Author

# H S Chen

Bio: H S Chen is an academic researcher from Massachusetts Institute of Technology. The author has contributed to research in topics: Mathieu function & Plane (geometry). The author has an hindex of 1, co-authored 1 publications receiving 36 citations.

##### Papers

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TL;DR: In this article, the mathematical solution to the diffraction problem is obtained on the basis of the linearized long-wave approximation for a shiplike body with beam-to-length ratio approximately equal to 0.2.

Abstract: Exciting forces and moments due to plane incident waves on a stationary platform are studied in the report. The platform is a vertical cylinder with a finite draft and elliptical cross section. The mathematical solution to the diffraction problem is obtained on the basis of the linearized long-wave approximation. Numerical results via Mathieu functions are presented for a shiplike body with beam-to-length ratio approximately equal to 0.2. Various draft-to-depth ratios and angles of incidence are considered. Results have been checked with the limiting case of a circular cylinder for the long-wavelength range. Aside from its own practical interest, the present theory provides a basis for comparison with other approximate theories of slender-body type and serves as a prelude to the corresponding calculations for arbitrary wavelengths. (Author)

38 citations

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TL;DR: In this article, a finite element model for the solution of Helmholtz problems at higher frequencies is described, which offers the possibility of computing many wavelengths in a single finite element.

Abstract: This paper describes a finite element model for the solution of Helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element. The approach is based on partition of unity isoparametric elements. At each finite element node the potential is expanded in a discrete series of planar waves, each propagating at a specified angle. These angles can be uniformly distributed or may be carefully chosen. They can also be the same for all nodes of the studied mesh or may vary from one node to another. The implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres. The wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced. Issues related to the integration and the conditioning are also discussed.

131 citations

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TL;DR: In this paper, two approximate methods are presented for the calculation of the wave induced forces and moments on a vertical, surface-piercing cylinder of elliptic cross section, which provide a substantial reduction in computational effort when Compared with the exact solution which involves the numerical evaluation of Mathieu functions.

Abstract: Two approximate methods are presented for the calculation of the wave induced forces and moments on a vertical, surface‐piercing cylinder of elliptic cross section. Both methods provide a substantial reduction in computational effort when Compared with the exact solution which involves the numerical evaluation of Mathieu functions. One method involves the expansion of the exact expressions for the forces and moments for small values of the elliptic eccentricity parameter. The second method is based on Green's theorem and gives rise to an integral equation for the fluid velocity potential on the cylinder surface. Numerical results are presented for a range of relevant parameters and show excellent agreement with the computed values of the exact solution.

45 citations

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TL;DR: In this article, an analytical method is proposed to investigate the wave diffraction of linear waves with a uniform, bottom-mounted cylinder with an arbitrary smooth cross-section, based on the condition that the radius function of the cylinder surface can be expanded into a Fourier series.

38 citations

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TL;DR: Numerical simulations show that the new SBFEM model offers a considerable improvement by far in its numerical performance, as well as in the range of physical phenomena that is capable of simulating.

31 citations

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TL;DR: The diffraction of small-amplitude surface waves by a horizontally submerged disk of elliptic cross section located at a finite depth beneath the free surface is investigated analytically in this article.

Abstract: The diffraction of small-amplitude surface waves by a horizontally submerged disk of elliptic cross section located at a finite depth beneath the free surface is investigated analytically. The fluid domain is divided into three regions, two internal regions, one above and one beneath the disk, and an external region extending to infinity in the horizontal plane. The theoretical formulation leads to solutions for the fluid velocity potentials in each region in terms of series of Mathieu and modified Mathieu functions of real argument. Numerical results are presented for the wave-induced forces and moments, and the variation of water surface elevation in the vicinity of the disk for a range of wave and structural parameters. In particular, the results for the hydrodynamic loads show significant differences from the corresponding estimates for a circular disk, while the results for the water surface elevation clearly show the effect of wave focusing around the rear of the disk.

25 citations