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This paper considers two issues related to iteratively solving the non-linear equations governing the flows and heads in a water distribution system network. The first concerns the use of the correct Jacobian for the Global Gradient Algorithm (GGA) when the Darcy-Weisbach head loss model is used. The second relates to dealing with zero flows in the iterative solution process. A regularization procedure for the GGA with the Hazen{Williams model is demonstrated on an example network which has zero flows but for which the (full) Jacobian is invertible.Sylvan Elhay and Angus R. Simpso

The Darcy-Weisbach Jacobian and Avoiding Zero Flow Failures in the Global Gradient Algorithm for the Water Network Equations