scholarly journals WAVE INDUCED OSCILLATIONS OF HARBORS WITH VARIABLE DEPTH

1976 ◽  
Vol 1 (15) ◽  
pp. 203 ◽  
Author(s):  
F. Raichlen ◽  
E. Naheer
Keyword(s):  
Finite Difference ◽  
Helmholtz Equation ◽  
Numerical Method ◽  
Wave Energy ◽  
Water Surface ◽  
Two Dimensional ◽  
Variable Depth ◽  
Open Sea ◽  
Complex Shapes ◽  
Wave Induced

A numerical method is presented to treat the wave-induced oscillations of a harbor with a variable depth and width. A two-dimensional finite difference approach is used inside the harbor matched at the entrance to a solution for the open-sea based on the Helmholtz Equation which includes incident, reflected, and radiated wave energy. Examples of the response and the modal shapes of the water surface are presented for harbors with simple and complex shapes.

scholarly journals SIXTH-ORDER ACCURATE FINITE DIFFERENCE SCHEMES FOR THE HELMHOLTZ EQUATION

2006 ◽  
Vol 14 (03) ◽  
pp. 339-351 ◽  
Author(s):  
I. SINGER ◽  
E. TURKEL
Keyword(s):  
Finite Difference ◽  
Helmholtz Equation ◽  
Truncation Error ◽  
Model Problem ◽  
Difference Schemes ◽  
Sixth Order ◽  
Finite Difference Schemes ◽  
Local Truncation Error ◽  
Two Dimensional ◽  
Truncation Order

We develop and analyze finite difference schemes for the two-dimensional Helmholtz equation. The schemes which are based on nine-point approximation have a sixth-order accurate local truncation order. The schemes are compared with the standard five-point pointwise representation, which has second-order accurate local truncation error and a nine-point fourth-order local truncation error scheme based on a Padé approximation. Numerical results are presented for a model problem.

scholarly journals GIS-based two-dimensional numerical simulation of rainfall-induced debris flow

2008 ◽  
Vol 8 (1) ◽  
pp. 47-58 ◽  
Author(s):  
C. Wang ◽  
S. Li ◽  
T. Esaki
Keyword(s):  
Numerical Model ◽  
Finite Difference ◽  
Debris Flow ◽  
Numerical Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Field Investigation ◽  
Uniform Grid ◽  
Water Mixture ◽  
Two Dimensional

Abstract. This paper aims to present a useful numerical method to simulate the propagation and deposition of debris flow across the three dimensional complex terrain. A depth-averaged two-dimensional numerical model is developed, in which the debris and water mixture is assumed to be continuous, incompressible, unsteady flow. The model is based on the continuity equations and Navier-Stokes equations. Raster grid networks of digital elevation model in GIS provide a uniform grid system to describe complex topography. As the raster grid can be used as the finite difference mesh, the continuity and momentum equations are solved numerically using the finite difference method. The numerical model is applied to simulate the rainfall-induced debris flow occurred in 20 July 2003, in Minamata City of southern Kyushu, Japan. The simulation reproduces the propagation and deposition and the results are in good agreement with the field investigation. The synthesis of numerical method and GIS makes possible the solution of debris flow over a realistic terrain, and can be used to estimate the flow range, and to define potentially hazardous areas for homes and road section.

scholarly journals Modified Explicit Decoupled Group Scheme οn Helmholtz Equation

2020 ◽  
Vol Volume 14 ◽  
Keyword(s):  
Computational Complexity ◽  
Finite Difference ◽  
Iterative Method ◽  
Helmholtz Equation ◽  
Group Scheme ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Group Method ◽  
Two Dimensional ◽  
New Formulation

In this paper, the formulation of a new group iterative method called the Modified Explicit Decoupled Group method in solving the two dimensional Helmholtz equation is described. The method is derived using a combination of the five-point finite difference approximation on the rotated grid stencil together with the five-point centred difference approximation on the standard grid stencils. Numerical experimentations of this new formulation shows significant improvement in computational complexity and execution timings over the original Explicit Decoupled Group method [2].

scholarly journals WAVE-INDUCED OSCILLATIONS IN HARBORS WITH WAVE-ABSORBING QUAY

1984 ◽  
Vol 1 (19) ◽  
pp. 63
Author(s):  
Akinori Yoshida ◽  
Takeshi Ijima ◽  
Hideaki Okuzono
Keyword(s):  
Integral Equation ◽  
Velocity Potential ◽  
Side Wall ◽  
Source Distribution ◽  
Powerful Method ◽  
Variable Depth ◽  
Open Sea ◽  
The Fourier Transform ◽  
Wave Induced ◽  
Wave Reduction

An artificial wave-absorber (wave-absorbing quay) has come to be widely used to counteract excessive wave action on ships and structures in harbors. Its two-dimensional characteristics on wave absorption have been investigated with several types of the wave-absorbing quay theoretically as well as experimentally, e.g., Jarlan (5), Terret, Osorio and Lean (9), Ijima, Tanaka and Okuzono (3), and Ijima and Okuzono (4), but the effects on the wave reduction in harbors seem to be not fully clear. This may be due to the lack of analytical methods for solving wave-induced oscillations in harbors with the wave-absorbing quay. When the side wall in the harbor basin is assumed to be perfectly reflective, many theoretical methods for solving wave-induced oscillations in harbors have been presented: Ippen and Goda (2) solved the problem of a rectangular harbor by using the Fourier Transform technique. Hwang and Tuck (1) presented powerful method, which is applicable to arbitrary shaped harbors, by using integral equation (source distribution along the boundary) for the expression of the velocity potential. A similar method to that of Hwang and Tuck, but more suitable one for numerical computation, was presented by Lee (6), who used integral equation separately in the harbor basin and in the open sea. Raichlen and Naheer (8), Mattioli (7), and Yoshida and Ijima (10) presented the methods being applicable to the harbors of arbitrary shape and variable depth by further extending Lee's method.

scholarly journals Calculation of exact frequency-dependent rays when the solution of the Helmholtz equation is known

2015 ◽  
pp. 586-594
Author(s):  
К.Г. Гадыльшин ◽  
М.И. Протасов
Keyword(s):  
Finite Difference ◽  
Helmholtz Equation ◽  
Numerical Method ◽  
Numerical Experiments ◽  
Ray Theory ◽  
Frequency Dependent ◽  
Distinctive Features ◽  
First Time

Предложен численный метод построения точных частотно-зависимых лучей, когда известно решение уравнения Гельмгольца. Впервые представлен анализ свойств частотно-зависимых лучей и их сравнение со стандартной лучевой теорией и с методом конечно-разностного моделирования. Изучена зависимость частотно-зависимых лучей от частоты зондирующего сигнала. Показано, что при увеличении частоты частотно-зависимые лучи стремятся к классическим лучам. Численные эксперименты демонстрируют отличительные особенности частотно-зависимых лучей, в частности их способность проникать в зоны тени, недоступные для классической лучевой теории. A numerical method is proposed for the calculation of exact frequency-dependent rays when the solution of the Helmholtz equation is known. The properties of frequency-dependent rays are analyzed and compared with the classical ray theory and with the method of finite-difference modeling for the first time. In this paper we study the dependence of these rays on the frequency of probing signals and show the convergence of the exact rays to the classical rays with increasing frequency. A number of numerical experiments demonstrate the distinctive features of exact frequency-dependent rays, in particular, their ability to penetrate into shadow zones impenetrable for the classical rays.

Modelling of Moisture Movement in Wood during Outdoor Storage

2001 ◽  
Vol 6 (2) ◽  
pp. 3-14 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
I. Juodeikienė ◽  
A. Kajalavičius
Keyword(s):  
Experimental Data ◽  
Finite Difference ◽  
Climatic Conditions ◽  
Two Dimensional ◽  
Moisture Movement ◽  
Finite Difference Technique ◽  
Long Term Storage ◽  
Space Formulation ◽  
Term Storage

A model of moisture movement in wood is presented in this paper in a two-dimensional-in-space formulation. The finite-difference technique has been used in order to obtain the solution of the problem. The model was applied to predict the moisture content in sawn boards from pine during long term storage under outdoor climatic conditions. The satisfactory agreement between the numerical solution and experimental data was obtained.

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