Time-Line Interpolation Errors in Pipe Networks

An exact method of assessing numerical errors in analyses of unsteady flows in pipe networks is introduced. The assessment is valid for fixed-grid method of characteristics analyses using time-line interpolations. A pipe polynomial transfer matrix is developed and is analogous to transfer function matrices used in free oscillation theory. The influence of reachback is assessed by comparing exact numerical predictions using a polynomial transfer matrix with exact analytical predictions obtained using free oscillation theory. The investigation is part of a long-term project aimed at automating the selection of numerical grid sizes in unsteady flow analyses. The eventual goal is to enable users of unsteady flow software to prescribe required degrees of accuracy instead of specifying the numerical grid itself. This paper is only a first step toward the long-term aim, but it is a big step toward an intermediate objective of providing exact benchmarking data for the assessment of approximate methods of automatic grid selection.