An hydraulics software system for a one-dimensional hydrodynamic numerical model for modeling unsteady flows in sewer and storm water urban drainage systems is provided. The inventive software uses as a numerical model, an implicit four-point, finite-difference solution technique to solve the one-dimensional Saint-Venant equations. The software is designed to select that numerical model, or equation that best describes, or best exhibits the behavior of each of the various structures and flows encountered in complex hydrodynamic systems such as a sewer and storm water drainage systems. Local partial initial modification for subcritical and supercritical transcritical flows is provided. Relaxation for pipe/channel networks are included for achieving computational performance and robustness for commercial software for practical use in water resource engineering.