Abstract
We demonstrated in Chapter 2 that the equations describing the transient flow in closed conduits are hyperbolic, partial differential equations, and discussed a number of numerical methods available for their solution. The details of the method of characteristics [Lister, 1960; Streeter and Lai, 1962; Perkins et al. 1964; Abbott, 1966, Evangelisti, 1969; Gray, 1953] are presented in this chapter.
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References
Abbott, M. B., 1966, An Introduction to the Method of Characteristics, American Elsevier, New York, NY.
Chaudhry, M. H. and Portfors, E. A., 1973, “A Mathematical Model for Analyzing Hydraulic Transients in a Hydroelectric Power Plant,” Proc. First Canadian Hydraulic Conference, published by the University of Alberta, Edmonton, Canada, May, pp. 298-314.
Chaudhry, M. H. and Yevjevich, V. (eds.), Closed-Conduit Flow, Water Resources Publications, Littleton, Co.
Chaudhry, M. H., 1982, “Numerical Solution of Transient-Flow Equations,” Proc. Hydraulic Specailty Conf., Amer. Soc. of Civil Engrs., Jackson, MS, Aug., pp. 633-656.
Chaudhry, M. H. and Hussaini, M. Y., 1983, “Second-Order Explicit Methods for Transient-Flow Analysis,” in Numerical Methods for Fluid Transient Analysis, C. S. Martin and M. H. Chaudhry (eds.), Amer. Soc. of Mech. Engrs., New York, pp. 9-15.
Chaudhry, M. H. and Holloway, M. B., 1984, “Stability of Method of Characteristics,” Proc. Hydraulics Division Specialty Conf., Amer. Soc. Civil Engrs., Coeur d’Alene, Idaho, Aug., pp. 216-220.
Chaudhry, M. H. and Hussaini, M. Y., 1985, “Second-Order Accurate Explicit Finite-difference Schemes for Waterhammer Analysis,” Jour. of Fluids Engineering, vol. 107, Dec., pp. 523-529.
Chaudhry, M. H. and Mays, L. W., 1994, (eds.), Computer Modeling of Free-Surface and Pressurized Flows,, Kluwer, the Netherlands, 741 pp.
Chaudhry, M. H., 2008, Open-Channel Flow, 2nd. ed., Springer, New York, NY, 523 pp.
Collatz, L., 1960, The Numerical Treatment of Differential Equalions, Third ed., Springer, Berlin, Germany.
Evangelisti, G., 1969, “Waterhammer Analysis by the Method of Characteristics,” L’Energia Elettrica, Nos. 10-12, pp. 673-692, 759-770,839-858.
Fischer, S. G., 1973, “The Westinghouse Leading Edgc Ultrasonic Flow Measurement System,” presented at the Spring Meeting, Amer. Soc. of Mech. Engrs., Boston, May.
Goldberg, D. E. and Wylie, E. B., 1983, “Characteristics Method Using Time-Line Interpolation,” Jour. Hydraulic Engineering, Amer. Soc. Civil Engrs., May, pp. 670-683.
Gray, C. A. M., 1954, “Analysis of Water Hammer by Characteristics,” Trans. of Amer. Soc. of Civil Engrs., vol. 119, pp. 1176-1194.
Holloway, M. B. and Chaudhry, M. H., 1985, “Stability and Accuracy of Waterhammer Analysis,” Advances in Water Resources, vol. 8, Sept., pp. 121-128.
Kaplan, M., Belonogoff, G. and Wentworth, R. C., 1972, “Economic Methods for Modelling Hydraulic Transient Simulation,” Proc. First Inlernalional Conference on Pressure Surges, Canterbury, England, published by British Hydromechanics Research Assoc., Sept., pp. A-33 - A4-38.
Lister, M., 1960 “The Numerical Solution of Hyperbolic Partial Differential Equations by the Method of Characteristics,” in Mathematical Methods for Digital Computers, edited by Ralston, A. and Wiley, H. S., John Wiley & Sons, New York, Chap. 15.
O’Brien, G. G., Hyman, M. A. and Kaplan, S., 1951, “A Study of the Numerical Solution of Panial Differential Equations,” Jour. Math. and Physics, No. 29, pp. 223-251.
Parmakian, J., Waterhammer Analysis, Dover Publications, Inc., New York, NY.
Perkins, F. E., Tedrow, A. C., Eagleson, P. S. and Ippen, A. T., 1964, Hydro-Power Plant Transients, Part II, Dept. of Civil Engineering, Hydrodynamics Lab. Report No. 71, Massachusetts Institute of Technology, Sept.
Portfors, E. A. and Chaudhry, M. H., 1972, “Analysis and Prototype Verifications of Hydraulic Transients in Jordan River Power Plant,” Proc. First International Conference on Pressure Surges, Canterbury, British Hydromechanics Research Assoc., September, pp. E4-57 to E4-72.
Rachford, H. H. and Todd, D., 1974, “A Fast, Highly Accurate Means of Modeling Transient Flow in Gas Pipeline Systems by Variational Methods,” Jour. Soc. of Petroleum Engrs., April, pp. 165-175. (See also Discussion by Stoner, M. A., and Authors’ Reply, pp. 175-178.)
Reddy, H. P., Silva-Araya, W. and Chaudhry, M. H., 2012, “Estimation of Decay Coefficients for Unsteady Friction for Instantaneous, Acceleration-Based Models” Jour. Hydraulic Engineering, vol. 138, no. 3, pp. 260-271.
Smith, G. D., 1978, Numerical Solution of Partial Differential Equations, Second ed., Clarendon Press, Oxford, England.
Streeter, V. L. and Lai, C., 1962, “Waterhammer Analysis Including Fluid Friction,” Jour. Hyd. Div., Amer. Soc. of Civ. Engrs., May, pp. 79-112.
Tournès, D., 2003, “Junius Massau et Lintégration Graphique,” Revue d’histoire des mathématiques, vol. 9, pp. 181-252.
Vardy, A. E., 1977, “On the Use of the Method of Characteristics for the Solution of Unsteady Flows in Networks,” Proc. Second International Conf. on Pressure Surges, British Hydromechanics Research Assoc., Bedford, England.
Wiggert, D. C. and Sundquist, M. J., 1977, “On the Use of Fixed Grid Characteristics for Pipeline Transients,” Jour. Hyd. Div., Amer. Soc. of Civil Engrs., vol. 103, Dec., pp. 1403-1416.
Wylie, E. B., Streeter, V. L. and Stoner, M. A., 1974, “Unsteady-State Natural Gas Transient Calculations in Complex Pipe Systems,” Jour. Soc. of Pelroleum Engrs., Feb., pp. 35-43.
Wylie, E. B., 1976, “Transient Aquifer Flows by Characteristics Method,” Jour. Hyd. Div., Amer. Soc. of Civil Engrs., vol. 102, March, pp. 293-305.
Wylie, E. B., 1983, “Advances in the Use of MOC in Unsteady Pipeline Flow,” Fourth International Conf. on Pressure Surges, British Hydromechanics Research Assoc., Bath, England, Sept. 21-23, pp. 27-37.
Wylie, E. B., 1983, “The Microcomputer and Pipeline Transients,” Jour. Hydraulic Engineering, Amer. Soc. Civil Engrs. Proc. Paper No. 18453, Vol. 109, No. 12, Dec., pp. 1723-1739.
Wylie, E. B., and Streeter, V. L. 1983, Fluid Transients, FEB Press, Ann Arbor, Mich..
Yow, W., 1972, “Numerical Error on Natural Gas Transient Calculations,” Trans. Amer. Soc. of Mech. Engrs., vol. 94, Series D, no. 2, pp. 422-428.
Additional References
Brown, F. T., 1968, “A Quasi Method of Characteristics with Application to Fluid Lines with Frequency Dependent Wall Shear and Heat Transfer,” Paper No. 68-WA/ Aut.-7, Amer. Soc. of Mech. Engrs., Dec.
Contractor, D. N., 1965, “The Reflection of Waterhammer Pressure Waves from Minor Losses,” Trans. Amer. Soc. Mech. Engrs., vol. 87, Series D, June.
Evangelisti, G., 1966, “On the Numerical Solution of the Equation of Propagalion by the Method of Characteristics,” Meccanica, vol. 1, No. 1/2, pp. 29-36.
Fox, J. A. and Henson, D. A., 1971, “The Prediction of the Magnitudes of Pressure Transients Generated by a Train Entering a Single Tunnel,” Proc., Institution of Civil Engrs., Paper 7365, vol. 49, May, pp. 53-69.
Miyashiro, H., 1967, “Waterhammer Analysis of Pump System,” Bull. Japan Soc. of Mech. Engrs., vol. 10, No. 42, pp. 952-958.
Proc. Pressure Surge Conferences, Proceedigs of British Hydromechanics Research, First, 1972; Second, 1977; Third,1980; Fourth, 1983; Fifith, 1986; Sixth, 1989; Seventh, 1992; Eighth, 1995; Nineth, 2004; Tenth, 2008; Eleventh, 2012.
Symposium 1965, Waterhammer in Pumped Storage Projects, Chicago, Nov., Amer. Soc. of Mech. Engrs.
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Chaudhry, M.H. (2014). Characteristics and Finite-Difference Methods. In: Applied Hydraulic Transients. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8538-4_3
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DOI: https://doi.org/10.1007/978-1-4614-8538-4_3
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