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Self-adaptive FEM numerical modeling of the mild-slope equation. (English) Zbl 1167.86300
Summary: Based on the linear wave theory, the mild-slope equation (MSE) is a preferred mathematical model to simulate nearshore wave propagation. A numerical model to solve the MSE is developed here on the basis of a self-adaptive finite element model (FEM) combined with an iterative method to determine the wave direction angle to the boundary and thus to improve the treatment of the boundary conditions. The numerical resolution of the waves into ideal domains and multidirectional waves through a breakwater gap shows that the numerical model developed here is effective in representing wave absorption at the absorbing boundaries and can be used to simulate multidirectional wave propagation. Finally, the simulated wave distribution in a real harbor shows that the numerical model can be used for engineering practice.

MSC:
86-08 Computational methods for problems pertaining to geophysics
86A05 Hydrology, hydrography, oceanography
76M10 Finite element methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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