse Theory

2015 ◽  
Author(s):  
Godine Kok Yan Chan ◽  
Paul D. Sclavounos ◽  
Jason Jonkman ◽  
Gregory Hayman
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Wind Turbines ◽  
Time Domain ◽  
The Body ◽  
Nonlinear Loads ◽  
Frequency Wave ◽  
Linear And Nonlinear ◽  
The Time Domain ◽  
Nonlinear Free Surface

A hydrodynamics computer module was developed to evaluate the linear and nonlinear loads on floating wind turbines using a new fluid-impulse formulation for coupling with the FAST program. The new formulation allows linear and nonlinear loads on floating bodies to be computed in the time domain. It also avoids the computationally intensive evaluation of temporal and spatial gradients of the velocity potential in the Bernoulli equation and the discretization of the nonlinear free surface. The new hydrodynamics module computes linear and nonlinear loads — including hydrostatic, Froude-Krylov, radiation and diffraction, as well as nonlinear effects known to cause ringing, springing, and slow-drift loads — directly in the time domain. The time-domain Green function is used to solve the linear and nonlinear free-surface problems and efficient methods are derived for its computation. The body instantaneous wetted surface is approximated by a panel mesh and the discretization of the free surface is circumvented by using the Green function. The evaluation of the nonlinear loads is based on explicit expressions derived by the fluid-impulse theory, which can be computed efficiently. Computations are presented of the linear and nonlinear loads on the MIT/NREL tension-leg platform. Comparisons were carried out with frequency-domain linear and second-order methods. Emphasis was placed on modeling accuracy of the magnitude of nonlinear low- and high-frequency wave loads in a sea state. Although fluid-impulse theory is applied to floating wind turbines in this paper, the theory is applicable to other offshore platforms as well.

scholarly journals Generalized eigenfunction method for floating bodies

2011 ◽  
Vol 667 ◽  
pp. 544-554 ◽  
Author(s):  
COLM J. FITZGERALD ◽  
MICHAEL H. MEYLAN
Keyword(s):  
Time Domain ◽  
Water Waves ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Two Dimensions ◽  
Floating Body ◽  
Floating Bodies ◽  
Abstract Wave Equation ◽  
Generalized Eigenfunction ◽  
The Time Domain

We consider the time domain problem of a floating body in two dimensions, constrained to move in heave and pitch only, subject to the linear equations of water waves. We show that using the acceleration potential, we can write the equations of motion as an abstract wave equation. From this we derive a generalized eigenfunction solution in which the time domain problem is solved using the frequency-domain solutions. We present numerical results for two simple cases and compare our results with an alternative time domain method.

scholarly journals Wave radiation and diffraction by a circular cylinder submerged below an ice sheet with a crack

2018 ◽  
Vol 845 ◽  
pp. 682-712 ◽  
Author(s):  
Zhi Fu Li ◽  
Guo Xiong Wu ◽  
Chun Yan Ji
Keyword(s):  
Green Function ◽  
Circular Cylinder ◽  
Body Surface ◽  
Ice Sheet ◽  
Integral Form ◽  
Multipole Expansion ◽  
The Body ◽  
Wave Radiation ◽  
Surface Boundary ◽  
The Green Function

Wave radiation and diffraction by a circular cylinder submerged below an ice sheet with a crack are considered based on the linearized velocity potential theory together with multipole expansion. The solution starts from the potential due to a single source, or the Green function satisfying both the ice sheet condition and the crack condition, as well as all other conditions apart from that on the body surface. This is obtained in an integral form through Fourier transform, in contrast to what has been obtained previously in which the Green function is in the series form based on the method of matched eigenfunction expansion in each domain on both sides of the crack. The multipole expansion is then constructed through direct differentiation of the Green function with respect to the source position, rather than treating each multipole as a separate problem. The use of the Green function enables the problem of wave diffraction by the crack in the absence of the body to be solved directly. For the circular cylinder, wave radiation and diffraction problems are solved by applying the body surface boundary condition to the multipole expansion, through which the unknown coefficients are obtained. Extensive results are provided for the added mass and damping coefficient as well as the exciting force. When the cylinder is away from the crack, a wide spacing approximation method is used, which is found to provide accurate results apart from when the cylinder is quite close to the crack.

Towards Fully Non-Linear Floating Body Simulations by a Potential Method

2012 ◽  
Author(s):  
Heinrich Söding
Keyword(s):  
Free Surface ◽  
Surface Condition ◽  
Computing Time ◽  
Potential Method ◽  
The Body ◽  
Floating Body ◽  
Rankine Source ◽  
Exact Boundary ◽  
Approximate Wave ◽  
Steep Waves

A 3-dimensional Rankine source panel method for simulating a rigid floating body in steep waves is being developed. The aim is to obtain the same quality as free-surface RANSE methods, which are well suited for this application, but to require only a small fraction of the computing time needed by RANSE methods. The body may have forward speed or perform maneuvering motions. The exact boundary conditions are satisfied at the actual location of the fluid boundaries. The waves are generated not by a material wave maker, but by an approximate wave potential which needs not satisfy the exact free-surface condition. No wave damping regions are required. Whereas for steep waves without a body the method appears satisfactory, it needs further improvements if a body is present.

Time-Domain Coupled Dynamic Analysis of Mooring Systems in Extreme Sea Condition

2018 ◽  
Author(s):  
Xuliang Han ◽  
ShiSheng Wang ◽  
Bin Xie ◽  
Wenhui Xie ◽  
Weiwei Zhou
Keyword(s):  
Dynamic Analysis ◽  
Body Surface ◽  
Time Domain ◽  
Mooring Line ◽  
Mooring System ◽  
Dynamic Coupling ◽  
Spar Platform ◽  
Coupled Dynamic Analysis ◽  
Motion Responses ◽  
The Time Domain

In order to predict the coupled motion and external wave load for the design of deepwater floating structure system, based on the three-dimensional time-domain potential flow theory, this paper present the indirect time-domain dynamic coupling method and the body nonlinear dynamic coupling method. The perturbation expansion theory is adopted to evaluate hydrodynamic on the fixed mean wetted body surface for the former method. The transient free surface Green function has been extended and applied to calculate the nonlinear hydrodynamic on the instantaneous wetted exact body surface for the latter method. The finite element model is employed to solve dynamic response of mooring line. Then asynchronous coupled method is adopted to achieve the coupled dynamic analysis of platform and mooring lines. The time-domain motion responses and spectrum analysis of Spar platform are verified and compared with the traditional indirect time-domain coupling dynamic method when the mooring system is completed. Also the time-domain motion responses and statistical characteristic of Spar platform are investigated with one mooring line broken in extreme sea condition. Some conclusions are obtained, that is, dynamic coupling effects are significant and transient position hydrodynamic calculation of platform has a great influence on the low frequency motion. The results also show that the influence on the global performance of mooring system is different when the broken line is in different place. A remarkable influence occurs when the broken mooring line is in the head-wave direction.

Computing Large Amplitude Motions of a Floating Offshore Structure in the Time Domain

2008 ◽  
Author(s):  
Wei Qiu ◽  
Hongxuan Peng
Keyword(s):  
Time Domain ◽  
Large Amplitude ◽  
Offshore Structures ◽  
The Body ◽  
Surface Boundary ◽  
Offshore Structure ◽  
Floating Structure ◽  
Time Step ◽  
Large Amplitude Motions ◽  
The Time Domain

Based on the panel-free method, large-amplitude motions of floating offshore structures have been computed by solving the body-exact problem in the time domain using the exact geometry. The body boundary condition is imposed on the instantaneous wetted surface exactly at each time step. The free surface boundary is assumed linear so that the time-domain Green function can be applied. The instantaneous wetted surface is obtained by trimming the entire NURBS surfaces of a floating structure. At each time step, Gaussian points are automatically distributed on the instantaneous wetted surface. The velocity potentials and velocities are computed accurately on the body surface by solving the desingularized integral equations. Nonlinear Froude-Krylov forces are computed on the instantaneous wetted surface under the incident wave profile. Validation studies have been carried out for a Floating Production Storage and Offloading (FPSO) vessel. Computed results were compared with experimental results and solutions by the panel method.

Transient axisymmetric motion of a floating cylinder

1985 ◽  
Vol 157 ◽  
pp. 17-33 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Free Surface ◽  
Frequency Domain ◽  
Impulse Response ◽  
Response Function ◽  
Time Domain ◽  
Impulse Response Function ◽  
Surface Effects ◽  
Added Mass ◽  
The Body ◽  
The Time Domain

A linear theory is developed in the time domain for vertical motions of an axisymmetric cylinder floating in the free surface. The velocity potential is obtained numerically from a discretized boundary-integral-equation on the body surface, using a Galerkin method. The solution proceeds in time steps, but the coefficient matrix is identical at each step and can be inverted at the outset.Free-surface effects are absent in the limits of zero and infinite time. The added mass is determined in both cases for a broad range of cylinder depths. For a semi-infinite cylinder the added mass is obtained by extrapolation.An impulse-response function is used to describe the free-surface effects in the time domain. An oscillatory error observed for small cylinder depths is related to the irregular frequencies of the solution in the frequency domain. Fourier transforms of the impulse-response function are compared with direct computations of the damping and added-mass coefficients in the frequency domain. The impulse-response function is also used to compute the free motion of an unrestrained cylinder, following an initial displacement or acceleration.

Transient Free-Surface Hydrodynamics Using Rational Approximation of the Green’s Function

1999 ◽  
Vol 43 (02) ◽  
pp. 95-106 ◽  
Author(s):  
Christopher J. Damaren
Keyword(s):  
Free Surface ◽  
Frequency Domain ◽  
Source Function ◽  
The Body ◽  
Floating Body ◽  
Order Ordinary Differential Equation ◽  
Radiation Impedance ◽  
Rational Dependence ◽  
The Time Domain ◽  
Domain Source

Rational approximations in the frequency domain are developed for the source function of linear free-surface hydrodynamics using the recently uncovered fourth-order ordinary differential equation (ODE) satisfied by the time-domain source function. The radiation problem for a floating body in deep water is formulated using a source plus wave-free potential expansion for the fluid. The inherent rational dependence on frequency of the wave-free potentials as well as the source approximation are used to develop a system of constant-coefficient ODE's for the radiation impedance which can be used to develop the motion of the body in a simple manner. The technique is applied to the heaving motion of a floating sphere with good results. The application to more general body geometries is explored by formulating the frequency-domain problem using the variational principle of Chen and Mei and exploiting its polynomial dependence on frequency.

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