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.

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.

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.

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.

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.

scholarly journals IMPLEMENTASI TRANSFORMASI FOURIER UNTUK TRANSFORMASI DOMAIN WAKTU KE DOMAIN FREKUENSI PADA LUARAN PURWARUPA ALAT PENDETEKSIAN GULA DARAH SECARA NON-INVASIF

2020 ◽  
Vol 4 (2) ◽  
pp. 234-244
Author(s):  
Umam Hidayaturrohman ◽  
Erfiani Erfiani ◽  
Farit M Afendi
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Frequency Domain ◽  
Blood Sugar ◽  
Processing Speed ◽  
Fourier Transformation ◽  
Dft Method ◽  
The Body ◽  
Non Invasive ◽  
The Time Domain

Diabetes mellitus is the result of changes in the body caused by a decrease of insulin performance which is characterized by an increase of blood sugar level. Detection of blood sugar can be done with Invasive methods or non-invasive methods. However, non-invasive methods are considered better because they can check early, faster and accurate. The prototype output is values of intensity in the time domain, thus fourier transformation is very much needed to transform into the frequency domain. In this study, Fourier transformation methods used are Discrete Fourier Transform (DFT), Fast Fourier Transform Radix-2, and Fast Fourier Transform Radix-4. Evaluation for the best method is done by comparing the processing speed of each method. The FFT Radix-4 method is more effective to perform the transformation into the frequency domain. The average processing speed with the FFT Radix-4 method reaches 2.67×105 nanoseconds, and this is much faster 5.06×106 nanoseconds than the FFT Radix-2 method and 2.40×107 nanoseconds faster than the DFT method.

scholarly journals Frequency-domain elastic wavefield simulation with hybrid absorbing boundary conditions

2019 ◽  
Vol 16 (4) ◽  
pp. 690-706
Author(s):  
Zhencong Zhao ◽  
Jingyi Chen ◽  
Xiaobo Liu ◽  
Baorui Chen
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Boundary Conditions ◽  
Frequency Domain ◽  
Time Domain ◽  
Absorbing Boundary Conditions ◽  
Elastic Media ◽  
Absorbing Boundary ◽  
Wavefield Simulation ◽  
The Time Domain

Abstract The frequency-domain seismic modeling has advantages over the time-domain modeling, including the efficient implementation of multiple sources and straightforward extension for adding attenuation factors. One of the most persistent challenges in the frequency domain as well as in the time domain is how to effectively suppress the unwanted seismic reflections from the truncated boundaries of the model. Here, we propose a 2D frequency-domain finite-difference wavefield simulation in elastic media with hybrid absorbing boundary conditions, which combine the perfectly matched layer (PML) boundary condition with the Clayton absorbing boundary conditions (first and second orders). The PML boundary condition is implemented in the damping zones of the model, while the Clayton absorbing boundary conditions are applied to the outer boundaries of the damping zones. To improve the absorbing performance of the hybrid absorbing boundary conditions in the frequency domain, we apply the complex coordinate stretching method to the spatial partial derivatives in the Clayton absorbing boundary conditions. To testify the validity of our proposed algorithm, we compare the calculated seismograms with an analytical solution. Numerical tests show the hybrid absorbing boundary condition (PML plus the stretched second-order Clayton absorbing condition) has the best absorbing performance over the other absorbing boundary conditions. In the model tests, we also successfully apply the complex coordinate stretching method to the free surface boundary condition when simulating seismic wave propagation in elastic media with a free surface.

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

scholarly journals Time and Frequency Domain Dynamic Analysis of Offshore Mooring

2021 ◽  
Vol 9 (7) ◽  
pp. 781
Author(s):  
Shi He ◽  
Aijun Wang
Keyword(s):  
Dynamic Analysis ◽  
Frequency Domain ◽  
Time Domain ◽  
Linearization Method ◽  
Euler Method ◽  
Single Component ◽  
Hydrodynamic Drag ◽  
Lumped Mass ◽  
Mooring Lines ◽  
The Time Domain

The numerical procedures for dynamic analysis of mooring lines in the time domain and frequency domain were developed in this work. The lumped mass method was used to model the mooring lines. In the time domain dynamic analysis, the modified Euler method was used to solve the motion equation of mooring lines. The dynamic analyses of mooring lines under horizontal, vertical, and combined harmonic excitations were carried out. The cases of single-component and multicomponent mooring lines under these excitations were studied, respectively. The case considering the seabed contact was also included. The program was validated by comparing with the results from commercial software, Orcaflex. For the frequency domain dynamic analysis, an improved frame invariant stochastic linearization method was applied to the nonlinear hydrodynamic drag term. The cases of single-component and multicomponent mooring lines were studied. The comparison of results shows that frequency domain results agree well with nonlinear time domain results.

Analysis of the First Order and Slowly Varying Motions of an Axisymmetric Floating Body in Bichromatic Waves

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
João Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Drift Motion ◽  
First Order ◽  
Motion Responses ◽  
Simple Geometry ◽  
Good Agreement

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and biharmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axisymmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in biharmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

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