Application of a fractional step method for the numerical solution of the shallow water waves in a rotating rectangular basin

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.

Keywords:

• rotating fluids
• shallow water equations
• fractional steps method
• riemann invariants
• cubic spline interpolation

2000 AMS Subject Classifications :

• 35Q35
• 68W05
• 76B15

Acknowledgements

The authors would like to express their gratitude to the American University in Cairo for offering a research grant to support this work (grant # 8551-040-1143-5319). One of the authors, namely Mina Abd-el-Malek, is grateful to Dr. Magdi M. Shoucri from the Institut de recherché d'Hydro-Quebec, Canada for directing his attention to the method of fractional steps. The authors would like to express their gratitude and thanks to the reviewers of the manuscript for their critical review and valuable comments that modified the paper greatly.

Additional information

Notes on contributors

Mina B. Abd-el-Malek

On leave from Dept. Eng. Math. & Phys., Faculty of Engineering Alexandria University Alexandria 21544 Egypt.