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Boundary element formulation of the Mild-Slope equation for harmonic water waves propagating over unidirectional variable bathymetries. (English) Zbl 1403.76063
Summary: This paper presents a boundary element formulation for the solution of the Mild-Slope equation in wave propagation problems with variable water depth in one direction. Based on Greens function approximation proposed by K. A. Belibassakis [Wave Motion 32, No. 4, 339–361 (2000; Zbl 1074.76598)], a complete fundamental-solution kernel is developed and combined with a boundary element scheme for the solution of water wave propagation problems in closed and open domains where the bathymetry changes arbitrarily and smoothly in a preferential direction. The ability of the proposed formulation to accurately represent wave phenomena like refraction, reflection, diffraction and shoaling, is demonstrated with the solution of some example problems, in which arbitrary geometries and variable seabed profiles with slopes up to 1:3 are considered. The obtained results are also compared with theoretical solutions, showing an excellent agreement that demonstrates its potential.

MSC:
 76M15 Boundary element methods applied to problems in fluid mechanics 65N38 Boundary element methods for boundary value problems involving PDEs 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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