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Application of a fractional step method for the numerical solution of the shallow water waves in a rotating rectangular basin
Faculty
Science
Year:
2010
Type of Publication:
Article
Pages:
2268-2280
Authors:
Helal, Medhat M, Abd-el-Malek, Mina B
DOI:
10.1080/00207160802624158
Journal:
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS TAYLOR \& FRANCIS LTD
Volume:
87
Research Area:
Mathematics
ISSN
ISI:000281320400011
Keywords :
rotating fluids, shallow water equations, fractional steps method, riemann invariants, cubic spline interpolation
Abstract:
A numerical method is applied to the problem of an incompressible fluid in a slowly rotating rectangular basin for the simulation of wave propagation in shallow water. The present work is a complete study of the wave motion through evaluation of the wave height and the velocity components. The results are found by the application of a fractional step method and illustrated graphically. The technique is applied by splitting the shallow water equations and successive integration in every direction along the characteristics using the Riemann invariants associated with cubic spline interpolation. It has the advantage of reducing the multidimensional matrix inversion problem into an equivalent one-dimensional problem. Numerical results are represented in three dimensions for the velocity components at different times. The distribution of temperature and concentration are also calculated and plotted.
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