An explicit finite difference model for simulating weakly nonlinear and weakly dispersive waves over slowly varying water depth |
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Authors: | Xiaoming Wang Philip L-F Liu |
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Institution: | School of Civil and Environmental Engineering, Cornell University, Ithaca, NY, USA; Institute of Hydrological and Oceanic Sciences, National Central University, Jhongli, Taiwan |
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Abstract: | In this paper, a modified leap-frog finite difference (FD) scheme is developed to solve Non linear Shallow Water Equations (NSWE). By adjusting the FD mesh system and modifying the leap-frog algorithm, numerical dispersion is manipulated to mimic physical frequency dispersion for water wave propagation. The resulting numerical scheme is suitable for weakly nonlinear and weakly dispersive waves propagating over a slowly varying water depth. Numerical studies demonstrate that the results of the new numerical scheme agree well with those obtained by directly solving Boussinesq-type models for both long distance propagation, shoaling and re-fraction over a slowly varying bathymetry. Most importantly, the new algorithm is much more computationally efficient than existing Boussinesq-type models, making it an excellent alternative tool for simulating tsunami waves when the frequency dispersion needs to be considered. |
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Keywords: | Tsunami Numerical modeling Shallow water waves Frequency dispersion Numerical dispersion Boussinesq equations |
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