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Diffraction of Water Waves Due to a Presence of Two Headlands

A. Essawy
H. El-Arabawy
Sh. El-Sawaby
Journal / Anthology

Journal of Computational and Applied Mathematics
Year: 1999
Volume: 104
Page range: 27-39

This paper is concerned with a boundary value problem for the Helmholtz equation on a horizontal infinite strip with obstacles. The derivation of Helmholtz equation form shallow water equations is given and the boundary value problem with an arbitrary shape of headland is stated. The boundary conditions are of the general Neumann type, and thus we use the finite difference method in numerical solution. The Helmholtz equation is replaced by the five-points formula and for the points close to the boundary, Taylors expansions are made useful with non-uniform spacing. For solving the resulting system of linear equations, the "Mathematica" package is used. The graphs show the velocity potential contours in the cases, of semielliptic, semicircular and narrow headland. Also, we discuss the problem in the presence of two headlands.

*Mathematics > Calculus and Analysis > Differential Equations
*Science > Physics > Wave Motion