# Efficient Code for Steady-State Flows in Networks

*by*Robert Epp, Grad. Student; Dept. of Mathematics, Princeton Univ., Princeton, NJ; formerly, Undergrad. Summer Student, Computing Ctr., Univ. of British Columbia, Vancouver, Canada,

Alvin G. Fowler, Asst. Dir.; Computing Ctr., Univ. of British Columbia, Vancouver, Canada,

**Serial Information**:

*Journal of the Hydraulics Division*, 1970, Vol. 96, Issue 1, Pg. 43-56

**Document Type:**Journal Paper

**Abstract:**

A complete algorithm for the computer solution of steady-state fluid flows in networks is given. Particular stress is placed on fast solution, minimal storage requirements and simplicity of the input data. Although the Hardy Cross method is the classical method of solution of this type of problem, convergence is slow for large networks. To overcome this problem, the whole network is considered simultaneous, and this produces a large system of non-linear equations. Newton's method is applied, which results in an iterative solution of a system of linear equations. In order to reduce computer storage requirements and to simplify the data input, a number of algorithms from graph theory are involved. The resulting matrix of coefficients associated with the system of linear equations is banded and symmetric for which efficient (in time and memory requirements) methods of solution exist.

**Subject Headings:**Algorithms | Steady states | Fluid flow | Steady flow | Linear functions | Computer networks | Convergence (mathematics) | Nonlinear analysis

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