An Accurate Finite Difference Scheme for Boussinesq Equations |
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| Authors: | J.M. Zhan O.W.H. Wai |
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| Affiliation: | 1. Department of Applied Mechanics and Engineering , Zhongshan University , 510275, Guangzhou, People's Republic of China;2. Department of Civil &3. Structural Engineering , The Hong Kong Polytechnic University , Hong Kong, People's Republic of China |
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| Abstract: | In this paper, a stable and accurate finite difference scheme using a space-staggered grid is proposed for solving the extended Boussinesq-type equations as derived by Nwogu [Journal of Waterway, Port Coastal and Ocean Engineering, ASCE, 119, (1993) 618–638]. The alternate direction iterative method combined with an efficient predictor–corrector scheme is adopted for the numerical solution of the governing differential equations. The proposed method is verified by two test cases where experimental data are available for comparison. The first case is wave focusing by bottom topography as studied by Whalin [The limit of applicability of linear wave refraction theory in a convergence zone. Res. Rep. H-71-3, U.S.Army Corps of Engrs. Waterways Expt. Station, Vicksburg (1971)]. The second case is wave runup around a circular cylinder as investigated experimentally by Isaacson (Journal of the Waterway, Port, Coastal and Ocean Division, ASCE, 104, (1978), 69–79). Numerical results agree very well with the corresponding experimental data in both cases. |
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| Keywords: | Boussinesq equations Space-staggered grid Finite difference scheme Tridiagonal system of equations |
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