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Shoaling of nonlinear steady waves: maximum height and angle of breaking

Franco, Sebastião Romero;  Farina, Leandro — 2015

Application of Mathematics 2015

A Fourier approximation method is used for modeling and simulation of fully nonlinear steady waves. The set of resulting nonlinear equations are solved by Newton's method. The shoaling of waves is simulated based on comparisons with experimental data. The wave heights and the angles of breaking are analysed until the limit of inadequacy of the numerical method. The results appear quite close to those criteria predicted by the theory of completely nonlinear surface waves and contribute to provide...

Solutions of hypersingular integral equations over circular domains by a spectral method

Farina, Leandro;  Ziebell, Juliana S. — 2013

Applications of Mathematics 2013

The problem of a solving a class of hypersingular integral equations over the boundary of a nonplanar disc is considered. The solution is obtained by an expansion in basis functions that are orthogonal over the unit disc. A Fourier series in the azimuthal angle, with the Fourier coefficients expanded in terms of Gegenbauer polynomials is employed. These integral equations appear in the study of the interaction of water waves with submerged thin plates.

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