Solve for flows and unknown nodal heas in a water distribution network, based on the Global Algorithm (Eq 16) in Todini & Rossman, 2013.
The current python script is Todini_fsolve_0410.py. It utilizes scipy.optimize.fsolve to solve the hydraulic system of equations representing the conservation of mass and the conservation of energy. It works with the case when no pipe flow is observed, while at least one nodal head has to be known.
When some pipe flows are observed, these known flows create redundancy in the hyraulic system of equations. scipy.optimize.fsolve cannot handle over-determined systems of equations properly, thus a target function needs to be supplied and optimization solvers such as scipy.optimize.minimize have to be used instead.
The folder named pipeline.data_to_sparse.matrix includes the python script for creating sparse matrix which represents the connection between nodes and links from real data.