Asymptotic Solutions and Radiation Conditions for Second-Order Diffracted Waves

1989 ◽  
Vol 111 (3) ◽  
pp. 203-207
Author(s):  
H. Huang ◽  
J. Li ◽  
X. Wang
Keyword(s):  
Finite Element ◽  
Circular Cylinder ◽  
Second Order ◽  
Asymptotic Solutions ◽  
Wave Forces ◽  
Far Field ◽  
Two Dimensional ◽  
Diffracted Waves ◽  
Artificial Boundaries ◽  
Radiation Conditions

The far-field asymptotic solutions for the second-order diffracted waves have been developed, both in three and two-dimensional problems. The radiation conditions for the second-order diffracted waves are derived by using the asymptotic solutions. The nonlinear wave forces on a half-circular cylinder on seabed are presented by using finite element methods with the radiation conditions imposed on the artificial boundaries.

scholarly journals The Computation of the Magnitude of the Far Field for an Eccentric Circular Cylinder

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Bülent Yılmaz
Keyword(s):  
Circular Cylinder ◽  
Plane Wave ◽  
Radiation Condition ◽  
Higher Order ◽  
Numerical Results ◽  
Surface Radiation ◽  
Far Field ◽  
Condition Method ◽  
Radiation Conditions

The specific case of scattering of a plane wave by a two-layered penetrable eccentric circular cylinder has been considered and it is about the validity of the on surface radiation condition method and its applications to the scattering of a plane wave by a two-layered penetrable eccentric circular cylinder. The transformation of the problem of scattering by the eccentric circular cylinder to the problem of scattering by the concentric circular cylinder by using higher order radiation conditions, is observed. Numerical results presented the magnitude of the far field.

Second-Order Radiation Condition of Scattering Wave and Its Application

1990 ◽  
Vol 112 (3) ◽  
pp. 177-180
Author(s):  
J. Li ◽  
H. Huang
Keyword(s):  
Differential Operators ◽  
Three Dimensional ◽  
Radiation Condition ◽  
Second Order ◽  
Wave Forces ◽  
Interior Region ◽  
Linear Differential Operators ◽  
Scattering Wave ◽  
Linear Differential ◽  
Radiation Conditions

The first and second-order radiation conditions for scattering waves in two and three-dimensional problems have been derived by virtue of a sequence of linear differential operators. The wave forces on a large circular cylinder are computed by using finite element methods with first and second-order radiation conditions and the Sommerfeld condition, respectively. The results show that an improvement in accuracy is achieved by employing the second-order radiation condition. The interior region in which finite elements are employed can be restricted to a much smaller one, compared with that using the Sommerfeld condition and the computing efforts and required storage in the computer are reduced.

A numerical method for two-dimensional nonlinear modified time-fractional fourth-order diffusion equation

2019 ◽  
Vol 10 (01) ◽  
pp. 1941005 ◽  
Author(s):  
Haiyan He ◽  
Kaijie Liang ◽  
Baoli Yin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Fourth Order ◽  
Time Derivative ◽  
Second Order ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Discrete Scheme ◽  
Fully Discrete

In this paper, we consider the finite element method for two-dimensional nonlinear modified time-fractional fourth-order diffusion equation. In order to avoid using higher order elements, we introduce an intermediate variable [Formula: see text] and translate the fourth-order derivative of the original problem into a second-order coupled system. We discretize the fractional time derivative terms by using the [Formula: see text]-approximation and discretize the first-order time derivative term by using the second-order backward differentiation formula. In the fully discrete scheme, we implement the finite element method for the spatial approximation. Unconditional stability of the fully discrete scheme is proven and its optimal convergence order is obtained. Numerical experiments are carried out to demonstrate our theoretical analysis.

A Theoretical Study on the Second-Order Wave Forces for Two-Dimensional Bodies

1989 ◽  
Vol 111 (1) ◽  
pp. 37-42 ◽  
Author(s):  
G. P. Miao ◽  
Y. Z. Liu
Keyword(s):  
Nonlinear Wave ◽  
Incident Wave ◽  
Theoretical Study ◽  
Nonlinear Effects ◽  
Offshore Structures ◽  
Second Order ◽  
Wave Forces ◽  
Two Dimensional ◽  
Regular Waves ◽  
Steady Wave

Nonlinear wave forces on fixed or floating offshore structures have attracted much attention recently. This paper deals with the nonlinear effects of regular waves on fixed two-dimensional bodies up to second-order terms. The second-order diffraction potential is solved consistently and the second-order steady wave forces and the biharmonic wave forces with frequency corresponding to the double of the incident wave frequency are obtained.

C1 CONTINUITY FINITE ELEMENT FORMULATION IN SECOND-ORDER COMPUTATIONAL HOMOGENIZATION SCHEME

2012 ◽  
Vol 04 (04) ◽  
pp. 1250013 ◽  
Author(s):  
TOMISLAV LESIČAR ◽  
ZDENKO TONKOVIĆ ◽  
JURICA SORIĆ
Keyword(s):  
Finite Element ◽  
Gradient Elasticity ◽  
Computational Homogenization ◽  
Second Order ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Two Dimensional ◽  
Triangular Finite Element ◽  
Patch Tests ◽  
Quadrilateral Finite Element

The paper describes a second-order two-scale computational homogenization procedure for modeling of heterogeneous materials at small strains. The Aifantis theory of linear elasticity has been described and implemented into the two dimensional C1 continuity triangular finite element formulation. The element has been verified on several patch tests and the computational efficiency of numerical integration of the element stiffness matrix has been tested as well. Furthermore, the C1 two dimensional triangular finite element based on full second gradient continuum is formulated and used for the macrolevel discretization in the frame of a multiscale scheme, where the RVE is discretized by the C0 quadrilateral finite element. The application of generalized periodic boundary conditions and the microfluctuation integral condition on RVE has been investigated. The presented numerical algorithms have been implemented into FE software ABAQUS via user subroutines and verified on a pure bending problem. The comparability of RVE size to the length scale parameter of gradient elasticity has been proved, and elastoplastic behavior of heterogeneous material has been also considered. The results obtained show good numerical efficiency of the proposed algorithms.

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