A pseudo-spectral method for non-linear wave hydrodynamics
نویسنده
چکیده
We present a new hybrid asymptotic-numerical method to study nonlinear wave-body interaction in threedimensional water of arbitrary depth. After solving a simplified body problem numerically using a distribution of singularities along the body surface, we reduce the nonlinear free surface problem to a closed system of two nonlinear evolution equations, using a systematic asymptotic expansion, for the free surface elevation and the velocity potential at the free surface. The system, correct up to third order in wave steepness, is then solved using a pseudo-spectral method based on Fast Fourier Transform. We study the evolution of unstable Stokes waves and the generation of nonlinear surface waves by translating twoand three-dimensional dipoles. In order to validate our numerical method, a translating circular cylinder is also considered and our numerical solution is compared with the fully nonlinear numerical solution.
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