Unified framework for deriving simultaneous equation algorithms for water distribution networks

Journal of Hydraulic Engineering

Volumn 139, Issue 5, 2013, Pages 511-526

  Todini, Ezio ^a   Rossman, Lewis A ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b U S ENVIRONMENTAL PROTECTION AGENCY   (United States)

Author keywords

Linear theory; Newton Raphson; Simultaneous equations algorithms; Water distribution networks

Indexed keywords

ANALYTICAL APPROACH; CONSERVATION OF MASS; CONVERGENCE CHARACTERISTICS; LINEAR THEORY; NON-LINEAR TRANSFORMATIONS; SIMULTANEOUS EQUATIONS; SYSTEM OF NONLINEAR EQUATIONS; WATER DISTRIBUTION NETWORKS;

ALGORITHMS; LINEAR TRANSFORMATIONS; NEWTON-RAPHSON METHOD; NONLINEAR EQUATIONS; WATER DISTRIBUTION SYSTEMS;

MATHEMATICAL TRANSFORMATIONS;

ALGORITHM; ANALYTICAL FRAMEWORK; EQUATION; HYDRAULICS; LINEARITY; WATER SUPPLY;

EID: 84879590807     PISSN: 07339429     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)HY.1943-7900.0000703     Document Type: Article

References (26)

1. Bhave, P. R. (1991). Analysis of flow in water distribution networks, Technomic Publishing, Lancaster, PA.
2. Carnahan, B., Luther, H. A., and Wilkes, J. O. (1969). Applied numerical methods, Wiley, New York.
3. Collins, M., Cooper, L., Helgason, R., Kenningston, J., and LeBlanc, L. (1978). "Solving the pipe network analysis problem using optimization techniques." Manage. Sci., 24(7), 747-760.
4. Cross, H. (1936). "Analysis of flow in networks of conduits or conductors." Bulletin No. 286, Engineering Experiment Station, Univ. of Illinois, Urbana, IL.
5. Donachie, R. P. (1974). "Digital program of water analysis." J. Hydraul. Div., 100(HY3), 393-403.
6. Epp, R., and Fowler, A. G. (1970). "Efficient code for steady-state flows in networks." J. Hydraul. Div., 96(HY1), 43-56.
7. Giustolisi, O. (2010). "Considering actual pipe connections in WDN analysis." J. Hydraul. Eng., 136, 889-900.
8. Gupta, R., and Prasad, T. D. (2000). "Extended use of linear graph theory for analysis of pipe networks." J. Hydraul. Eng., 126(1), 56-62.
9. Hamam, Y., and Brameller, A. (1971). "Hybrid method for the solution of piping network." Proc., IEE, 118(11), 1607-1612.
10. Isaacs, L. T., and Mills, K. G. (1980). "Linear theory for pipe network analysis." J. Hydraul. Div., 106(HY7), 1191-1201.
11. Kesavan, H. K., and Chandrashekar, M. (1972). "Graph-theoretic models for pipe network analysis." J. Hydraul. Div., 98(HY2), 345-363.
12. Lam, C. F., and Wolla, M. L. (1972a). "Computer analysis of water distribution systems: Part I-Formulation of equations." J. Hydraul. Div., 98(HY2), 335-344.
13. Lam, C. F., and Wolla, M. L. (1972b). "Computer analysis of water distribution systems: Part II-Numerical solution." J. Hydraul. Div., 98(HY3), 447-460.
14. Lemieux, P. F. (1972). "Efficient algorithms for distribution networks." J. Hydraul. Div., 98(HY11), 1911-1920.
15. Martin, D.W., and Peters, G. (1963). "The application of Newton's method to network analysis by digital computer." J. Inst. Water Eng., 17, 115-129.
16. Mignosa, P. (1987). "Sui problemi di verifica delle reti di distribuzione idrica complesse." Idrotecnica, 6, 257-273 (in Italian).
17. Osiadacz, A. J. (1988). "Comparison of numerical methods for steady-state simulation of gas networks." Civ. Eng. Syst., 5, 25-30.
18. Osiadacz, A. J., and Pienkosz, K. (1988). "Methods of steadystate simulation for gas networks." Int. J. Syst. Sci., 19(7), 1311-1321.
19. Rahal, H. (1995). "A co-tree flows formulation for steady state in water distribution networks." Adv. Eng. Softw., 22, 169-178.
20. Rossman, L. A. (2000). "EPANET 2 users manual." Rep. No. EPA/600/ R-00/057, Water Supply and Water Resources Division, National Risk Management Research Laboratory, Cincinnati.
21. Shamir, U., and Howard, C. D. D. (1968). "Water distribution systems analysis." J. Hydraul. Div., 94(HY1), 219-234.
22. Todini, E. (1999). "A unifying view on the different looped pipe network analysis algorithms." Computing and control for the water industry, R. Powell and K. S. Hindi, eds., Research Studies, Baldock, Hertfordshire, UK, 63-80.
23. Todini, E. (2006). "On the convergence properties of the different pipe network algorithms." Proc., 8th Annual Water Distribution Systems Analysis Symposium (CD-ROM), ASCE, Cincinnati, 1-16.
24. Todini, E., and Pilati, S. (1988). "A gradient method for the solution of looped pipe networks." Computer applications in water supply, B. Coulbeck and C. H. Orr, eds., Vol. 1 (System analysis and simulation), Wiley, London, 1-20.
25. Wood, D. J., and Charles, C. O. A. (1972). "Hydraulic network analysis using linear theory." J. Hydraul. Div., 98(HY7), 1157-1170.
26. Wood, D. J., and Rayes, A. G. (1981). "Reliability algorithms for pipe network analysis." J. Hydraul. Div., 107(HY10), 1145-1161.