On the accuracy of the desingularized boundary integral method in free surface flow problems

Lalli, F.

doi:10.1002/(sici)1097-0363(19971130)25:10<1163::aid-fld614>3.0.co;2-5

Cited by 14 publications

(21 citation statements)

References 6 publications

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“…By using a one-point quadrature integrating scheme, the integrals can be replaced by the summation of a finite number of singularities (or their derivatives); thus no integration is needed. The approach has been successfully applied to simulate both steady and time-dependent water-wave problems [12][13][14].…”

supporting

confidence: 85%

“…For investigating the effects on the accuracy of the desingularized distance of the desingularized boundary-integral method in free-surface flow problems, Lalli [13] carried out several test cases, including wave patterns generated by the steady motion of two different submerged bodies. One of these two submerged bodies was a spheroid of length-to-diameter ratio 0.2, while the other one is a streamlined circular cylinder with a half-sphere-shaped "bow" and the "stern" composed of a half-spheroid.…”

Section: Wave Pattern Generated By Objects Of Different Shapesmentioning

confidence: 64%

“…When the steady state of the flow in the vicinity of the spheroid is achieved, the resistance force acting on the body can be calculated by the following integral: [13] where ρ denotes the density of the fluid, ∂ B denotes the body surface, and u is the relative velocity with respect to the moving spheroid. Therefore u = v − U b i .…”

Section: Fig 12mentioning

confidence: 99%

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Applicability of the method of fundamental solutions to 3-D wave–body interaction with fully nonlinear free surface

Tsay

2008

J Eng Math

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A numerical model for three-dimensional fully nonlinear free-surface waves is developed by applying a boundary-type meshless approach with a leap-frog time-marching scheme. Adopting Gaussian Radial Basis Functions to fit the free surface, a non-iterative approach to discretize the nonlinear free-surface boundary is formulated. Using the fundamental solutions of the Laplace equation as the solution form of the velocity potential, free-surface wave problems can be solved by collocations at only a few boundary points since the governing equation is automatically satisfied. The accuracy of the present method is verified by comparing the simulated propagation of a solitary wave with an exact solution. The applicability of the present model is illustrated by applying it to the problem of a solitary wave running up on a vertical surface-piercing cylinder and the problem of wave generation in infinite water depth by a submerged moving object.

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confidence: 85%

Section: Wave Pattern Generated By Objects Of Different Shapesmentioning

confidence: 64%

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Applicability of the method of fundamental solutions to 3-D wave–body interaction with fully nonlinear free surface

Tsay

2008

J Eng Math

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“…(7) and (8). The factors of r 1 and r 2 indeed play a major role to stabilize the conventional Trefftz method.…”

Section: B Comments On the New Methodsmentioning

confidence: 99%

“…Another way to avoid the singularity was proposed in [7][8][9], which move the computing nodes away from the boundary and outside the real domain of the problem. Even, this new approach can overcome the difficulties of singular integrals, it has another problem of ill-posedness due to the appearence of the first-kind Fredholm integral equations.…”

Section: Introductionmentioning

confidence: 98%

A highly accurate collocation Trefftz method for solving the Laplace equation in the doubly connected domains

Liu

2007

Numerical Methods Partial

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A highly accurate new solver is developed to deal with the Dirichlet problems for the 2D Laplace equation in the doubly connected domains. We introduce two circular artificial boundaries determined uniquely by the physical problem domain, and derive a Dirichlet to Dirichlet mapping on these two circles, which are exact boundary conditions described by the first kind Fredholm integral equations. As a direct result, we obtain a modified Trefftz method equipped with two characteristic length factors, ensuring that the new solver is stable because the condition number can be greatly reduced. Then, the collocation method is used to derive a linear equations system to determine the unknown coefficients. The new method possesses several advantages: mesh-free, singularity-free, non-illposedness, semi-analyticity of solution, efficiency, accuracy, and stability.

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Nonsingular boundary integral equation for two‐dimensional electromagnetic scattering problems

Young

Chiu

Fan

2006

Micro & Optical Tech Letters

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This paper is concerned with the application of the nonsingular boundary integral equation (NSBIE) for 2D electromagnetic scattering problems in the frequency domain. In the proposed NSBIE, the conventional treatment of the singular integral for the boundary integral equation is circumvented by employing the Gauss flux theorem and the concept of equipotential. Then the NSBIE for the Helmholtz equation is used to predict the scattering of plane wave by a perfectly electric conducting circular cylinder of infinite length at normal incidence. Based on the good results, as compared with solutions of the analytical and boundary‐element methods, it is verified that the NSBIE is a highly simple and efficient numerical scheme for 2D electromagnetic scattering simulations. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 760–765, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21467

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On the accuracy of the desingularized boundary integral method in free surface flow problems

Cited by 14 publications

References 6 publications

Applicability of the method of fundamental solutions to 3-D wave–body interaction with fully nonlinear free surface

Applicability of the method of fundamental solutions to 3-D wave–body interaction with fully nonlinear free surface

A highly accurate collocation Trefftz method for solving the Laplace equation in the doubly connected domains

Nonsingular boundary integral equation for two‐dimensional electromagnetic scattering problems

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