Alternative integral representations for the Green function of the theory of ship wave resistance

1981 ◽  
Vol 15 (4) ◽  
pp. 241-265 ◽  
Author(s):  
F. Noblesse
Keyword(s):  
Green Function ◽  
Wave Resistance ◽  
Integral Representations ◽  
Ship Wave ◽  
The Green Function

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.

Near Field Expression of Ship Wave Resistance by Yeung’s Method

2017 ◽  
Author(s):  
Takashi Tsubogo
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Water Pressure ◽  
Near Field ◽  
Field Method ◽  
Wave Resistance ◽  
Alternative Methods ◽  
Far Field ◽  
Ship Wave ◽  
Direct Pressure

The ship wave resistance can be evaluated by two alternative methods after solving the boundary value problem. One is the far field method e.g. Havelock’s formula, and another is the near field method based on direct pressure integration over the wetted hull surface. As is well known, there exist considerable discrepancies between wave resistance results by far field method and by near field method. This paper presents a Lagally expression in consistency with Havelock’s formula. In order to derive the Lagally expression, the symmetry of Havelock’s Green function is used in the same manner as Yeung et al (2004). Another expression to examine the relation with water pressure integrations or to ensure physical consistency is also derived by slightly deforming that expression. Some numerical comparisons of wave resistance of Wigley, KCS and KVLCC2 models among by Havelock’s formula, some direct pressure integration methods and present two new near field expressions, are shown to demonstrate consistency numerically.

Green Function of Steady Motion in Finite Water Depth

2006 ◽  
Vol 50 (02) ◽  
pp. 120-137
Author(s):  
Qinzheng Yang ◽  
Odd M. Faltinsen ◽  
Rong Zhao
Keyword(s):  
Green Function ◽  
Shallow Water ◽  
Wave Resistance ◽  
Partial Sums ◽  
Vertical Force ◽  
Slender Body Theory ◽  
Local Disturbance ◽  
Wave Part ◽  
Pitch Moment ◽  
The Green Function

The Green function associated with a steady translating source on a straight horizontal course in water with finite constant depth and infinite horizontal extent satisfying the classical free surface condition is studied by decomposing it into three parts: an array of Rankine singularities A, local disturbance D, and downstream wave part S. Each of the three parts is studied by several methods. This is used to verify the numerical scheme and find the most time-efficient procedure. The method of repeated averaging of partial sums for oscillating series is efficiently used to evaluate the infinite sum of Rankine singularities and the downstream wave part. The local disturbance needed in vertical force and pitch moment calculations is most demanding. The Green function is used in combination with thin ship theory to calculate wave resistance, vertical force, pitch moment, and far-field wash for a Wigley hull. The results are compared with Tuck's (1966) slender body theory for shallow water and experimental and theoretical results of wave resistance by Everest and Hogben (1970). The agreement is satisfactory. A shallow water wave resistance ratio r expressing the ratio between wave resistance in finite depth and infinite depth is introduced as an indirect way to minimize wash. It is demonstrated that a large influence of critical depth Froude number requires the ratio between fluid depth and ship length to be small.

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

Electrostatic oscillations in cold inhomogeneous plasma I. Differential equation approach

1971 ◽  
Vol 5 (2) ◽  
pp. 239-263 ◽  
Author(s):  
Z. Sedláček
Keyword(s):  
Differential Equation ◽  
Green Function ◽  
Normal Mode Analysis ◽  
Inhomogeneous Plasma ◽  
Mode Analysis ◽  
Complex Frequency ◽  
Plasma Oscillations ◽  
The Laplace Transform ◽  
Collective Oscillations ◽  
The Green Function

Small amplitude electrostatic oscillations in a cold plasma with continuously varying density have been investigated. The problem is the same as that treated by Barston (1964) but instead of his normal-mode analysis we employ the Laplace transform approach to solve the corresponding initial-value problem. We construct the Green function of the differential equation of the problem to show that there are branch-point singularities on the real axis of the complex frequency-plane, which correspond to the singularities of the Barston eigenmodes and which, asymptotically, give rise to non-collective oscillations with position-dependent frequency and damping proportional to negative powers of time. In addition we find an infinity of new singularities (simple poles) of the analytic continuation of the Green function into the lower half of the complex frequency-plane whose position is independent of the spatial co-ordinate so that they represent collective, exponentially damped modes of plasma oscillations. Thus, although there may be no discrete spectrum, in a more general sense a dispersion relation does exist but must be interpreted in the same way as in the case of Landau damping of hot plasma oscillations.

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