A modified global gradient algorithm based on topological decomposition

Abstract

In this paper a modified version of the well-known global gradient algorithm for the hydraulic steady-state calculation or simulation of pressurized pipe networks is presented. The method is based on the identification using decomposition of components of the network graph that have different connectivity. The information resulting from the decomposition is used for a reordering of the topological incidence matrix of the network graph. The method is referred to as Topological Decomposition Global Gradient Algorithm (TDGGA). It will be shown that the permuted system can be decomposed into local solutions and the global solution. Using simple algebraic manipulations the size of the linear system that has to be solved during each iteration is reduced to the number of nodes that connect at least three pipes. For all pipe models of real world applications that are derived from GIS datasets this means a dramatic reduction of the size of the mathematical problem that has to be solved. After a brief review of the traditional GGA the new topological decomposition method is explained in detail. Finally, its application is demonstrated for an example system.