Enhancement of Convergence of Pipe Network Solutions

by Glen N. Williams, (M.ASCE), Asst. Prof.; Dept. of Industrial Engrg., Computer Sci. Div., Texas A&M Univ., College Station, TX,

Serial Information: Journal of the Hydraulics Division, 1973, Vol. 99, Issue 7, Pg. 1057-1067

Document Type: Journal Paper


In order to enhance the convergence properties of the Hardy Cross loop algorithm as applied to pipe networks, two approaches were studied. First, the exact flow corrective quantities were found and applied to the lines in each loop on each system iteration. (This is in contrast to the current approach of evaluating an equation based on a truncated Taylor's series expansion.) This attempt was unsuccessful. Second, simple multipliers, called convergence acceleration factors, were applied to the standard loop corrective amount in order to correct the system faster. This effort reduced the number of solution iterations by as much as 80% for the larger networks studied. An equation was then developed that estimates the optimal acceleration factor for any given system.

Subject Headings: Convergence (mathematics) | Pipelines | Algorithms

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