Piecewise Linear Regularization of Wagner’s Outflow–Pressure Relationship to Deal with Low Nodal Outflows

This technical note presents a technique for the regularization of Wagner’s outflow−pressure relationship, which is an alternative to the regularization used in EPANET 2.2. The proposed technique is based on approximating the zero vicinity of Wagner’s relationship by a piecewise linear function. The approximating function is constructed in such a way that the approximation error is kept within a specified tolerance. At a reasonable approximation accuracy, the lower bound on the outflow derivative of the pressure can be made several orders of magnitude greater than in EPANET 2.2, thus potentially lowering the condition number of the head solution matrix of the EPANET 2 hydraulic solver. In an extended period simulation of large pressure-deficient networks, the EPANET 2.0 implementation of the proposed technique showed an about 2−2.5-fold reduction in the number of iterations and a 2-fold reduction in run time in comparison with EPANET 2.2.