181
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Gradually varied flow profile based on adaptive pattern

&
Pages 223-231 | Received 11 Sep 2016, Accepted 16 Nov 2017, Published online: 18 Dec 2017

References

  • Ash, J.H. (1965). “An Adams Runge-Kutta subroutine for systems of ordinary differential equations.” Master’s thesis, Univ., of Toronto, Ontario, Canada.
  • Bakhmeteff, B.A. (1932). Hydraulics of open channels, McGraw-Hill Book Company, New York, NY.
  • Bresse, J.A.C. (1860). Course in applied mechanics, Hydraulics, Hallet-Bachelier, Paris.
  • Chaudhry, H.M. (2008). Open-channel flow, Springer Science, Business Media, New York, NY, Chapter 6.10.1007/978-0-387-68648-6
  • Chow, V.T. (1955). “Integrating the equation of gradually varied flow.” Proc., Paper No. 838, ASCE, New York, NY, 81, 1–32.
  • Chow, V.T. (1959). Open-channel hydraulics, McGraw-Hill, New York.
  • Dey, S. (2000). “Chebyshev solution as aid in computing GVF by standard step method.” J. Irrig. Drain. Eng., 126(4), 271–274.10.1061/(ASCE)0733-9437(2000)126:4(271)
  • Dubin, J.R. (1999). “On gradually varied flow profiles in rectangular open-channels.” J. Hydraulic Res., 37(1), 99–106.10.1080/00221689909498534
  • Enright, W.H. (1989). “Analysis of error control strategies for continuous Runge–Kutta methods.” SlAM J. Numer. Anal., 26(3), 588–599.10.1137/0726035
  • Enright, W.H. (1989). “A new error-control for initial value solvers.” Appl. Math. Comput., 31, 288–301.
  • Faires, j. D., and Burden, R. L. (2012). Numerical methods, Dublin City University, Dublin, Ireland.
  • Fehlberg, E. (1969). Low-order classical Runge-Kutta formulas with step size control and their application to some heat transfer problems, NASA Technical Report 315, National aeronautics and space administration, Washington.
  • Fread, D.L., and Harbaugh, T.E. (1971). “Open-channel profiles by Newton’s iteration technique.” J. Hydrology, 13, 70–80.10.1016/0022-1694(71)90202-2
  • French, R.H. (1985). Open-channel hydraulics, McGraw-Hill Book McGraw-Hill Book, New York, NY.
  • Henderson, F.M. (1966). Open channel flow, MacMillan MacMillan, New York, NY.
  • Higham, D.J. (1991). “Runge-Kutta defect control using Hermite-Birkoff interpolation.” SIAM J. Sci. Statist. Comput., 12(5), 991–999.10.1137/0912053
  • Jan, C.D., and Chen, C.L. (2012). “Use of the Gaussian hypergeometric function to solve the equation of gradually-varied flow.” J. Hydrology, 456–457, 139–145.10.1016/j.jhydrol.2012.06.023
  • Kaya, B. (2011). “Investigation of gradually varied flows using differential quadrature method.” Sci. Res. Essays, 6(13), 2630–2638.
  • Kincaid, D., Cheney, W. (1990). Numerical analysis, The University of Texas, Austin, TX, Chapters 3 and 8.
  • Kumar, A., Chezy, and Bresse. (1978). “Integral solutions of the gradually varied equation for rectangular and triangular channels.” Proc. Inst. Civ. Eng., 65(2), 509–515.
  • Kurnatowski, J. (2011). “Comparison of analytical and numerical solutions for steady gradually varied open-channel Flow.” J. Environ. Stud., 20(4), 925–930.
  • Lizhong, H.Q., Bo, X., and Zhenzhen, G. (2011). “The research on calculation of water surface profile in channel by Runge – Kutta method.” Int. Symp. Water Res. Environ. Protect., 408–412.
  • Ortega, J.M., and Reinbolt, W.C. (1970). Iterative solution of nonlinear equations in several variable, Academic Press, San Diego, CA.
  • Paine, J.N. (1992). “Open-channel flow algorithm in Newton-Raphson form.” J. Irrig. Drain. Eng., 118(2), 306–319.10.1061/(ASCE)0733-9437(1992)118:2(306)
  • Patil, R.G., Diwanji, V.N., and Khatsuria, R.M. (2001). “Integrating equation of gradually varied flow.” J. Hydr. Eng., 127(7), 624–625.10.1061/(ASCE)0733-9429(2001)127:7(624)
  • Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. (1986). Numerical recipes, The art of scientific computing, Cambridge University Press, New York.
  • Rhodes, D.G. (1995). “Newton-Raphson solution for gradually varied flow.” J. Hydr. Res., 33(2), 213–218.10.1080/00221689509498671
  • Rhodes, D.G. (1998). “Gradually varied flow solution in Newton-Raphson form.” J. Irrig. Drain. Eng., 124(4), 233–235.10.1061/(ASCE)0733-9437(1998)124:4(233)
  • Schaefer, R.L. (1985). “Bakwatr-computation of gradually varied flow.” J. Adv. Eng. Software, 7(4), 170–172.10.1016/0141-1195(85)90045-2
  • Shampine, L.F., and Gordon, M.K. (1975). Numerical solution of ordinary differential equations, Society for Industrial and Applied Mathematics, W. H. Freeman, San Francisco, CA.
  • Shampine, L.F., and Watts, H.A. (1977). “The art of writing a Runge-Kutta code.” Mathematical Software III, Academic, New York, NY, 257–275.
  • Shampine, L.F., and Watts, H.A. (1979). “The art of writing a Runge-Kutta code.” II. Appl. Math. Comp., 5(2), 93–121.10.1016/0096-3003(79)90001-8
  • Sikorski, K.A. (2001). Optimal solutions of nonlinear equations, University Press, Oxford.
  • Stewart, N.E. (1965). “An integration subroutine using a Runge-Kutta method.” Master’s thesis, Univ., of Toronto, Ontario, Canada.
  • Venutelli, M. (2004). “Direct integraton of the equation of gradually varied flow.” J. Irrig. Drain. Eng., 13(1), 88–91.10.1061/(ASCE)0733-9437(2004)130:1(88)
  • Zaghloul, N.A., and Anwar, M.N. (1991). “Numerical integration of gradually varied flow in trapezoidal channel.” J. Comput. Methods Appl. Mech. Eng., 88(2), 259–272.10.1016/0045-7825(91)90258-8
  • Zaghloul, N.A., and Darwish, A.Y. (1987). “Solution of gradually varied flow problems using the direct step method with the IBM PC Lotus 1-2-3 system.” J. Environ. Software., 2(4), 199–206.10.1016/0266-9838(87)90035-9
  • Zhang, J.M., Wang, Y.R., Xu, W.L., and Lio, H. (2005). “New iteration method for calculating water level of gradually varied steady flow.” J. Hydraulic Eng., 36, 501–504.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.