Meeting Computational Challenges Presented by Transitioning Flow Patterns at Pipe Junctions

Abstract

This article addresses the issues, related to transitioning junction flow patterns, that afflict the hydraulic simulation of pipe network. At transition points, the values of head change caused by a junction are not unique, and thus the head change versus flow rate function is not differentiable. Nonlinear solution algorithms including Newton’s method are likely to fail when faced with such discontinuities, or at best produce solutions that depend on the initial guess for starting the solution. The difficulties can be removed by replacing dual junction head changes with unique values that can be determined based on the transitioning flow patterns and then incorporating the unique values into smooth interpolating functions that replace the step functions. Splines in tension serve as the interpolation functions. Existing flow solvers can be retrofitted with the proposed procedure. Implementation of this procedure is demonstrated for T junctions by solving several steady-state and time-accurate network flows. In all cases the strong convergence property of Newton’s method is restored.