Numerical study on a hybrid water wave radiation condition by a 3D boundary element method (original) (raw)

Second-Order Radiation Boundary Condition for Water Wave Simulation with Large Angle Incidence

Journal of Engineering Mechanics, 2003

A finite-element method ͑FEM͒ is used to simulate water wave propagation with large angle incidence at exterior boundaries. In this paper, the radiation boundary condition is expanded to a second-order approximation and a quadratic shape function is used in the FEM wave model. Cases used for verifications include wave scattering around a vertical cylinder and wave propagation over a submerged circular shoal with concentric contours. Numerical calculations based on this second-order radiation boundary condition are found to be in good agreement with theoretical and experimental results available. The numerical predictions show that this model has made a very good improvement over the first-order radiation boundary conditions for oblique wave incidence in coastal engineering.

2-D numerical wave Tank by boundary element method using different numerical techniques

In this article, numerical modeling of a 2-D wave tank has been investigated by applying completely nonlinear condition for water surface elevation. This has been accomplished based on potential theory, the combined Eulerian-Lagrangian scheme for time marching and using boundary element method. Other physical and numerical attributes of the current work are: physical modeling in time domain, time integration by 4 th order Runge-Kutta method, implementation of appropriate condition at the entrance boundary for wave generation, application of artificial dampers at the exit part of the wave tank, and ultimately numerical smoothing of the resulting free surface by using interpolation through spline functions. At the end, effective parameters on the generated wave have been analyzed and the generated wave has also been validated against the result of the linear wave theory.

A hybrid element method for diffraction of water waves by three-dimensional bodies

International Journal for Numerical Methods in Engineering, 1978

A hybrid elcment method developed recently for two-dimensional problems of water waves in an infinite fluid is extended to three dimensions. In this method only a limited fluid domain close to irregular bodies is discretized into conventional finite elements, while the remaining infinite domain is treated as one element with analytical representations of high accuracy. Continuity at the junction surface is treated as natural boundary conditions in a variational principle. Computation experience and numerical results for several ocean structures are presented.

Singular boundary method for water wave problems

This article presents the singular boundary method (SBM) for water wave-structure interaction analysis. The SBM is a novel recent boundary meshless collocation method, which uses the singular fundamental solutions of governing equation as basis function in the interpolation formulation and introduces the concept of source intensity factors to avoid the singularities of the fundamental solutions at origin. It is a strong-form meshless boundary collocation technique with the merits being easy-to-implement and integration-free. In this study, two types of water wave-structure interactions, water wave interaction of multiple-cylinder-array structure and semicircular harbor, are considered. Numerical results show the efficiency and accuracy of the present SBM scheme in comparison with the analytical solutions, the method of fundamental solutions and the null field boundary integral element method. Then the near trapped mode phenomenon of ten-cylinder structure and the focusing effect of the semicircular harbor are revisited by using the present SBM.

Transient analysis of three-dimensional wave propagation using the boundary element method

International Journal for Numerical Methods in Engineering, 1987

In the past the time domain solution of the wave equation has been limited to simplified problems. This was due to the limitations of analytical methods and the capacity of computers to manipulate and store 'large' blocks of spatial information. With the advent of 'super computers' the ability to solve such problems has significantly increased. This paper outlines a method for transient analysis of wave propagation in arbitrary domains using a boundary element method. The technique presented will allow the definition ofa domain, the input of impedance conditions on the domain's surface, the specification of inputs on the surface, and the specification of initial conditions within the domain. It will produce a complete solution of the wave equation inside the domain. The techniques are demonstrated using a program with a boundary element formulation of Kirchhoff s equation. The elements used are triangular and compatible. TNTRODUCTTON Numerical solution of time domain wave propagation studies is possible using a variety of techniques, including the generalized finite difference and finite element methods. However, there are certain advantages to using boundary integral methods since the complete spatial domain of interest need not be discretized. Furthermore, since a Green's function solution is inherent in the boundary integral formulation, some of the interpolation errors which are characteristic of both finite difference and finite element methods are avoided. The original boundary integral time domain wave propagation formulations were developed by Cruse and Rizzo' and Cruse2 to study stress wave propagation in arbitrary domains. The technique solved the integral equations in the Laplace domain and then inverse transformed the solution to obtain the time domain solution. Reference 3 is a more recent work by Rizzo et al., on the three-dimensional treatment of elastic waves in frequency domain. Manolis and Beskos4 numerically solved the formulation of Cruse and Rizzo for two-dimensional dynamic stress concentration studies. This transformation technique requircs a large number of boundary integral evaluations in the Laplace domain in order that the time domain solution be accurate and have a large bandwidth. Thus, the Laplace transform-based techniques are relatively expensive, especially for three-dimensional problems. Direct time domain solutions of scalar wave propagation have been developed by Mansur and

Water wave diffraction analysis by boundary elements

Applied Mathematical Modelling, 1994

This paper presents a mathematicalformulation for the boundary element method and its application in solving water-wave-related boundary value problems. The approach presented here permits relation of the method to other numerical techniques, such as finite elements, and more importantly gives an easy and flexible way of introducing and implementing boundary elements. The introduction of many useful concepts now widely used by the finite-element method would give us a better understanding of the fundamental principles shared by the two methods and of their basic difference, hence the possibility of better selection, combination, and mutual contribution of these two powerful methods for solving particular problems. Two examples of water wave dijiiaction have been provided. Some of the results are for boundary elements as well as water wave diffi-action. Comparison of the computed results with existing numerical andanalytical results shows excellent agreement.

Refraction and diffraction of water waves using finite elements with a DNL boundary condition

A discrete non-local (DNL) boundary condition is used to solve diffraction and refraction water waves problems. The finite elements with a DNL boundary condition are used to solve a wide range of unbounded surface wave problems. Two order low strategies are examined in rectangular and/or circular two-dimensional coordinates system. Numerical studies reveal the advantages of using this numerical approach and its limitations in case of variations of wave number in direction to infinity. Two new procedures to improve the accuracy of DNL boundary in case of significant variations of wave number in the domain are therefore developed. These procedures are based on the addition of a term to the numerical scheme, that collects the error away from the open boundary. Such term can be incorporated into the DNL formula as a source term or as an additional layer. This improvement permits the development of a suitable solution method, which is tested against analytical solutions and other methods, for bi-dimensional water waves problems defined on rectangular or circular geometries. Also, implementation details are reported. Satisfactory numerical results confirm the improvement of DNL method in case of dependent range, which allow us to conclude that the DNL method is an achievable method for the solution of unbounded water waves problems governed by the Helmholtz equation.

Wave Radiation by a Floating Body in Water of Finite Depth Using an Exact DtN Boundary Condition

Journal of Ocean University of China, 2023

The present paper focuses on the wave radiation by an oscillating body with six degrees of freedom by using the DtN artificial boundary condition. The artificial boundary is usually selected as a circle or spherical surface to solve various types of fields, such as sound waves or electromagnetic waves, provided that the considered domain is infinite or unbounded in all directions. However, the substantial wave motion is considered in water of finite depth, that is, the fluid domain is bounded vertically but unbounded horizontally. Thus, the DtN boundary condition is given on an artificial cylindrical surface, which divides the water domain into an interior and exterior region. The boundary integral equation is adopted to implement the present model. In the case of a floating cylinder, the results of hydrodynamic coefficients of a chamfer box are discussed.

Three-dimensional numerical wave generation with moving boundaries

Coastal Engineering, 2015

In this work the numerical model IHFOAM is extended to incorporate moving-boundary wave generation and absorption capabilities. The goal is to obtain a solver that includes free surface flow through porous media, able to replicate the wave generation procedures of physical wave basins. For this purpose a new boundary condition to mimic the action of multi-paddle piston wavemakers is developed and the dynamic mesh capabilities present in OpenFOAM ® are enhanced. A set of experiments is carried out in the laboratory and is reproduced numerically to validate the correct operation of the new module. Additional numerical experiments are carried out to test the efficiency of active wave absorption. The results indicate a high degree of accordance between the experimental and numerical results and a correct performance of active wave absorption at the moving boundary.