A hybrid spectral/DG method for solving the phase-averaged ocean wave equation: Algorithm and validation

作者：Yildirim B; Karniadakis George Em^*

来源：Journal of Computational Physics, 2012, 231(14): 4921-4953.

DOI：10.1016/j.jcp.2012.04.013

• Action balance equation
• Absorbing boundary layer
• Spectral element
• Unstructured grid

We develop a new high-order hybrid discretization of the phased-averaged (action balance) equation to simulate ocean waves. We employ discontinuous Galerkin (DG) discretization on an unstructured grid in geophysical space and Fourier-collocation along the directional and frequency coordinates. The original action balance equation is modified to facilitate absorbing boundary conditions along the frequency direction; this modification enforces periodicity at the frequency boundaries so that the fast convergence of Fourier-collocation holds. In addition, a mapping along the directional coordinate is introduced to cluster the collocation points around steep directional spectra. Time-discretization is accomplished by the TVD Runge-Kutta scheme. The overall convergence of the scheme is exponential (spectral). We successfully verified and validated the method against several analytical solutions, observational data, and experimental results.

• 出版日期2012-5-20