Study of river flow based on finite element analysis and GPS-echo-sounder measurement

Abstract

Currents of a river are analyzed numerically by introducing data concerning the water depth into a finite element analysis of the partial differential equations of the flow. Techniques to simulate currents generated in the river are described. The region is divided in the vertical direction into layers, and a finite element discretization in the horizontal direction is applied. Results of the simulation of flow generated in the Yoshii River in Okayama Prefecture of Japan are shown. We also introduce our techniques to measure the river bed topography using a hardware system consisting of a global positioning system and an echo sounder. Data obtained by using the system are introduced into the analysis of flow and corresponding numerical results are generated. References

• O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, Volume 3, Fluid Dynamics, Fifth Edition, Butterworth-Heinemann, Oxford, 2000 (First published in 1967 by McGraw-Hill).
• R. G. Dean and R. A. Dalrymple, Water Wave Mechanics for Engineers and Scientists, Advanced Series on Ocean Engineering, Volume 2, World Scientific, Singapore, 1991.
• M. Kawahara, M. Kobayashi, K. Nakata, Multiple level finite element analysis and its applications to tidal current flow in Tokyo Bay, Appl. Math. Modelling, Vol. 7, June 1983.
• Jan J. Leendertse, Richard C. Alexander, Shiao-Kung Liu, A three-dimensional model for estuaries and costal seas: Volume I, Principles of computation, R-1417-OWRR, December 1973
• Yoshiiaki Iwasa, Engineering Limnology, Sankaido Publishing Co., Ltd., 1990 (In Japanese)
• Ying Liu, Kazuhiro Yamamoto, Majda Ceric, Masaji Watanabe, Numerical study of flow generated in a lake and experiment using gps, Proceedings of the 14th Biennial Computational Techniques and Applications Conference. CTAC-2008, Editors: Geoffry N. Mercer and A. J . Roberts, ANZIAM J. vol. 50, pp.C912--C929, 2009. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1470
• Masaji Watanabe, A Numerical Simulation of Lake Flow and a gps-Float Experiment, The Second International Symposium on Water Environment, Okayama University, September 13--14, 1999, Journal of the Faculty of Environmental Science and Technology, Okayama University (Special Edition), pp.111--116.
• Masaji Watanabe, Ying Liu, Kazuhiro Yamamoto, Majda Ceric, Numerical study of flow generated in a lake and experimental technique for verification, Proceedings of the 2nd International Symposium on Shallow Flows, HKUST, Hong Kong, December 10--12, 2008.
• http://www.mlit.go.jp/