Numerical Modeling of Three-Dimensional Potential Waves


Chalikov D. V.

A simple and exact numerical scheme for a long-term simulation of three-dimensional po-tential fully-nonlinear periodic gravity waves is suggested. The scheme is based on a sur-face-following non-orthogonal curvilinear coordinate system. A velocity potential is represented as a sum of analytical and nonlinear components. The Poisson equation for non-linear component of velocity potential is solved iteratively. The Fourier transform method, second-order accuracy approximation of the vertical derivatives on a stretched vertical grid and the fourth-order Runge—Kutta time stepping are used. The scheme is validated by si-mulation of steep Stokes waves. The one-processor version of the model for PC allows us to simulate an evolution of a wave field with thousands degrees of freedom for hundreds of wave periods. The scheme is designed for investigation of the nonlinear two-dimensional surface waves, generation of extreme waves and direct calculations of nonlinear interac-tions. After implementation of the wave breaking parameterization and wind input, the model can be used for the direct simulation of a two-dimensional wave field evolution under the action of wind, nonlinear wave-wave interactions and dissipation.

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