Fully-Nonlinear Wave-Current-Body Interaction Analysis by a Harmonic Polynomial Cell Method

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Yan-Lin Shao ◽  
Odd M. Faltinsen
Keyword(s):  
Circular Cylinder ◽  
Boundary Element ◽  
Nonlinear Wave ◽  
Wave Diffraction ◽  
Harmonic Polynomial ◽  
Boundary Element Methods ◽  
Fully Nonlinear ◽  
Marine Hydrodynamics ◽  
Body Interaction ◽  
Cell Method

A new numerical 2D cell method has been proposed by the authors, based on representing the velocity potential in each cell by harmonic polynomials. The method was named the harmonic polynomial cell (HPC) method. The method was later extended to 3D to study potential-flow problems in marine hydrodynamics. With the considered number of unknowns that are typical in marine hydrodynamics, the comparisons with some existing boundary element- based methods, including the fast multipole accelerated boundary element methods, showed that the HPC method is very competitive in terms of both accuracy and efficiency. The HPC method has also been applied to study fully-nonlinear wave-body interactions; for example, sloshing in tanks, nonlinear waves over different sea-bottom topographies, and nonlinear wave diffraction by a bottom-mounted vertical circular cylinder. However, no current effects were considered. In this paper, we study the fully-nonlinear time-domain wave-body interaction considering the current effects. In order to validate and verify the method, a bottom-mounted vertical circular cylinder, which has been studied extensively in the literature, will first be examined. Comparisons are made with the published numerical results and experimental results. As a further application, the HPC method will be used to study multiple bottom-mounted cylinders. An example of the wave diffraction of two bottom-mounted cylinders is also presented.

Fully-Nonlinear Wave-Current-Body Interaction Analysis by a Harmonic Polynomial Cell (HPC) Method

2013 ◽  
Author(s):  
Yan-Lin Shao ◽  
Odd M. Faltinsen
Keyword(s):  
Circular Cylinder ◽  
Boundary Element ◽  
Nonlinear Wave ◽  
Wave Diffraction ◽  
Interaction Analysis ◽  
Harmonic Polynomial ◽  
Boundary Element Methods ◽  
Fully Nonlinear ◽  
Marine Hydrodynamics ◽  
Body Interaction

In the Ronald W. Yeung Honoring Symposium on Offshore and Ship Hydrodynamics in OMAE2012 hold in Rio de Janeiro, Shao & Faltinsen [1] have proposed a new numerical 2D cell method based on representing the velocity potential in each cell by harmonic polynomials. The method was named the Harmonic Polynomial cell (HPC) method. The method was later extended to 3D to study potential-flow problems in marine hydrodynamics [2]. With the considered number of unknowns that are typical in marine hydrodynamics, the comparisons with some existing boundary element based methods including the Fast Multipole Accelerated Boundary Element Methods showed that the HPC method is very competitive in terms of both accuracy and efficiency. The HPC method has also been applied to study fully-nonlinear wave-body interactions [1, 2], for example, sloshing in tanks, nonlinear waves over different sea-bottom topographies and nonlinear wave diffraction by a bottom-mounted vertical circular cylinder. However, no current effects were considered. In this paper, we study the fully-nonlinear time-domain wave-body interaction considering the current effects. In order to validate and verify the method, a bottom-mounted vertical circular cylinder which has been studied extensively in the literature will first be examined. Comparisons are made with published numerical results and experimental results. As a further application, the HPC method will be used to study multiple bottom-mounted cylinders. An example of the wave diffraction of two bottom-mounted cylinders is also presented.

Efficient Computations of Fully-Nonlinear Wave Interactions With Floating Structures

2010 ◽  
Author(s):  
Hongmei Yan ◽  
Yuming Liu
Keyword(s):  
Boundary Element ◽  
High Efficiency ◽  
Three Dimensional ◽  
Nonlinear Effects ◽  
Computational Effort ◽  
Boundary Element Methods ◽  
Computational Method ◽  
Wave Interactions ◽  
Time Step ◽  
Fully Nonlinear

We consider the problem of fully nonlinear three-dimensional wave interactions with floating bodies with or without a forward speed. A highly efficient time-domain computational method is developed in the context of potential flow formulation using the pre-corrected Fast Fourier Transform (PFFT) algorithm based on a high-order boundary element method. The method reduces the computational effort in solving the boundary-value problem at each time step to O(NlnN) from O(N2∼3) of the classical boundary element methods, where N is the total number of unknowns. The high efficiency of this method allows accurate computations of fully-nonlinear hydrodynamic loads, wave runups, and motions of surface vessels and marine structures in rough seas. We apply this method to study the hydrodynamics of floating objects with a focus on the understanding of fully nonlinear effects in the presence of extreme waves and large-amplitude body motions.

Numerical Simulation of Nonlinear Wave Diffraction by a Vertical Cylinder

1992 ◽  
Vol 114 (1) ◽  
pp. 36-44 ◽  
Author(s):  
C. Yang ◽  
R. C. Ertekin
Keyword(s):  
Experimental Data ◽  
Circular Cylinder ◽  
Nonlinear Wave ◽  
Wave Diffraction ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Radiation Condition ◽  
Wave Force ◽  
Second Order ◽  
Time Stepping

A three-dimensional time domain approach is used to study nonlinear wave diffraction by a fixed, vertical circular-cylinder that extends to the sea floor. In this approach, the development of the flow can be obtained by a time-stepping procedure, in which the velocity potential of the flow at any instant of time is obtained by the boundary-element method. In the numerical calculations, the exact body-boundary condition is satisfied on the instantaneous wetted surface of the cylinder, and an extended Sommerfeld condition is developed and used as the numerical radiation condition. The fourth-order Adams-Bashford method is employed in the time stepping scheme. Calculations are done to obtain the nonlinear diffraction of solitary waves and Stokes second-order waves by a vertical circular-cylinder. Numerical results are compared with the available linear and second-order wave-force predictions for some given wave height and wavelength conditions, and also with experimental data. Present horizontal force results agree better with the experimental data than the previous predictions.

Fully-Nonlinear Simulation of the Hydrodynamics of a Floating Body in Surface Waves by a High-Order Boundary Element Method

2015 ◽  
Author(s):  
Chengxi Li ◽  
Yuming Liu
Keyword(s):  
Boundary Element Method ◽  
Rigid Body ◽  
Surface Waves ◽  
Boundary Element ◽  
Nonlinear Wave ◽  
Empirical Modeling ◽  
Body Motion ◽  
Viscous Effect ◽  
Fully Nonlinear ◽  
Element Method

The objective of this work is to understand and evaluate the hydrodynamics modeling of a floating rigid body in regular and irregular ocean surface waves. Direct time-domain numerical simulation, based on the potential-flow formulation with the use of a quadratic boundary element method, is employed to compute the response of the body under the action of surface waves including fully-nonlinear wave-body interaction effects associated with steep waves and large-amplitude body motions. The viscous effect due to flow separation and turbulence is included by empirical modeling. The simulation results of body motions are compared with laboratory experimental measurements. The nonlinear effects due to body motion and wave motion are quantified and compared to the viscous effect. Their relative importance in the prediction and modeling of a rigid body motion under various wave conditions is investigated. This study may provide essential information pertaining to develop effective modeling of nonlinear wave-body interactions which is needed in design of offshore structures and wave energy conversion devices.

Scaled Boundary FEM Solution of Wave Diffraction by a Circular Cylinder

2007 ◽  
Author(s):  
Hao Song ◽  
Longbin Tao
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Circular Cylinder ◽  
Differential Equations ◽  
Wave Diffraction ◽  
Wave Structure ◽  
Boundary Element Methods ◽  
Surface Boundary ◽  
Unbounded Medium ◽  
Matrix Differential

The scaled boundary finite-element method (SBFEM) is a novel semi-analytical approach, with the combined advantages of both finite-element and boundary-element methods. The basic idea behind SBFEM is to discretize the surface boundary by FEM and transform the governing partial differential equations to ordinary differential equations of the radial parameter. The radial differential equation is then solved analytically. It has the inherent advantage for solving problems in unbounded medium with discretization to the interface only. In this paper, SBFEM is applied to solve the wave diffraction by a circular cylinder. The final radial matrix differential equation is solved fully analytically without adoption of any numerical scheme. Comparisons to the previous analytical solutions demonstrate the excellent computation accuracy and efficiency of the present SBFEM approach. It also revealed the great potential of the SBFEM to solve more complex wave-structure interaction problems.

Towards Efficient Fully-Nonlinear Potential-Flow Solvers in Marine Hydrodynamics

2012 ◽  
Author(s):  
Yan-Lin Shao ◽  
Odd M. Faltinsen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Nonlinear Wave ◽  
Potential Flow ◽  
Two Dimensions ◽  
The Other ◽  
Linear Wave ◽  
Fully Nonlinear ◽  
Marine Hydrodynamics ◽  
Element Method

Solving potential-flow problems using the Boundary Element Method (BEM) is a strong tradition in marine hydrodynamics. An early example of the application of BEM is by Bai & Yeung [1]. The bottleneck of the conventional BEM in terms of CPU time and computer memory arises as the number of unknowns increases. Wu & Eatock Taylor [2] suggested that the Finite Element Method (FEM) field solver is much faster than the BEM based on their comparisons in a wave making problem. In this paper, we aim to find a highly efficient method to solve fully-nonlinear wave-body interaction problems based on potential-flow theory. We compare the efficiency and the accuracy of five different methods for the potential flows in two dimensions (2D), two of which are BEM-based while the other three are field solvers. The comparisons indicate that it is beneficial to use either an accelerated matrix-free BEM, e.g. Fast Multipole Method accelerated BEM (FMM-BEM), or any field solvers whose resulting matrix are sparse. Another highlight of this paper is that an efficient numerical potential-flow method named the harmonic polynomial cell (HPC) method is developed. The flow in each cell is described by a set of harmonic polynomials. The presented procedure has approximately 4th order accuracy, while its resulting matrix is sparse similarly as the other field solvers, e.g. Finite Element Method (FEM), Finite Difference Method (FDM) and Finite Volume Method (FVM). The method is verified by a linear wave making problem for which the steady-state analytical solution is available, and the forced oscillation of a semi-submerged circular cylinder for which the frequency-domain added mass and damping coefficients are compared. The fully-nonlinear wave making problem and nonlinear propagating waves over a submerged bar are also studied for validation purposes. Only 2D cases are studied in this paper.

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