Abstract

In this paper, we investigate the scattering of obliquely incident surface water waves on a hurdle as a form of a thick symmetric wall with a gap immersed in a finite depth water body having a cover of a thin ice sheet. In the context of the linear theory of water waves, this two-dimensional problem is formulated as a first-kind integral equation by splitting the velocity potential into symmetric and antisymmetric parts. The integral equation is tackled by using two numerical methods. The first method is the boundary element method where the range of integration is divided into a finite number of small line elements, and choosing the unknown function of the integral equation as constant in each line interval, we reduce the integral equation into a linear system of an algebraic equation. The second method is the multi-term Galerkin Approximation method where the basis functions are chosen as ultraspherical Gegenbauer polynomials to reduce the integral equation to a system of an algebraic equation. These systems of equations are then solved to obtain the unknown function of the integral equation in both methods. Here, very accurate numerical estimates are obtained for the reflection coefficient by both methods which are depicted graphically against the wave number for different parameters involving this problem. Also, there is a good agreement between the results of the reflection coefficient by the two methods.

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