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Mathematical Problems in Engineering
Volume 2012, Article ID 417950, 18 pages
Research Article

A Direct Solution Approach to the Inverse Shallow-Water Problem

1Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand
2School of Mechanical and Industrial Engineering, Bahir Dar University, P.O. Box 26, Bahir Dar, Ethiopia

Received 26 July 2012; Revised 28 October 2012; Accepted 29 October 2012

Academic Editor: Fatih Yaman

Copyright © 2012 Alelign Gessese and Mathieu Sellier. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. A. Cunge, F. M. Holly, and A. Verwey, Practical Aspects of Computational River Hydraulics, Pitam Publishing, London, UK, 1980.
  2. R. Hilldale and D. Raff, “Assessing the ability of airborne LiDAR to map river bathymetry,” Earth Surface Processes and Landforms, vol. 33, pp. 773–783, 2008. View at Google Scholar
  3. K. Marks and P. Bates, “of high-resolution topographic data with floodplain flow models,” Integration Hydrological Processes, vol. 14, pp. 2109–2122, 2000. View at Google Scholar
  4. R. M. Westaway, S. N. Lane, and D. M. Hicks, “The development of an automated correction procedure for digital photogrammetry for the study of wide, shallow, gravel-bed rivers,” Earth Surface Processes and Landforms, vol. 25, pp. 209–225, 2000. View at Google Scholar
  5. H. Roux and D. Dartus, “Estimating hydraulic parameters and geometric characteristics of a river from remote sensing data using optimization methods,” in Proceedings of the 2nd International Conference on Fluvial Hydraulics, A. A. BALKEMA, Napoly, Italy, 2004.
  6. R. M. Westaway, S. N. Lane, and D. M. Hicks, “Remote sensing of clear-water, shallow, gravel-bed rivers using digital photogrammetry,” Photogrammetric Engineering & Remote Sensing, vol. 67, no. 11, pp. 1271–1281, 2001. View at Google Scholar
  7. Y. Hirose and Y. Imai, “Airborne remote sensing for river environmental assessment,” The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences:, vol. 37, pp. 1149–1152, 2008. View at Google Scholar
  8. A. F. Gessese, M. Sellier, E. Van Houten, and G. Smart, “Inferring channel bed topography from known free surface data,” in Proceedings of the 34th World Congress of the International Association for Hydro-Environment Engineering and Research (IAHR '11), Brisbane, Australia, June 2011.
  9. A. F. Gessese, M. Sellier, E. Van Houten, and G. Smart, “Reconstruction of river bed topography from free surface data using a direct numerical approach in one-dimensional shallow water flow,” Inverse Problems, vol. 27, no. 2, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. A. F. Gessese, G. Smartc, C. Heiningd, and M. Sellier, “One-dimensional bathymetry based on velocity measurements,” Inverse Problems in Science and Engineering, pp. 1–17, 2012. View at Google Scholar
  11. M. Sellier, “Substrate design or reconstruction from free surface data for thin film flows,” Physics of Fluids, vol. 20, no. 6, Article ID 062106, 2008. View at Publisher · View at Google Scholar
  12. C. Heining and N. Aksel, “Bottom reconstruction in thin-film flow over topography: steady solution and linear stability,” Physics of Fluids, vol. 21, no. 8, Article ID 083605, 10 pages, 2009. View at Publisher · View at Google Scholar
  13. M. Sellier and S. Panda, “Beating capillarity in thin film flows,” International Journal for Numerical Methods in Fluids, vol. 63, pp. 431–448, 2009. View at Google Scholar
  14. C. Heining, M. Sellier, and N. Aksel, “The inverse problem in creeping film flows,” Acta Mechanica, vol. 223, no. 4, pp. 841–847, 2012. View at Publisher · View at Google Scholar
  15. A. Gessese, K. M. Wa, and M. Sellier, “Bathymetry reconstruction based on the zero-inertia shallow water approximation,” Theoretical and Computational Fluid Dynamics. In press.
  16. W. Castaings, D. Dartus, M. Honnorat, F.-X. Le Dimet, Y. Loukili, J. Monnier et al., “Automatic differentiation: a tool for variational data assimilation and adjoint sensitivity analysis for flood modelling,” Lecture Notes in Computational Science and Engineering, vol. 50, pp. 249–262, 2006. View at Google Scholar
  17. M. Honnorat, J. Monnier, and F.-X. Le Dimet, “Lagrangian data assimilation for river hydraulics simulations,” Computing and Visualization in Science, vol. 12, no. 5, pp. 235–246, 2009. View at Publisher · View at Google Scholar
  18. M. H. Chaudhry, Open-Channel Flow, Springer, New York, NY, USA, 2nd edition, 2007.
  19. X. Ying, A. A. Khan, and S. S. Y. Wang, “Upwind conservative scheme for the Saint Venant equations,” Journal of Hydraulic Engineering, vol. 130, no. 10, pp. 977–987, 2004. View at Google Scholar
  20. Q. Liang and A. G. L. Borthwick, “Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography,” Computers & Fluids, vol. 38, no. 2, pp. 221–234, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. Y. Xing and C.-W. Shu, “High order finite difference WENO schemes with the exact conservation property for the shallow water equations,” Journal of Computational Physics, vol. 208, no. 1, pp. 206–227, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. F. M. Henderson, Open Channel Flow, Macmillan, New York, NY, USA, 1966.