In this paper, several settings were considered to distinguish the optimal design to the interaction of small-amplitude monochromatic water waves with steep bottom undulation consisting of multiple sinusoids. Doubly-sinusoidal bars consisting of both slowly-varying components and rapidly-varying components are concluded in the water depth. Zhang et al. (1999) numerical results and numerical calculation values of primary and sub-harmonic Bragg reflection of mean value, standard deviation, maximum error value and percentage of maximum error value ratio to reflection value by changing slowly-varying components and rapidly-varying components are distinguished in this paper. In addition, Guazzelli et al.'s (1992) experimental data and numerical calculation values of primary Bragg reflection mean error values and standard derivation by changing slowly-varying components and rapidly-varying components are also compared in the paper. According to the above comparison results, the optimal design for Hybrid Mild-Slope Equation method are proposed in this paper.
For linear waves, Berkhoff (1972) used the water depth integral method to derive the Mild-Slope Equation (MSE), which describes the effect of water waves transformations such as shoaling, refraction, diffraction, and reflection by suiting proper boundary condition. Chamberlain and Porter (1995) added the higher-order terms in the MES to propose a Modified Mild-Slope Equation (MMSE). Suh et al. (1997) extended the MSE to develop the time-dependent Hyperbolic type MSE (HMSE), which contains the high order terms of bottom slope term and bottom curvature term. Lee et al. (1998) recast the HMSE into the form of a pair of first-order equation. Hsu and Wen (2001) proposed the time-dependent Parabolic Mild-Slope Equation (PMSE) to solve the HMSE. According to Hsu and Wen's (2001) results, the PMSE has the benefit of saving the storage and computing time for a large computational domain when compared with the HMSE.
