Control-volume Method for Extralarge Network Hydraulic Analysis

The authors have made the transition from the mass balance equations based on the Kirchhoff laws in solution of network hydraulic with discretized of the continuity equation. It is reduced to the numerical solution of the second order Poisson's equation for pressure equation. It makes possible to solve extralarge network hydrodynamic problems order of 10 million nodes and links.Moreover, this method is numerically stable even for hydraulic networks, in which the friction factor and minor losses in pipes may differ by more than 10 orders and global gradient algorithm, used in EPANET, became not enough suitable for use.Convergence of the proposed method is higher then “loop” or “node” methods, and close to the Todini global gradient algorithm convergence and yields only 1 − 2 iterations. Also the convergence almost doesn’t depend on problem dimension. The convergence comparison was carried out by the program EPANET and different “loop” and “node” methods.