Green Function Solutions for the Transient Motion of Water Sections

2002 ◽  
Vol 46 (02) ◽  
pp. 99-120
Author(s):  
D. S. Holloway ◽  
M. R. Davis
Keyword(s):  
Green Function ◽  
Computational Algorithm ◽  
Liquid Surface ◽  
Domain Boundary ◽  
Analytic Solutions ◽  
Function Solution ◽  
Fixed Frame ◽  
Strip Theory ◽  
High Froude Number ◽  
The Green Function

A time-domain boundary element method based on a Green function solution is derived for two-dimensional motions in the presence of a free liquid surface. Particular attention is given to the numerical evaluation of the required Green functions with regard to accuracy and speed of solution by choice of a computational algorithm appropriate to the domain of particular computations. The method is validated with reference to analytic solutions for submerged and floating cylinders in steady, transient and periodic motion. The intended application of the method is in the computation of wave response of slender ships at high Froude number by a fixed frame strip theory where the Green function obviates the necessity to panel the free surface with elements.

scholarly journals AN ANALYTICAL TEMPERATURE SOLUTION ANALYSIS FOR A MULTILAYER HEAT CONDUCTION PROBLEM

2014 ◽  
Vol 13 (2) ◽  
pp. 89
Author(s):  
G. C. Oliveira ◽  
A. P. Fernandes ◽  
G. Guimarães
Keyword(s):  
Heat Conduction ◽  
Green Function ◽  
Analytical Solution ◽  
Heat Conduction Problem ◽  
Direct Method ◽  
Function Solution ◽  
Solution Equation ◽  
Temperature Solution ◽  
The Green Function ◽  
A Direct Method

This paper presents a method of obtaining an analytic temperature solution for a two-layer heat conduction problem. Obtaining the temperature analytical solution for a multilayer heat conduction problem is not a direct method. The way to indentify the eigenvalues and to derive the Green function solution equation requires a different treatment since there are more than one domain to solve. This work presents a solution of a thermal twolayer problem based on Green’s functions.

Application of the Green Function Method to the XY Model in a Magnetic Field

1974 ◽  
Vol 52 (17) ◽  
pp. 1660-1665 ◽  
Author(s):  
D. J. Austen
Keyword(s):  
Magnetic Field ◽  
Green Function ◽  
Three Dimensions ◽  
Xy Model ◽  
Zero Field ◽  
Green Function Method ◽  
Function Solution ◽  
Cubic Lattices ◽  
The Green Function ◽  
Improved Accuracy

This paper exhibits a simple, approximate Green function solution for the XY model of ferromagnetism in three dimensions from which we obtain the critical temperature, magnetization, internal energy, free energy, and entropy as a function of a magnetic field in the z direction. Comparison with Padé analysis of known high temperature series indicates an accuracy for TC in zero field to within 2% on all three cubic lattices and improved accuracy for nonzero fields. Solutions are obtained only for T ≥ TC.

Random fiber network loaded by a point force

2021 ◽  
pp. 1-11
Author(s):  
Catalin Picu ◽  
Jacob Merson
Keyword(s):  
Green Function ◽  
Linear Elasticity ◽  
Displacement Field ◽  
Point Force ◽  
Fiber Network ◽  
Function Solution ◽  
Network Parameters ◽  
The Green Function ◽  
Nonlocal Nature

Abstract This article presents the displacement field produced by a point force acting on an athermal random fiber network (the Green function for the network). The problem is defined within the limits of linear elasticity and the field is obtained numerically for nonaffine networks characterized by various parameter sets. The classical Green function solution applies at distances from the point force larger than a threshold which is independent of the network parameters in the range studied. At smaller distances, the nonlocal nature of fiber interactions modifies the solution.

scholarly journals Penerapan Fungsi Green dari Persamaan Poisson pada Elektrostatika

2021 ◽  
Vol 1 (1) ◽  
pp. 56-79
Author(s):  
Fathul Khairi ◽  
Malahayati
Keyword(s):  
Green Function ◽  
Dirichlet Boundary ◽  
Delta Function ◽  
Dirac Delta Function ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Dirac Delta ◽  
Function Solution ◽  
The Poisson Equation ◽  
The Green Function

The Dirac delta function is a function that mathematically does not meet the criteria as a function, this is because the function has an infinite value at a point. However, in physics the Dirac Delta function is an important construction, one of which is in constructing the Green function. This research constructs the Green function by utilizing the Dirac Delta function and Green identity. Furthermore, the construction is directed at the Green function of the Poisson's equation which is equipped with the Dirichlet boundary condition. After the form of the Green function solution from the Poisson's equation is obtained, the Green function is determined by means of the expansion of the eigen functions in the Poisson's equation. These results are used to analyze the application of the Poisson equation in electrostatic.

scholarly journals The Approximate and Analytic Solutions of the Time-Fractional Intermediate Diffusion Wave Equation Associated with the Fokker–Planck Operator and Applications

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 230
Author(s):  
Entsar A. Abdel-Rehim
Keyword(s):  
Wave Equation ◽  
Green Function ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Fractional Operator ◽  
Fractional Wave Equation ◽  
Constant Coefficients ◽  
The Green Function ◽  
Time Fractional Wave Equation ◽  
Fokker Planck

In this paper, the time-fractional wave equation associated with the space-fractional Fokker–Planck operator and with the time-fractional-damped term is studied. The concept of the Green function is implemented to drive the analytic solution of the three-term time-fractional equation. The explicit expressions for the Green function G3(t) of the three-term time-fractional wave equation with constant coefficients is also studied for two physical and biological models. The explicit analytic solutions, for the two studied models, are expressed in terms of the Weber, hypergeometric, exponential, and Mittag–Leffler functions. The relation to the diffusion equation is given. The asymptotic behaviors of the Mittag–Leffler function, the hypergeometric function 1F1, and the exponential functions are compared numerically. The Grünwald–Letnikov scheme is used to derive the approximate difference schemes of the Caputo time-fractional operator and the Feller–Riesz space-fractional operator. The explicit difference scheme is numerically studied, and the simulations of the approximate solutions are plotted for different values of the fractional orders.

scholarly journals Tidally generated internal-wave attractors between double ridges

2011 ◽  
Vol 669 ◽  
pp. 354-374 ◽  
Author(s):  
P. ECHEVERRI ◽  
T. YOKOSSI ◽  
N. J. BALMFORTH ◽  
T. PEACOCK
Keyword(s):  
Green Function ◽  
Numerical Solutions ◽  
Tidal Flow ◽  
Numerical Procedure ◽  
Internal Tides ◽  
Function Technique ◽  
Function Solution ◽  
Flow Over Topography ◽  
Grid Points ◽  
The Green Function

A study is presented of the generation of internal tides by barotropic tidal flow over topography in the shape of a double ridge. An iterative map is constructed to expedite the search for the closed ray paths that form wave attractors in this geometry. The map connects the positions along a ray path of consecutive reflections from the surface, which is double-valued owing to the presence of both left- and right-going waves, but which can be made into a genuine one-dimensional map using a checkerboarding algorithm. Calculations are then presented for the steady-state scattering of internal tides from the barotropic tide above the double ridges. The calculations exploit a Green function technique that distributes sources along the topography to generate the scattering, and discretizes in space to calculate the source density via a standard matrix inversion. When attractors are present, the numerical procedure appears to fail, displaying no convergence with the number of grid points used in the spatial discretizations, indicating a failure of the Green function solution. With the addition of dissipation into the problem, these difficulties are avoided, leading to convergent numerical solutions. The paper concludes with a comparison between theory and a laboratory experiment.

Exponentially Convergent Approximation to the Elliptic Solution Operator

2006 ◽  
Vol 6 (4) ◽  
pp. 386-404 ◽  
Author(s):  
Ivan. P. Gavrilyuk ◽  
V.L. Makarov ◽  
V.B. Vasylyk
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Solution Operator ◽  
Hyperbolic Operator ◽  
Elliptic Solution ◽  
Elliptic Boundary Value ◽  
Sine Family ◽  
The Green Function

AbstractWe develop an accurate approximation of the normalized hyperbolic operator sine family generated by a strongly positive operator A in a Banach space X which represents the solution operator for the elliptic boundary value problem. The solution of the corresponding inhomogeneous boundary value problem is found through the solution operator and the Green function. Starting with the Dunford — Cauchy representation for the normalized hyperbolic operator sine family and for the Green function, we then discretize the integrals involved by the exponentially convergent Sinc quadratures involving a short sum of resolvents of A. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [0, 1].

The Green function method for the two-surface problem

1970 ◽  
Vol 8 (13) ◽  
pp. 1069-1071 ◽  
Author(s):  
F. Flores ◽  
F. Garcia-Moliner ◽  
J. Rubio
Keyword(s):  
Green Function ◽  
Function Method ◽  
Green Function Method ◽  
The Green Function
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