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Numerical integration of the shallow water equations over a sloping shelf
Author(s) -
Johns B.
Publication year - 1982
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650020304
Subject(s) - shore , computation , shallow water equations , geology , waves and shallow water , finite difference method , finite difference , numerical analysis , scale (ratio) , mechanics , mathematics , mathematical analysis , physics , oceanography , algorithm , quantum mechanics
A finite‐difference method is described for the numerical integration of the one‐dimensional shallow water equations over a sloping shelf that allows for a continuously moving shoreline. An application of the technique is made to the propagation of non‐breaking waves towards the shoreline. The results of the computation are compared with an evaluation based upon an exact analytical treatment of the non‐linear equations. Excellent agreement is found for both tsunami and tidal scale oscillations.