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Validity Test of the Eigenfunction Expansion Method in the Transient Wave Propagation Simulation

To test the validity of the eigenfunction expansion method (EEM), a great deal of wave profiles calculated by EEM are compared with the corresponding results obtained by the boundary element method (BEM), which has been verified by many experiments. The comparisons shown that the relative errors of the maximum wave height between them are smaller than 5.5% after 10 periods when the initial wave steepness is below 0.157. However, the errors exceed 12.3% if the initial wave steepness greater than 0.198. As references, we also compared them with the linear solutions. The investigation confirmed that EEM is only valid in the transient wave propagation simulation for small or moderate wave steepness as expected. The corresponding spectrum analysis also reveals that EEM fails to capture harmonics with high wave numbers for the steep waves.