A finite element method for two-dimensional water-wave problems

Kim, J.W.; Bai, Kwang June

doi:10.1002/(sici)1097-0363(19990515)30:1<105::aid-fld822>3.0.co;2-f

Cited by 13 publications

(7 citation statements)

References 9 publications

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“…The three dimensional vorticity differential equations have been solved by Finite element method [10]. The finite element method for solving two dimensional non linear water wave equations has been described [11].…”

Section: 2: Finite Element Methodsmentioning

confidence: 99%

A Comprehensive Review on Several Techniques for Solving 2D and 3D Partial Differential Equations

Singh¹,

Singh²

2022

Int. J. Res. Publ. Rev.

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Many Physical phenomenon in Sciences and engineering are modeled in the form of Partial differential equations. Partial differential equations arise in formulation of many mathematical problems may be of one dimensional, two dimensional, three dimensional etc. In this paper, various types of Partial differential equations and methods available in literature for solving two dimensional and three dimensional Partial differential equations are discussed.

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Section: 2: Finite Element Methodsmentioning

confidence: 99%

A Comprehensive Review on Several Techniques for Solving 2D and 3D Partial Differential Equations

Singh¹,

Singh²

2022

Int. J. Res. Publ. Rev.

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“…Some historical perspectives and reflections of ship waves are given by Tulin [5], as well. A finite element method for two-dimensional bodies below free surface was described in water of finite depth in [6]. Viscous effects on the free surface has also been considered using the complete Reynolds-averaged Navier-Stokes (RANS) equations in [7,8].…”

Section: Introductionmentioning

confidence: 99%

Prediction of wave pattern and wave resistance of surface piercing bodies by a boundary element method

Bal

2007

Numerical Methods in Fluids

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SUMMARYAn iterative boundary element method, which was originally developed for both two-and three-dimensional cavitating hydrofoils moving steadily under a free surface, is modified and extended to predict the wave pattern and wave resistance of surface piercing bodies, such as ship hulls and vertical struts. The iterative nonlinear method, which is based on the Green theorem, allows the separation of the surface piercing body problem and the free-surface problem. The free-surface problem is also separated into two parts; namely, left and right (with respect to x axis) free-surface problems. Those all (three) problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The wetted surface of the body (ship hull or strut, including cavity surface if exists) and the left and right parts with respect to x axis of free surface are modelled with constant strength dipole and constant strength source panels. In order to prevent upstream waves, the source strengths from some distance in front of the body to the end of the truncated upstream boundary are enforced to be zero. No radiation condition is enforced for downstream and transverse boundaries. A transverse wave cut technique is used for the calculation of wave resistance. The method is first applied to a point source and a three-dimensional submerged cavitating hydrofoil to validate the method and a Wigley hull and a vertical strut to compare the results with those of experiments.

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“…Another aspect of this variational principle is that the variational formulation can be considered as the basis for a finite element discretization and have the benefits of preserving energy at the discrete level. Finite element methods based on a variational principle for free surface waves are developed in the works of Bai and Kim [8], Kim and Bai [28] and Kim et al [29]. Classical numerical methods such as finite element methods for three dimensional nonlinear free surface waves are relatively new and can be found in the works of Cai et al [18], Ma et al [41,42], Ma and Yan [43] and Westhuis [68], Wu and Taylor [70], and Wu and Hu [71].…”

Section: Modeling Deep Water Wavesmentioning

confidence: 99%

“…After summation of the weak formulation (2.27) over all space-time elements K n k in the space-time interval I n , we can rearrange the element boundary integrals into a summation of interior face integrals and boundary face integrals, and use relation (2.25) to get 28) where F K , U K h and W K h are the limiting trace values on the face S m taken from the inside of the element K K , K = l or r; and, n K K is the outward unit normal vector. Now, we enforce the continuity of the flux [[F i ]] = 0 and introduce a consistent and conservative numerical flux…”

Section: Discontinuous Galerkin Weak Formulationmentioning

confidence: 99%

“…Variational formulations also provide a basis for the construction of approximate finite element solutions. Such variational finite element methods for free surface waves can be found in Bai and Kim [8], Kim and Bai [28] and Kim et al [29]. Klopman et al [32] derive a variational Boussinesq model from Luke's variational principle; in essence their Boussinesq model is a vertical discretization thereof.…”

Section: Introductionmentioning

confidence: 99%

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Forecasting water waves and currents : a space-time approach

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A finite element method for two-dimensional water-wave problems

Cited by 13 publications

References 9 publications

A Comprehensive Review on Several Techniques for Solving 2D and 3D Partial Differential Equations

A Comprehensive Review on Several Techniques for Solving 2D and 3D Partial Differential Equations

Prediction of wave pattern and wave resistance of surface piercing bodies by a boundary element method

Forecasting water waves and currents : a space-time approach

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