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ODE solution to the characteristic form of the Saint-Venant equations

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Abstract

An ordinary differential equation algorithm was formulated to approximate the solution to the characteristic form of the Saint-Venant equations for one-dimensional, gradually varied, unsteady open-channel flow in prismatic irrigation canals. The algorithm was applied by developing a network of characteristics using difference equations for randomly spaced intervals in the x − t (space–time) plane. Consistency, convergence and numerical stability of the equations are demonstrated, and a method to estimate the error of the predictor–corrector scheme is proposed. A mathematical model was developed to test the algorithm using a hypothetical case of unsteady flow, and it was compared to the results from two other mathematical simulation models, providing a high degree of agreement.

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Abbreviations

a :

interpolation coefficient

A :

cross-sectional flow area

c :

shallow-water wave speed (celerity)

E :

local truncation error

g :

gravitational acceleration constant

H :

total hydraulic head

J :

Jacobian matrix

n :

Manning roughness parameter

N :

number of steps

p :

interpolating polynomial

Q :

volumetric flow rate

S f :

energy loss gradient

S o :

longitudinal bed slope

t :

elapsed time

T :

top width of flow

V :

mean flow velocity

W p :

wetted perimeter

x :

longitudinal distance in downstream direction

y :

water depth

z :

elevation of the channel bed

α :

initial distance or divided difference

β :

polynomial root or divided difference

λ :

constant coefficient

ξ :

integration variable

μ :

temporal variable

i, j, k :

counters

n :

node designator

(+):

positive characteristics

(−):

negative characteristics

References

  • Atkinson KE (1989) An introduction to numerical analysis, 2nd edn. Willey, New York

    Google Scholar 

  • Burden RL, Faires JD (1985) Numerical analysis, 3rd edn. PWS Publishers, Boston

    Google Scholar 

  • Conte SD, Boor CD (1980) Elementary numerical analysis, an algorithmic approach. McGraw-Hill Book Company, Inc., New York

    Google Scholar 

  • Holly FM, Parrish JB (1993) Description and evaluation of program: CARIMA. J Irrig Drain Eng ASCE 119(4):703–713

    Article  Google Scholar 

  • Johnson LW, Riess RD (1982) Numerical analysis, 2nd edn. Addison–Wesley, Reading

    Google Scholar 

  • Katopodes ND, Strelkoff T (1977) Hydrodynamics of border irrigation—complete model. J Irrig Drain Div ASCE 103(3):309–324

    Google Scholar 

  • Merkley GP (2006) RootCanal: user’s guide and technical reference. Biological and Irrig. Engrg Dept. Utah State Univ., Logan, Utah. http://www.engineering.usu.edu/bie/faculty/merkley/

  • Parrish JB, Burt CM (1993) Cal Poly canal model. J Irrig Drain Div ASCE 103(3):673–678

    Article  Google Scholar 

  • Rogers DC, Merkley GP (1993) Description and evaluation of program USM. J Irrig Drain Eng ASCE 119(4):703–13

    Article  Google Scholar 

  • Wylie EB, Streeter VL (1983) Fluid transients, corrected edn. FEB Press, Ann Arbor

    Google Scholar 

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Author information

Authors and Affiliations

  1. Rural Development Corporation, Anyang, Kyunggi, South Korea

    S. J. Chun

  2. Biological and Irrigation Engineering Department, Utah State University, Logan, UT, 84322-4105, USA

    G. P. Merkley

Authors
  1. S. J. Chun
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  2. G. P. Merkley
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Corresponding author

Correspondence to G. P. Merkley.

Additional information

Communicated by P. Waller.

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Chun, S.J., Merkley, G.P. ODE solution to the characteristic form of the Saint-Venant equations. Irrig Sci 26, 213–222 (2008). https://doi.org/10.1007/s00271-007-0087-7

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  • DOI: https://doi.org/10.1007/s00271-007-0087-7

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