On the Numerical Radiation Condition in the Steady-State Ship Wave Problem

1987 ◽  
Vol 31 (01) ◽  
pp. 14-22
Author(s):  
Peter Schjeldahl Jensen
Keyword(s):  
Green Function ◽  
Three Dimensional ◽  
Radiation Condition ◽  
Function Technique ◽  
Wave Problem ◽  
Ship Wave ◽  
Rankine Source ◽  
Wigley Hull ◽  
The Green Function ◽  
The Waves

The waves created by a thin ship sailing in calm water are examined. The velocity potential of the ship in the zero Froude number case is known and the additional potential due to the waves is calculated by the Green function technique. The simple Green function corresponding to the Rankine source potential is used here. Two major problems exist with this method. In the Neumann-Poisson boundary-value problem- probably the first iteration toward a full nonlinear solution to the ship wave problem _it is necessary to impose a radiation condition in order to get uniqueness. This problem is related to the second one, which arises due to the existence of eigensolutions. The two-dimensional situation is here analyzed first, thereby easing the three-dimensional analysis. A numerical scheme is constructed and results for the twodimensional waves generated by a submerged vortex and for the three-dimensional waves due to the Wigley hull are presented.

A Slender-Ship Theory of Wave Resistance

1983 ◽  
Vol 27 (01) ◽  
pp. 13-33
Author(s):  
Francis Noblesse
Keyword(s):  
Froude Number ◽  
Wave Resistance ◽  
Successive Approximations ◽  
Zeroth Order ◽  
Remarkable Effect ◽  
Ship Wave ◽  
First Order ◽  
Wigley Hull ◽  
Low Froude Number ◽  
The Waves

A new slender-ship theory of wave resistance is presented. Specifically, a sequence of explicit slender-ship wave-resistance approximations is obtained. These approximations are associated with successive approximations in a slender-ship iterative procedure for solving a new (nonlinear integro-differential) equation for the velocity potential of the flow caused by the ship. The zeroth, first, and second-order slender-ship approximations are given explicitly and examined in some detail. The zeroth-order slender-ship wave-resistance approximation, r(0) is obtained by simply taking the (disturbance) potential, ϕ, as the trivial zeroth-order slender-ship approximation ϕ(0) = 0 in the expression for the Kochin free-wave amplitude function; the classical wave-resistance formulas of Michell [1]2 and Hogner [2] correspond to particular cases of this simple approximation. The low-speed wave-resistance formulas proposed by Guevel [3], Baba [4], Maruo [5], and Kayo [6] are essentially equivalent (for most practical purposes) to the first-order slender-ship low-Froude-number approximation, rlF(1), which is a particular case of the first-order slender-ship approximation r(1): specifically, the first-order slender-ship wave-resistance approximation r(1) is obtained by approximating the potential ϕ in the expression for the Kochin function by the first-order slender-ship potential ϕ1 whereas the low-Froude-number approximation rlF(1) is associated with the zero-Froude-number limit ϕ0(1) of the potentialϕ(1). A major difference between the first-order slender-ship potential ϕ(1) and its zero-Froude-number limit ϕ0(1) resides in the waves that are included in the potential ϕ(1) but are ignored in the zero-Froude-number potential ϕ0(1). Results of calculations by C. Y. Chen for the Wigley hull show that the waves in the potential ϕ(1) have a remarkable effect upon the wave resistance, in particular causing a large phase shift of the wave-resistance curve toward higher values of the Froude number. As a result, the first-order slender-ship wave-resistance approximation in significantly better agreement with experimental data than the low-Froude-number approximation rlF(1) and the approximations r(0) and rM.

Zero Speed Rankine-Kelvin Hybrid Method With a Cylinder Control Surface

2015 ◽  
Author(s):  
Hui Li ◽  
Hao Lizhu ◽  
Huilong Ren ◽  
Xiaobo Chen
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Hybrid Method ◽  
Exterior Domain ◽  
Control Surface ◽  
Surface Boundary ◽  
Rankine Source ◽  
Free Surface Boundary Condition ◽  
Interior Domain ◽  
The Green Function

The solution of hydrodynamic problem with forward speed still has some well-known problems such as high oscillation and slow convergence of the wave term when using a moving and oscillating source as the Green function. Recently, Ten and Chen (2010) has come up with a new method to benefit the merits of both the Rankine source and moving and oscillating source by taking a hemisphere as the control surface which separates the fluid region into two domains, but some troubles have been induced in the process of solution. Therefore, in this paper, a cylindrical surface instead of a hemisphere is selected to be the control surface to make the solution easy, and in this method, the control surface isn’t divided into panels. In the interior domain near the ship, the Rankin Green function is used to simplify the calculation. In the exterior domain some distance from the ship, there is no panels representing the free surface by using the Green function which satisfy the free surface boundary condition. The whole fluid region matches by the condition that the velocity potentials and their normal derivatives in the interior domain and exterior domain are equal on the control surface separately. In this paper, we have validated the Rankine-Kelvin hybrid method is applicable by adopting it to solve the zero speed problem in this work.

scholarly journals Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in three-dimensional space

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160255 ◽  
Author(s):  
Oscar P. Bruno ◽  
Stephen P. Shipman ◽  
Catalin Turc ◽  
Stephanos Venakides
Keyword(s):  
Green Function ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Green Functions ◽  
Lattice Sums ◽  
Periodic Arrays ◽  
The Green Function ◽  
Three Dimensional Space

This work, part I in a two-part series, presents: (i) a simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well as (ii) an associated boundary-integral equation method for the numerical solution of problems of scattering of waves by doubly periodic arrays of scatterers in three-dimensional space. Except for certain ‘Wood frequencies’ at which the quasi-periodic Green function ceases to exist, the proposed approach, which is based on smooth windowing functions, gives rise to tapered lattice sums which converge superalgebraically fast to the Green function—that is, faster than any power of the number of terms used. This is in sharp contrast to the extremely slow convergence exhibited by the lattice sums in the absence of smooth windowing. (The Wood-frequency problem is treated in part II.) This paper establishes rigorously the superalgebraic convergence of the windowed lattice sums. A variety of numerical results demonstrate the practical efficiency of the proposed approach.

The Curie temperature of a Heisenberg-Ising ferromagnet with uniaxial anisotropy

1982 ◽  
Vol 60 (3) ◽  
pp. 273-278 ◽  
Author(s):  
M. Tiwari ◽  
R. N. Srivastava
Keyword(s):  
Green Function ◽  
Curie Temperature ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Uniaxial Anisotropy ◽  
Function Technique ◽  
Phase Approximation ◽  
Ising Ferromagnet ◽  
The Green Function

Effects of Ising anisotropy on Curie temperature have been studied in the presence of single ion anisotropy for a spin S = 1 system. The Green function technique with random phase approximation has been used taking into account all possible intersite correlations.

scholarly journals Three-dimensional quasi-periodic shifted Green function throughout the spectrum, including Wood anomalies

2017 ◽  
Vol 473 (2207) ◽  
pp. 20170242 ◽  
Author(s):  
Oscar P. Bruno ◽  
Stephen P. Shipman ◽  
Catalin Turc ◽  
Venakides Stephanos
Keyword(s):  
Green Function ◽  
Blow Up ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Three Dimensions ◽  
Scattering Problems ◽  
Periodic Surfaces ◽  
Lattice Sum ◽  
The Green Function ◽  
First Time

This work, part II in a series, presents an efficient method for evaluation of wave scattering by doubly periodic diffraction gratings at or near what are commonly called ‘Wood anomaly frequencies’. At these frequencies, there is a grazing Rayleigh wave, and the quasi-periodic Green function ceases to exist. We present a modification of the Green function by adding two types of terms to its lattice sum. The first type are transversely shifted Green functions with coefficients that annihilate the growth in the original lattice sum and yield algebraic convergence. The second type are quasi-periodic plane wave solutions of the Helmholtz equation which reinstate certain necessary grazing modes without leading to blow-up at Wood anomalies. Using the new quasi-periodic Green function, we establish, for the first time, that the Dirichlet problem of scattering by a smooth doubly periodic scattering surface at a Wood frequency is uniquely solvable. We also present an efficient high-order numerical method based on this new Green function for scattering by doubly periodic surfaces at and around Wood frequencies. We believe this is the first solver able to handle Wood frequencies for doubly periodic scattering problems in three dimensions. We demonstrate the method by applying it to acoustic scattering.

Isotropic radiation from a steadily pulsating multidimensional distribution

1971 ◽  
Vol 323 (1555) ◽  
pp. 555-580 ◽  
Keyword(s):  
Green Function ◽  
Source Function ◽  
Radiation Condition ◽  
Constant Frequency ◽  
Axisymmetric Solution ◽  
Multidimensional Distribution ◽  
Unbounded Medium ◽  
Spherically Symmetric Solution ◽  
The Green Function ◽  
Isotropic Radiation

A multidimensional dynamical configuration is considered, com prising an isotropic homogeneous unbounded medium steadily oscillating in response to a real constant frequency imparted by an embedded source. A Green function to the problem is first derived, and leads to the compounding of the general exact solution for an arbitrary spatial distribution of the source function. Specializations are made to yield an asymptotic solution, a spherically symmetric solution and an axisymmetric solution. All physical results satisfy an initially imposed radiation condition, whose consequence is subsequently accommodated during the construction of the Green function. Significances are attached and interpretations provided, namely, in terms of the associated isotropic waves. A cursory application is made to examine the oscillatory motion, when reduced to the isotropic state, of a rotating magnetoelastic system. An appendix is included to deal with a certain spherical integral encountered during the investigation into the axisymmetric case.

EFFECT OF DOPING ON SUPERCONDUCTIVITY AND CHEMICAL POTENTIAL IN La2-xSrxCuO4

2009 ◽  
Vol 23 (16) ◽  
pp. 3417-3427 ◽  
Author(s):  
B. K. SAHOO ◽  
B. N. PANDA ◽  
G. C. ROUT
Keyword(s):  
Critical Temperature ◽  
Green Function ◽  
Doping Concentration ◽  
Chemical Potential ◽  
Function Technique ◽  
Model Parameters ◽  
Pairing Mechanism ◽  
Doping Dependence ◽  
The Green Function ◽  
Effect Of Doping

We examine the doping dependence of SC gap (Δ) and chemical potential (μ) of the hole-doped cuprates by using the Fulde model. It is assumed that SC arises due to BCS pairing mechanism in lattices of Cu–O planes. The expression for SC, AFM, and doping concentration are calculated analytically by using the Green function technique of D. N. Zubarev. The value of SC gap (Δ) and chemical potential (μ) are solved self-consistently for different model parameters. The variation of critical temperature and chemical potential with doping are also studied.

Three-dimensional interaction between uniform current and a submerged horizontal cylinder in an ice-covered channel

2021 ◽  
Vol 928 ◽  
Author(s):  
Y.F. Yang ◽  
G.X. Wu ◽  
K. Ren
Keyword(s):  
Green Function ◽  
Circular Cylinder ◽  
Body Surface ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Ice Sheet ◽  
The Body ◽  
Thin Elastic Plate ◽  
Uniform Current ◽  
The Green Function

The problem of interaction of a uniform current with a submerged horizontal circular cylinder in an ice-covered channel is considered. The fluid flow is described by linearized velocity potential theory and the ice sheet is treated as a thin elastic plate. The potential due to a source or the Green function satisfying all boundary conditions apart from that on the body surface is first derived. This can be used to derive the boundary integral equation for a body of arbitrary shape. It can also be used to obtain the solution due to multipoles by differentiating the Green function with its position directly. For a transverse circular cylinder, through distributing multipoles along its centre line, the velocity potential can be written in an infinite series with unknown coefficients, which can be determined from the impermeable condition on a body surface. A major feature here is that different from the free surface problem, or a channel without the ice sheet cover, this problem is fully three-dimensional because of the constraints along the intersection of the ice sheet with the channel wall. It has been also confirmed that there is an infinite number of critical speeds. Whenever the current speed passes a critical value, the force on the body and wave pattern change rapidly, and two more wave components are generated at the far-field. Extensive results are provided for hydroelastic waves and hydrodynamic forces when the ice sheet is under different edge conditions, and the insight of their physical features is discussed.

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