A higher-order mild-slope equation (HOMSE) is derived based on theory of Hsu et al. . Depth function is approximated up to third-order accurate in terms of both wave nonlinearity and bottom slope. Classical Galerkin method is used to solve HOMSE. Developed model is verified with a series of benchmark tests, including propagation of a sinusoidal wave past a submerged bar, wave propagating on a sloping bed, wave propagating over an elliptic shoal on a uniform slope, and wave propagating through a semicircular slope bottom, respectively. Computed results are compared with experiment data and prediction of low-order mild-slope equation model as well as Boussinesq equations model, and show good agreement.
Lan, Yuan-Jyh; Hsu, Tai-Wen; Lin, Ta-Yuan; and Liang, Shin-Jye
"DESIGN AND IMPLEMENTATION OF AN SIMULATION OF WATER WAVE TRANSFORMATION USING HIGHER ORDER MILD-SLOPE EQUATION,"
Journal of Marine Science and Technology: Vol. 20:
5, Article 16.
Available at: https://jmstt.ntou.edu.tw/journal/vol20/iss5/16