The Goddard Coastal Wave Model. Part I: Numerical Method

Abstract

To select a wind wave model as the basis for developing a coupled wind wave-current model for coastal dynamics, the numerical schemes used in state-of-the-art wind wave models are examined analytically. The schemes used in the existing models contain serious numerical aliases leading to dissipation and dispersion. These numerical aliases could mistakenly be interpreted as part of the physical phenomena. To alleviate these shortcomings, a fourth-order semi-implicit scheme for transport-type models and a second-order semi-implicit scheme with a gradient-dependent directional filter for the conservation-type models are proposed. The traditional difficulty of a hyperbolic conservation law is surmounted by this directional filter. These new schemes and the new filter are insensitive to the sizes of the time step and spatial grid and the magnitude of the group velocity; therefore, aliasing of the physical phenomena will not occur. Furthermore, the numerical dissipation and the dispersion of the new method are practically zero. Even though each computation step of these new schemes requires greater computing time, the total computing time is still considerably shorter than that in previous models because the time steps of the new schemes can be an order of magnitude greater than those used previously.