Near Field Expression of Ship Wave Resistance by Green’s Theorem

2016 ◽  
Author(s):  
Takashi Tsubogo
Keyword(s):  
Integral Equation ◽  
Near Field ◽  
Field Method ◽  
Momentum Conservation ◽  
Wave Resistance ◽  
Boundary Integral ◽  
Far Field ◽  
Ship Wave ◽  
Direct Pressure ◽  
Run Up

The ship wave resistance can be estimated by two alternative methods after solving the boundary integral equation. One is the far field method e.g. Havelock’s formula based on momentum conservation in fluid domain, and another is the near field method based on direct pressure integration over the wetted body surface. Nakos and Sclavounos (1994) had shown a new near field expression of ship wave resistance from the momentum conservation law in the fluid domain with linearized free surface condition. Their new expression differs slightly from the traditional near field form. This problem of near field expression is reconsidered in terms of Green’s second identity. After linearization of the free suface condition and some transformation of equations, the present paper will agree with the Nakos and Sclavounos’ near field expression for the ship wave resistance. Some numerical calculations of wave resistance from the far field method and from the near field method are shown using the classical Kelvin sources distributed on the centerplane of thin ship but solving the different boundary integral equation. Numerical results suggest that the problematic run-up square integration along the waterline is to be omitted as a higher order small quantity. If this run-up term is omitted in each method except for far field, the traditional direct pressure integrtaion is equal to the Nakos and Sclavounos’ near field expression.

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.

scholarly journals Local Enhancements of the Mean Drift Wave Force on a Vertical Column Shielded by an Exterior Thin Porous Shell

2020 ◽  
Vol 8 (5) ◽  
pp. 349 ◽  
Author(s):  
Peiwen Cong ◽  
Yingyi Liu
Keyword(s):  
Near Field ◽  
Wave Interaction ◽  
Wave Force ◽  
Momentum Conservation ◽  
Far Field ◽  
Vertical Column ◽  
Porous Shell ◽  
Drift Wave ◽  
Direct Pressure ◽  
The Mean

The wave interaction with a vertical column shielded by an exterior porous shell is studied within the framework of potential flow theory. The structures are fixed rigidly at the sea bottom. The interior cylinder is impermeable, and the exterior shell is slightly porous and thin. Additionally, the exterior shell is assumed to have fine pores, and a linear pressure drop is adopted at the porous geometry. The mean drift wave force on the system is thereby formulated by two alternative ways, based respectively on the direct pressure integration, i.e., the near-field formulation, and the application of the momentum conservation theorem in the fluid domain, i.e., the far-field formulation. The consistency of the two formulations in calculating the mean drift wave force is assessed for the present problem. Numerical results illustrate that the existence of the porous shell can substantially reduce the mean drift wave force on the interior column. It also appears that the far-field formulation consists of a conventional part as well as an additional part caused by the energy dissipation through the porous geometry. The mean drift wave force on the system is dominated by the first part, which resembles that on an impermeable body. Local enhancements of the mean drift wave force are found at some specific wave frequencies at which certain propagation modes of the fluid satisfy a no-flow condition at the porous shell.

Comparison of ultralow-sidelobe-antenna far-field patterns using the planar-near-field method and the far-field method

1995 ◽  
Vol 37 (6) ◽  
pp. 7-15 ◽  
Author(s):  
M.H. Francis ◽  
A.C. Newell ◽  
K.R. Grimm ◽  
J. Hoffman ◽  
H.E. Schrank
Keyword(s):  
Near Field ◽  
Field Method ◽  
Far Field ◽  
Field Patterns

scholarly journals Stern waves with vorticity

2002 ◽  
Vol 43 (3) ◽  
pp. 321-332 ◽  
Author(s):  
Y. Kang ◽  
J.-M. Vanden-Broeck
Keyword(s):  
Integral Equation ◽  
Numerical Solutions ◽  
Free Surface Flow ◽  
Integral Equation Method ◽  
Surface Flow ◽  
Boundary Integral ◽  
Analytical Relation ◽  
Far Field ◽  
Two Dimensional ◽  
The Waves

AbstractSteady two-dimensional free surface flow past a semi-infinite flat plate is considered. The vorticity in the flow is assumed to be constant. For large values of the Froude number F, an analytical relation between F, the vorticity parameter ω and the steepness s of the waves in the far field is derived. In addition numerical solutions are calculated by a boundary integral equation method.

Far-Field Performances Prediction of High Frequency Projectors Using Secondary Source Array Method

2016 ◽  
Vol 25 (02) ◽  
pp. 1750002 ◽  
Author(s):  
Shiquan Wang
Keyword(s):  
High Frequency ◽  
Near Field ◽  
Directivity Pattern ◽  
Field Method ◽  
Voltage Response ◽  
Secondary Source ◽  
Far Field ◽  
Comparison Of The Results ◽  
Source Array ◽  
Good Agreement

This paper investigates the prediction of the far-field performances of high frequency projectors using the second source array method (SSAM). The far-field parameters can be calculated accurately using the complex acoustic pressure data of two very close parallel planes which lie in the near-field region of the projector. The paper simulates the feasibility of predicting the far-field parameters such as transmitting voltage response and the far-field directivity pattern. The predicting results are compared with that calculated using boundary element method (BEM). It shows very good agreement between the two methods. A planar high frequency projector is measured using the near-field method. In order to verify the predicting results, the far-field measurement is performed for the same projector. The comparison of the results shows that the near-field method is capable to precisely predict the far-field parameters of the projector.

The direct and inverse scattering problems for an arbitrary cylinder: Dirichlet boundary conditions

1980 ◽  
Vol 86 (1-2) ◽  
pp. 29-42 ◽  
Author(s):  
David Colton ◽  
Ralph Kleinman
Keyword(s):  
Integral Equation ◽  
Plane Wave ◽  
Boundary Integral Equation ◽  
Inverse Scattering ◽  
Dirichlet Boundary ◽  
Scattering Problem ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Moment Problems ◽  
Far Field

SynopsisThe exterior Dirichlet problem for the Helmholtz equation in two dimensions is reduced to a boundary integral equation which is soluble by iteration. A standard application of Green's theorem leads to boundary integral equations which are not uniquely soluble because the operator has an eigenvalue. The present approach modifies the operator in such a way that the former eigenvalue is in the resolvent spectrum for low frequencies. The results are applied to the inverse scattering problem wherein the far field is known for a limited frequency range and one seeks the curve on which a plane wave is incident and a Dirichlet boundary condition is assumed. The first iterate in the solution of the boundary integral equation is used to obtain a sequence of moment problems relating the Fourier coefficients of the far field to the coefficients of the Laurent expansion of the conformai transformation which maps the exterior of a circle onto the exterior of the unknown curve. These moment problems are soluble in terms of the mapping radius which in turn may be determined from scattered far field data for an incident plane wave from a second direction.

scholarly journals Spectral boundary integral method for simulating static and dynamic fields from a fault rupture in a poroelastodynamic solid

2021 ◽  
Author(s):  
Elias Heimisson ◽  
Antonio Pio Rinaldi
Keyword(s):  
Pore Pressure ◽  
Integral Method ◽  
Near Field ◽  
Boundary Integral ◽  
Pressure Response ◽  
Boundary Integral Method ◽  
P Wave ◽  
Computational Time ◽  
Far Field ◽  
Pore Pressure Response

The spectral boundary integral method is popular for simulating fault, fracture, and frictional processes at a planar interface. However, the method is less commonly used to simulate off-fault dynamic fields. Here we develop a spectral boundary integral method for poroelastodynamic solid. The method has two steps: first, a numerical approximation of a convolution kernel and second, an efficient temporal convolution of slip speed and the appropriate kernel. The first step is computationally expensive but easily parallelizable and scalable such that the computational time is mostly restricted by computational resources. The kernel is independent of the slip history such that the same kernel can be used to explore a wide range of slip scenarios. We apply the method by exploring the short-time dynamic and static responses: first, with a simple source at intermediate and far-field distances and second, with a complex near-field source. We check if similar results can be attained with dynamic elasticity and undrained pore-pressure response and conclude that such an approach works well in the near-field but not necessarily at an intermediate and far-field distance. We analyze the dynamic pore-pressure response and find that the P-wave arrival carries a significant pore pressure peak that may be observed in high sampling rate pore-pressure measurements. We conclude that a spectral boundary integral method may offer a viable alternative to other approaches where the bulk is discretized, providing a better understanding of the near-field dynamics of the bulk in response to finite fault ruptures.

Potential of Michell’s Integral for Ship Wave Resistance

2014 ◽  
Author(s):  
Takashi Tsubogo
Keyword(s):  
Integral Equation ◽  
Froude Number ◽  
Computing Time ◽  
Wave Resistance ◽  
Boundary Integral ◽  
Hull Form ◽  
Number Range ◽  
Gradient Effect ◽  
Depth Direction ◽  
Wigley Hull

The Michell’s integral (Michell 1898) for the wave making resistance of a thin ship has not been used widely in practice, since its accuracy is questioned especially for a Froude number range about 0.2 to 0.35 for conventional ships. We examine calculations by Michell’s integral for some ship forms, e.g. a parabolic strut, Wigley hull and so on. As a result, one reason of the disagreement with experiments is revealed. It must be the gradient of hull form in the depth direction. Then a thin ship theory including the hull gradient effect in the depth direction is presented, which improves slightly in low Froude numbers but needs more computing time than Michell’s integral so as to solve a boundary integral equation.

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