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Title: A compact numerical algorithm for solving the time-dependent mild slope equation
Authors: Lin, P. 
Keywords: Compact numerical algorithm
Real-time wave forecast
Storm wave simulation
Time-dependent mild slope equation
Wave diffraction
Wave refraction
Issue Date: 30-Jun-2004
Citation: Lin, P. (2004-06-30). A compact numerical algorithm for solving the time-dependent mild slope equation. International Journal for Numerical Methods in Fluids 45 (6) : 625-642. ScholarBank@NUS Repository.
Abstract: The mild slope equation has been widely used to describe combined wave refraction and diffraction. In this study, a new numerical algorithm is developed to solve the time-dependent mild slope equation in a second-order hyperbolic form. The numerical algorithm is based on a compact and explicit finite difference method that is second-order accurate in both time and space. The algorithm has the similar structure to the leap-frog method but is constructed on three time levels for the second-order time derivative term. The numerical model has the capability of simulating transient wave motion by correctly predicting the speed of wave energy propagation, which is important for the real-time forecast of the arrival time of storm waves generated in the far field. The model is validated against analytical solution for wave shoaling and experimental data for combined wave refraction and diffraction over a submerged elliptic shoal on a slope (Coastal Eng. 1982; 6:255). Lastly, the realistic scale Homma's island (Geophys. Mag. 1950; 21:199) is studied with the use of various wave periods of T = 720 s, T = 120 s, and T = 24 s. These wave periods correspond to long, intermediate, and short waves for the given topography, respectively. Comparisons are made between numerical results and existing analytical solutions in terms of the wave amplification around the island, which serves as the indicator for the potential wave runup. Excellent agreements are obtained. The model runs on a PC (Pentium IV 1.8GHz) and the computer capacity allows the computation of a mesh system up to 3000 × 3000, which is equivalent to about 150 × 150 waves or a large area of 540 km × 540 km for a wave train with the period of T - 60 s. © 2004 John Wiley and Sons, Ltd.
Source Title: International Journal for Numerical Methods in Fluids
ISSN: 02712091
DOI: 10.1002/fld.716
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