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Infinite elements for water wave radiation and scattering
Author(s) -
Chen H. S.
Publication year - 1990
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650110507
Subject(s) - mathematics , finite element method , mathematical analysis , basis function , infinity , scattering , simple (philosophy) , domain (mathematical analysis) , numerical integration , variational principle , physics , optics , philosophy , thermodynamics , epistemology
The infinite element method is employed to approximate the solutions of Webster's horn equation and Berkhoff's equation for water wave radiation and scattering in an unbounded domain. Functionals based on the first variational principle are presented. Two new infinite elements, which exactly satisfy the one‐ and two‐dimensional Sommerfeld radiation condition, are presented; the simple shape functions are constructed on the basis of the asymptotic behaviour of the scattered wave at infinity. All the integrals in the functionals involving each infinite element are integrated analytically and, as a result, no numerical integration is required. The programming requirements and computational efficiency are essentially no different than those of the conventional finite element method. For the test cases presented, the numerical results are acceptably accurate when compared with the existing solutions and laboratory data.