Flexible discretization algorithm for fixed-grid MOC in pipelines

The problem of selecting a time step that exactly satisfies the Courant condition arises most commonly when the fixed-grid method of characteristics (MOC) is applied to multipipe systems. Traditionally, this problem has been solved by employing one of a variety of interpolation techniques or by allowing small adjustments in the value of wave speed. In this paper, the number of available strategies is increased substantially by allowing several new kinds of interpolation as well as blended combinations of these interpolation approaches with the wave-speed-adjustment technique. The new hybrid approaches include interpolation along a secondary characteristic line and minimum-point interpolation, which minimizes the distance from the interpolated point to the primary characteristic. An intuitively appealing technique involving direct adjustment of the wave path is rejected because it is potentially unstable. The entire flexible algorithm is implemented as a preprocessor step, uses memory efficiently, executes quickly, and provides a flexible tool for investigating the importance of discretization errors in pipeline systems. The properties of the new algorithm are analyzed theoretically and illustrated by example.