The Simulation of Ship Motions Using a B-Spline–Based Panel Method in Time Domain

2007 ◽  
Vol 51 (03) ◽  
pp. 267-284
Author(s):  
Ranadev Datta ◽  
Debabrata Sen
Keyword(s):  
Time Domain ◽  
Three Dimensional ◽  
Basis Functions ◽  
The Body ◽  
Irregular Waves ◽  
Ship Motions ◽  
B Spline ◽  
Head Waves ◽  
Wigley Hull ◽  
Spline Basis

In this paper, a B-spline-based higher-order method is developed for simulating three-dimensional ship motions with forward speed. The problem is formulated in time domain using a transient free surface Green function. The body geometry is defined by open uniform or nonuniform B-spline basis functions depending on the hull type, whereas the unknown field variables are described by open uniform B-spline basis functions. The collocation method is applied to discretize the integral equation and then solved for the unknown potentials and source strengths. Motion computations in head waves are carried out for three types of ship hulls: a mathematically defined Wigley hull, a typical containership (S175 hull), and a Series 60 hull. Results are obtained for regular and irregular waves and compared with available experimental and computational results. It is found that the results from the present method are in very good agreement with the published results, and in particular with experimental data. Long-duration simulations have also been carried out with an ordinary desktop PC (PIV with 512 MB RAM) to demonstrate the ability of the method to simulate motions over long periods without any visible deterioration using only modest computational resources.

Numerical Study on Ship Parametric Roll in Head Waves

2020 ◽  
Author(s):  
Huawei Zhou ◽  
Fuhua Wang ◽  
Renchuan Zhu ◽  
Kaiyuan Shi
Keyword(s):  
Time Domain ◽  
Function Method ◽  
Numerical Study ◽  
Three Dimensional ◽  
Domain Model ◽  
Ship Motions ◽  
Parametric Roll ◽  
Head Waves ◽  
Restoring Forces ◽  
Response Function Method

Ship parametric roll is one of the main reasons for marine accidents and is introduced into the second-generation intact stability criteria by the International Maritime Organization (IMO) recently. In this paper, a 6-DOF three-dimensional time-domain model based on the IRF (Impulse Response Function) method is constructed to predict large-amplitude ship motions and investigate the phenomenon of parametric roll in head waves as well as major factors. The F-K forces and the restoring forces are calculated on the instantaneous wet surface while the radiation and diffraction forces are kept linear and transformed from frequency-domain results calculated with the three-dimensional Havelock form translating-pulsating source green function method. The proposed weakly nonlinear time-domain model is used to simulate motions of the C11 containership, which predicts the occurrence of the parametric roll successfully and shows a good agreement with the experimental data in amplitude. The inner mechanism of parametric roll is revealed by investigating the time-history and resonance frequencies of restoring forces and coefficients numerically.

Research of the real-time interpolation based on piecewise power basis functions

2018 ◽  
Vol 233 (3) ◽  
pp. 889-899 ◽  
Author(s):  
Hui Wang ◽  
Chao Liu ◽  
Jianhua Wu ◽  
Zhenhua Xiong
Keyword(s):  
Computational Complexity ◽  
Real Time ◽  
Recursive Algorithm ◽  
Three Dimensional ◽  
Basis Functions ◽  
Numerical Control ◽  
B Spline ◽  
The Real ◽  
Power Basis ◽  
Spline Basis

With the outstanding geometric properties of B-spline, its recursive algorithm has been widely applied in numerical control systems to compute interpolation points and their derivatives. However, some of the B-spline basis functions in the recursive algorithm are computed repeatedly during the numerical control interpolation, which makes the interpolation efficiency greatly deteriorated. To deal with this issue, an effective approach by converting B-spline to piecewise power basis functions is proposed in this article. With the proposed power basis functions, formulas for computing interpolation point and its derivative can be established explicitly. Thus, the repeated computation due to the implicit expression can be avoided. To further improve the real-time interpolation performance, curve subdivision based on the proposed power basis functions is implemented simultaneously. Theoretical analysis shows that the computational complexity of the proposed method can be reduced by 71.1% compared with the DeBoor-Cox algorithm during the computation of interpolation points and their derivatives. Furthermore, the computational complexity of the curve subdivision can be reduced by 64.5%. Experimental results on a two-dimensional butterfly and a three-dimensional pigeon show that the proposed methods can greatly improve the computational efficiency.

A B-Spline Time Domain Solution for the Forward Speed Diffraction Problems

2006 ◽  
Author(s):  
Ranadev Datta ◽  
Debabrata Sen
Keyword(s):  
Time Domain ◽  
Present Method ◽  
Diffraction Problem ◽  
The Body ◽  
Forward Speed ◽  
Transient Time ◽  
B Spline ◽  
Long Duration ◽  
Spline Basis ◽  
Motion Problem

A B-spline based panel method is developed for the solution of the forward speed diffraction problem in time-domain. The body geometry is defined by an open uniform B-spline, and the unknown potentials and the source strengths are described by the same B-spline basis functions. The 3D potential flow boundary value problem is formulated based on a transient (time domain) Green’s function. Computed results are validated by comparing them with a wide variety of available results, including 3D numerical computations and experimental results. The present method agrees well with published results. Many of the existing 3D codes for the forward speed ship motion problem require high computing resources. The present method is however capable of producing the time simulation results over long duration using only a presently available PC, which is the main advantage of the proposed development.

Prediction of Ship Motions Via a Three-Dimensional Time-Domain Method Following a Quad-Tree Adaptive Mesh Technique

2020 ◽  
Vol 27 (1) ◽  
pp. 29-38
Author(s):  
Teng Zhang ◽  
Junsheng Ren ◽  
Lu Liu
Keyword(s):  
Free Surface ◽  
Incident Wave ◽  
Time Domain ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Wave Profile ◽  
Time Domain Method ◽  
Ship Motions ◽  
Quad Tree ◽  
Mesh Technique

AbstractA three-dimensional (3D) time-domain method is developed to predict ship motions in waves. To evaluate the Froude-Krylov (F-K) forces and hydrostatic forces under the instantaneous incident wave profile, an adaptive mesh technique based on a quad-tree subdivision is adopted to generate instantaneous wet meshes for ship. For quadrilateral panels under both mean free surface and instantaneous incident wave profiles, Froude-Krylov forces and hydrostatic forces are computed by analytical exact pressure integration expressions, allowing for considerably coarse meshes without loss of accuracy. And for quadrilateral panels interacting with the wave profile, F-K and hydrostatic forces are evaluated following a quad-tree subdivision. The transient free surface Green function (TFSGF) is essential to evaluate radiation and diffraction forces based on linear theory. To reduce the numerical error due to unclear partition, a precise integration method is applied to solve the TFSGF in the partition computation time domain. Computations are carried out for a Wigley hull form and S175 container ship, and the results show good agreement with both experimental results and published results.

A Quasi-three-dimensional Finite-volume Shallow Water Model for Green Water on Deck

2013 ◽  
Vol 57 (03) ◽  
pp. 125-140
Author(s):  
Daniel A. Liut ◽  
Kenneth M. Weems ◽  
Tin-Guen Yen
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Green Water ◽  
Water Model ◽  
Ship Motions ◽  
Shallow Water Model

A quasi-three-dimensional hydrodynamic model is presented to simulate shallow water phenomena. The method is based on a finite-volume approach designed to solve shallow water equations in the time domain. The nonlinearities of the governing equations are considered. The methodology can be used to compute green water effects on a variety of platforms with six-degrees-of-freedom motions. Different boundary and initial conditions can be applied for multiple types of moving platforms, like a ship's deck, tanks, etc. Comparisons with experimental data are discussed. The shallow water model has been integrated with the Large Amplitude Motions Program to compute the effects of green water flow over decks within a time-domain simulation of ship motions in waves. Results associated to this implementation are presented.

Time Domain Computation of the Wave-Making Resistance of Ships

2005 ◽  
Vol 49 (02) ◽  
pp. 144-158 ◽  
Author(s):  
F. Kara ◽  
D. Vassalos
Keyword(s):  
Steady State ◽  
Time Domain ◽  
Three Dimensional ◽  
Impulse Response Function ◽  
The Body ◽  
Source Distribution ◽  
Research Centre ◽  
Surface Source ◽  
Calm Water ◽  
Marine Engineering

The Ship Stability Research Centre, Department of Naval Architecture and Marine Engineering, The Universities of Glasgow and Strathclyde, Scotland, UKA linearized three-dimensional potential flow formulation in time domain is applied to calculate wave-making resistance of ships in calm water. Steady-state perturbation potentials for resistance are obtained as the steady-state limit of the surge radiation impulse response function using the transient free surface source distribution over the body surface. Five different vessels are used to validate the present numerical approximation. The results, including steady-state wave-making resistance, sinkage force, trim moment, and wave profile along the waterline, are compared with other published numerical and experimental results.

Near-Optimal Time-Domain Control of Small Buoys in Irregular Waves

2014 ◽  
Author(s):  
Umesh A. Korde ◽  
R. Cengiz Ertekin
Keyword(s):  
Optimal Control ◽  
Impulse Response ◽  
Time Domain ◽  
The Body ◽  
Irregular Waves ◽  
Single Frequency ◽  
Impulse Response Functions ◽  
Control Force ◽  
Response Functions ◽  
Absorbed Power

Within the linear theory framework, smooth optimal control for maximum energy conversion in irregular waves requires independent synthesis of two non-causal impulse response functions operating on the body oscillations near the free surface, and one non-causal impulse response function relating the exciting force to the incident wave profile at the body. Full cancellation of reactive forces and matching of radiation damping thus requires knowledge or estimation of device velocity into the future. As suggested in the literature, the control force can be synthesized in long-crested waves by suitably combining the ‘full’ impulse response functions with wave surface elevation information at an appropriately determined distance up-wave of the device. This paper applies the near-optimal control approach investigated earlier by one of the authors (Korde, UA, Applied Ocean Research, to appear) to small floating cylindrical buoys. Absorbed power performance is compared with two other cases, (i) when single-frequency tuning is used based on non-real time adjustment of the reactive and resistive loads to maximize conversion at the spectral peak frequency, and (ii) when no control is applied with damping set to a constant value. Time domain absorbed power results are discussed.

scholarly journals Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2102
Author(s):  
Abdul Majeed ◽  
Muhammad Abbas ◽  
Faiza Qayyum ◽  
Kenjiro T. Miura ◽  
Md Yushalify Misro ◽  
...  
Keyword(s):  
Geometric Modeling ◽  
Shape Parameter ◽  
3D Models ◽  
Basis Functions ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curves ◽  
Spline Basis ◽  
Cubic Polynomial ◽  
2D And 3D

Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.

scholarly journals Predictions of Ship Extreme Hydroelastic Load Responses in Harsh Irregular Waves and Hull Girder Ultimate Strength Assessment

2019 ◽  
Vol 9 (2) ◽  
pp. 240 ◽  
Author(s):  
Jialong Jiao ◽  
Yong Jiang ◽  
Hao Zhang ◽  
Chengjun Li ◽  
Chaohe Chen
Keyword(s):  
Ultimate Strength ◽  
Time Domain ◽  
Three Dimensional ◽  
Direct Calculation ◽  
Wave Force ◽  
Irregular Waves ◽  
Restoring Force ◽  
Strength Assessment ◽  
Hull Girder ◽  
Rule Approach

In this paper, the hydroelastic motion and load responses of a large flexible ship sailing in irregular seaways are predicted and the hull girder ultimate strength is subsequently evaluated. A three-dimensional time-domain nonlinear hydroelasticity theory is developed where the included nonlinearities are those arising from incident wave force, hydrostatic restoring force and slamming loads. The hull girder structure is simplified as a slender Timoshenko beam and fully coupled with the hydrodynamic model in a time domain. Segmented model towing-tank tests are then conducted to validate the proposed hydroelasticity theory. In addition, short-term and long-term predictions of ship responses in irregular seaways are conducted with the help of the developed hydroelastic code in order to determine the extreme design loads. Finally, a simplified strength-check equation is proposed, which will provide significant reference and convenience for ship design and evaluation. The hull girder ultimate strength is assessed by both the improved Rule approach and direct calculation.

THE BOUNDARY FACE METHOD WITH VARIABLE APPROXIMATION BY B-SPLINE BASIS FUNCTION

2012 ◽  
Vol 09 (01) ◽  
pp. 1240009 ◽  
Author(s):  
JINLIANG GU ◽  
JIANMING ZHANG ◽  
XIAOMIN SHENG
Keyword(s):  
Numerical Solutions ◽  
Basis Functions ◽  
Spline Functions ◽  
Well Performance ◽  
Geometric Information ◽  
B Spline ◽  
Numerical Tests ◽  
Boundary Integration ◽  
Spline Basis ◽  
Boundary Face

B-spline basis functions as a new approximation method is introduced in the boundary face method (BFM) to obtain numerical solutions of 3D potential problems. In the BFM, both boundary integration and variable approximation are performed in the parametric spaces of the boundary surfaces, therefore, keeps the exact geometric information of a body in which the problem is defined. In this paper, local bivariate B-spline functions are proposed to alleviate the influence of B-spline tensor product that will deteriorate the exactness of numerical results. Numerical tests show that the new method has well performance in both exactness and convergence.

Sign in / Sign up

Export Citation Format

Share Document