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FINITE ELEMENT METHOD FOR INTERACTION OF OBLIQUE SURFACE WAVES WITH DUAL VERTICAL BARRIERS OVER ARBITRARY BOTTOM

Part of: Incompressible inviscid fluids

Published online by Cambridge University Press:  17 April 2026

NAVEEN KUMAR  and
S. C. MARTHA Open the ORCID record for S. C. MARTHA [Opens in a new window]
NAVEEN KUMAR
Affiliation:
Government College Krishan Nagar, Mahendergarh 123001, India; e-mail: nvnbharti237@gmail.com Department of Mathematics, Indian Institute of Technology Ropar , Rupnagar 140001, India
S. C. MARTHA*
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar , Rupnagar 140001, India
*
e-mail: scmartha2022@gmail.com
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Abstract

Within the framework of small-amplitude water wave theory, the scattering of obliquely incident monochromatic surface waves by dual thick vertical barriers over an arbitrary bottom topography is analysed. A numerical model based on the finite element method is developed by formulating the governing well-posed mixed boundary value problem over each element within a truncated finite domain. This domain is obtained by limiting the originally infinite domain to a finite distance. Two types of bottom profiles, namely parabolic and rectangular, are considered for the numerical analysis. To ensure the accuracy of the present numerical results, an energy identity relation is derived using Green’s identity and verified numerically. Additionally, for validation purposes, the numerical results are compared with existing results available in the literature. The number of zeros on the reflection and transmission coefficient curves is investigated with respect to the gap between identical and nonidentical barriers. The effects of various physical parameters, including the gap between the vertical barriers, the height of the bottom topography, the thickness and length of the barriers, and the angle of wave incidence on the reflection and transmission coefficients, as well as on the nondimensional horizontal force acting on the front and rear barriers, are examined using the proposed numerical model. This study contributes to understanding of wave–structure interaction and will be useful in addressing similar problems in applied mathematics and fluid mechanics.

Keywords

wave scatteringfinite element methodreflection and transmission coefficientshorizontal forceoblique incidencearbitrary bottom topography

MSC classification

Primary: 76B07: Free-surface potential flows
Secondary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 68 , 2026 , e9
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Copyright
© The Author(s), 2026. Published by Cambridge University Press on behalf of The Australian Mathematical Publishing Association Inc.

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