A split operator scheme for ocean wave simulation

A coupled discrete spectral model was developed for the prediction of ocean waves by solving the energy conservation equation of the two‐dimensional wave spectrum. The model includes the dispersion correction terms in the governing equation to account for the dispersive effect due to the frequency‐dependent velocities of waves. A split operator scheme is used to deal with the numerical problems arising from different terms of the governing equation. The advection terms are solved by the proven accurate minimax characteristics method to avoid excessive numerical damping or oscillations. The dispersion correction terms are solved by central differencing. The source and sink terms are solved by a quasi‐second‐order explicit scheme with limitation on energy growth per time step to allow the use of a large time step. The model was verified by ideal test cases and wave‐hindcasting studies under typhoon conditions in the South China Sea near Hong Kong.