Improved solution for potential flow about arbitrary axisymmetric bodies by the use of a higher-order surface source method

Hess, John L.

doi:10.1016/0045-7825(75)90003-1

Cited by 27 publications

(24 citation statements)

References 4 publications

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“…Integral equation formulation of Laplace boundary-value problems has been established as one of the standard tools for calculating inviscid, incompressible flow characteristics (velocity and pressure) around 2D and 3D bodies and geometrical systems; see, e.g., Hess (1975), Katz-Plotkin (1991). Some of the most important advantages of this approach include the reduction of dimensionality, facilitation of calculations around complex geometrical configurations (especially in 3D), consistent handling of conditions at infinity, high convergence rates when the domain boundary and boundary data are (relatively) smooth and easy implementation to optimization (inverse-type) problems.…”

Section: Introductionmentioning

confidence: 99%

“…In low-order BEM the body surface is usually discretized by a finite number of elements or patches, each carrying a simple distribution of the unknown function; see, e.g., Hess (1975). On the contrary, high-order BEM, characterised by an increased order of approximation both with respect to geometry and the surface singularity distribution, has the property of faster convergence as element-size diminishes, and yields more accurate results with coarser grid resolutions; see, e.g., Gennaretti et al (1998).…”

Section: Introductionmentioning

confidence: 99%

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A BEM-isogeometric method for the ship wave-resistance problem

et al. 2013

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In the present work IsoGeometric Analysis is applied to the solution of the Boundary Integral Equation associated with the Neumann-Kelvin problem and the calculation of the wave resistance of ships. As opposed to low-order panel methods, where the body is represented by a large number of quadrilateral panels and the velocity potential is assumed to be piecewise constant (or approximated by low degree polynomials) on each panel, the isogeometric concept is based on exploiting the same NURBS basis, used for representing exactly the body geometry, for approximating the singularity distribution (and, in

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A BEM-isogeometric method for the ship wave-resistance problem

et al. 2013

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“…Some of the most important advantages of this approach are: i) reduction of the dimensionality of the problem by one, facilitating calculations around complex geometrical configurations (especially in 3-D problems) and ii) consistent treatment of conditions at infinity. As regards the numerical solution of the integral equations, Boundary Element Methods (BEM) serve today as the main tool, [Hess 1975], [Brebbia et al 1984], [Paris and Canas 1997], [Brebbia 2002], although various other techniques are also available, such as spectral methods using basis functions of global support on the boundary surface.…”

Section: Introductionmentioning

confidence: 99%

An isogeometric BEM for exterior potential-flow problems in the plane

Politis

Ginnis²,

Kaklis³

et al. 2009

2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling

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“…The singularity distributions are approximated on each element by piecewise constant, linear or quadratic functions. Following the work of Hess, [6,7], we evaluate the first and second derivatives of the singularity distributions at the collocation nodes by divided differences of the node values with respect to the arc-length evaluated on the surface approximation by curved panels. Accordingly, the unknowns in the discretized form of the integral equation Eq.…”

Section: Order Of Local Truncation Errormentioning

confidence: 99%

“…We follow the work of Hess, [6,7] and Romate [17] who used smallcurvature expansions to obtain locally consistent approximations to the velocity and potential integrals. The potential integrals may then be evaluated analytically.…”

Section: Introductionmentioning

confidence: 99%

A numerical study on low and higher-order potential based BEM for 2D inviscid flows

Vaz

Campos²,

Eça³

2003

Computational Mechanics

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A formal error analysis of the order of approximation of a potential based boundary element method (BEM) for two-dimensional flows is performed in order to derive consistent approximations for the potential integrals. Two higher-order approaches satisfying consistency requirements to attain second and third order convergence in the potential are selected for numerical implementation. From the formal local expansions of the potential integrals the influence coefficients are derived and evaluated analytically. In order to assess the methods accuracy, the low and higher-order methods are applied to two-dimensional steady flows around analytical foils. A numerical error analysis is done and a comparison between their theoretical and numerical asymptotic order of accuracy performed. IntroductionBoundary element methods (BEM) have been used successfully for many years in the solution of compressible and incompressible inviscid flows around complex configurations, [8]. In the aerodynamic and hydrodynamic fields, these methods, also known as panel methods, have matured to a level which allows their use as design tools on a routine basis. In spite of the success achieved in many hydrodynamic applications, there are situations where BEM computations may still pose considerable challenges, both from the modelling and the computational points of view. This appears to be the case in the non-linear computations of partial and super-cavitating flows on hydrofoils and marine propellers, e.g. [10,12]. From the computational point of view, BEM solutions of such flow problems require the use of accurate and efficient numerical algorithms which need to be applied on considerably fine grids. Maskew, [13], has shown that the low-order potential based BEM, [9,15], was able to provide solutions for the pressure distribution with accuracy comparable to higher-order methods for a small number of panels. However, in non-linear computations of cavity flows on foils accurate solutions may only be obtained with a large number of elements, especially in regions of high geometry curvature, such as the leading edge and the cavity closure region, [2,5]. This still involves large computation times in the three-dimensional flow case, which makes its application in design studies rather time consuming. In such situations higher-order methods may become attractive to further reduce computation times.In the present paper, we concentrate on the application of higher-order boundary element methods to the twodimensional case of the steady incompressible potential flow around foils in the absence of cavitation. The work of Kinnas and Hsin [11] showed that the rate of convergence of the low-order BEM on foils is slow due to the effect of the local error on the sharp trailing edge. Therefore, significant improvements are expected from higher-order BEM formulations. Such improvements may turn out to be of practical relevance in the application of the method to the computation of 2D unsteady cavitating flows needed for design purposes. Our objective is to inv...

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Improved solution for potential flow about arbitrary axisymmetric bodies by the use of a higher-order surface source method

Cited by 27 publications

References 4 publications

A BEM-isogeometric method for the ship wave-resistance problem

A BEM-isogeometric method for the ship wave-resistance problem

An isogeometric BEM for exterior potential-flow problems in the plane

A numerical study on low and higher-order potential based BEM for 2D inviscid flows

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