A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions

Mola, Andrea; Heltai, Luca; DeSimone, Antonio

doi:10.1016/j.enganabound.2012.09.005

Cited by 23 publications

(46 citation statements)

References 16 publications

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“…(11) and (12) are satisfied, there is no restriction on their individual choice. Thus when the analytical solution is available for η I and ϕ I , such as the higher order Stokes waves, they can be the foundation for the choice of (ϕ b , η b ).…”

Section: Decomposition Of the Solutionmentioning

confidence: 95%

“…Bai and Eatock Taylor [9,10], and Bai et al [11] studied wave interactions with a fixed cylinder, a fixed and freely floating structure with flare, and an array of fixed cylinders, respectively. Mola et al [12] considered unsteady and nonlinear ship-wave interaction. While this model reflects the experimental practice well, it has similar problems as a physical tank when modelling the true ocean environment in the open sea, principally due to side wall effect.…”

Section: Introductionmentioning

confidence: 99%

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Fully nonlinear wave interaction with freely floating non-wall-sided structures

Zhou

Teng

2015

Engineering Analysis with Boundary Elements

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Section: Decomposition Of the Solutionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Fully nonlinear wave interaction with freely floating non-wall-sided structures

Zhou

Teng

2015

Engineering Analysis with Boundary Elements

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“…The flexibility and the accuracy of the nonsingular IGA BEM makes it also a good candidate to replace or complement more complex fluid structure interaction methods, such as the ones presented in [34,21,11].…”

Section: Discussionmentioning

confidence: 99%

“…(33) and (34) and of the Dirichlet to Neumann maps (42). The integration in both operators is desingularized extending the techniques introduced in [27,26,43] for standard boundary element methods to the isogeometric approximation introduced here.…”

Section: Boundary Integral Representationmentioning

confidence: 99%

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Nonsingular isogeometric boundary element method for Stokes flows in 3D

Heltai

Arroyo

DeSimone

2014

Computer Methods in Applied Mechanics and Engineering

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While the finite element isogeometric analysis (FE IGA) has received most of the attention of the scientific community, only few results are available for boundary element methods (BEM) and boundary integral equations (BIE) in general. In 2D, there are some works on potential flows, such as [36,44], and on elastostatic analysis [40]. Three dimensional appli cations are of great interest in the maritime community, and there are some works on NURBS based panel methods to study, for example, marine propellers [25] or the wavemaking resistance problem [10]. Three dimensional IGA BEM linear elasticity has recently been studied in [20] while some work on shape optimization has been presented in [29]. Boundary element isogeometric analysis (IGA BEM) is very attractive for the solution of homogeneous elliptic PDEs, both in the interior and in the exterior cases, since it requires the solution of integral equations only on the boundary of the enclos ing (or enclosed) domain, which is typically the only information that is generated by standard CAGD tools. In contrast, FE IGA requires the extension of the computational domain inside (or outside) the enclosing CAGD surface, an outstand ing problem in IGA.While the dimensional reduction of the domain diminishes significantly both the number of degrees of freedom and the computational cost associated with the handling of the geometry, there are two main drawbacks which require special attention, and are common to all boundary integral discretizations: (i) the system matrices that are produced with a bound ary integral method are full, and (ii) the integrands contain ð1=rÞ singularities or worse (in three dimensions) around the source point, arising from the fundamental solutions in formulating the boundary integrals. Both issues have perhaps con tributed in keeping the IGA community away from boundary integral formulations.In the literature, the first issue is usually tackled by acceleration techniques such as the fast multipole method [39] (see [31] for a survey of this technique applied to BEM), which allow one to solve the system without assembling the full matri ces, and at the same time reduce the cost of the matrix vector multiplication from Oðn 2 Þ to OðnÞ (this technique has already been applied to Laplace problems in two dimensional IGA BEM in [44]). The second issue is more delicate and its solution depends highly on the degree of the discrete functional spaces and of the geometry description, remaining one of the most difficult aspects of the implementation of BEM. Different approaches are possible, (see, for example, [23]) but high order methods and curved geometries still remain challenging.Popular approaches to tackle singular integration involve a local change of variables for the quadrature rules, following the principle that the Jacobian of the transformation can be used to eliminate locally the kernel singularities. Examples of these methods are given by Lachat and Watson [28] and by Telles [45]. Both methods are elegant and produce accurate re sults, but t...

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Boundary‐Element Methods and Wave Loading on Ships

Κώστας¹,

Kaklis

Politis

et al. 2017

Encyclopedia of Computational Mechanics Second Edition

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The hydrodynamic problem of a ship moving with constant forward speed while undergoing small‐amplitude oscillatory motions about its mean steady‐state position is modeled as a boundary‐integral equation (BIE) involving surface distributions of the fundamental solution of Laplace's equation and its derivatives and alternative Green functions. The chapter reviews the various low‐order and higher order boundary‐element methods (BEMs) developed for the numerical solution of these BIEs via collocation or Galerkin techniques involving finite‐dimensional bases for representing the involved geometric configuration and approximating the unknown physical quantities. Then, we focus on presenting and discussing recent experience gained from embedding BEMs into isogeometric analysis (IGA) for the linear wave‐resistance problem. Two IGA‐BEM solvers, based on nonuniform rational B‐spline (NURBS) and T‐spline representations of the ship hull, are presented and compared for the so‐called Neumann–Kelvin formulation of this problem. The local refinement capabilities of the adopted T‐spline representation of the ship geometry leads to a solver with higher accuracy and efficiency as compared to the corresponding NURBS‐based solver. Furthermore, the developed hydrodynamic solvers, along with the corresponding ship‐parametric models, are integrated within an optimization environment, which is tested in two optimization problems. The first problem, of local optimization character, focuses on the optimization of the bulbous shape of a container ship against the criterion of minimum wave resistance. The second case performs a global hull‐shape optimization of a container ship targeting the minimization of both the total resistance and the deviation from a target deadweight. The chapter ends with a brief discussion for further research toward broadening the coverage of IGA‐BEM methods in application areas related to ship wave loads.

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A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions

Cited by 23 publications

References 16 publications

Fully nonlinear wave interaction with freely floating non-wall-sided structures

Fully nonlinear wave interaction with freely floating non-wall-sided structures

Nonsingular isogeometric boundary element method for Stokes flows in 3D

Boundary‐Element Methods and Wave Loading on Ships

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