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Numerical Solutions for Transient and Nearly Periodic Waves in Shallow Water

by James T. Kirby, Univ of Delaware, Newark, United States,
Christina Rasmussen, Univ of Delaware, Newark, United States,



Document Type: Proceeding Paper

Part of: Mechanics Computing in 1990's and Beyond

Abstract:

This paper presents a study of several numerical methods for solving transient (time-dependent) model equations for waves in shallow water by means of the method of lines. The physical models studied include a time dependent mild-slope equation for narrow-banded linear waves in intermediate water depth, and nonlinear models for weakly dispersive long waves in Boussinesq and Green-Naghdi form. The models treat spatial dependence using second and fourth-order accurate finite-differences, and time integration is accomplished using a variety of methods including Euler predictor-corrector, fourth-order Runge-Kutta, and the Bulirsch-Stoer method using a modified midpoint scheme with polynomial extrapolation and adaptive step size.

Subject Headings: Water waves | Surface waves | Numerical methods | Wave equations | Wave propagation | Physical models | Numerical analysis

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