Comprehensive error estimation of simulations of pipe flows with elastic water column model

本文讨论了如何用时间线内插法估计特征差分方程组的数值误差，该方法适用于小马赫数管道中的水击问题。通过将解析导出的数值解与管网中驻波的精确解进行比较，建立了时间线上相邻两个网格间的内插和沿特征线的摩擦力项的时间积分引起的误差估计方法。它将是通过精度控制生成足够的网格的有用工具，如时间推进恒定流方法，控制精度最差，导致驻波的基模快速衰减。

The paper deals with how to estimate numerical errors of characteristic finite difference equations using time-line interpolations, valid for water hammer in pipes with small Mach number. The method of estimating errors due to interpolations between two adjacent grids in time line and time integration of friction terms along characteristic lines is formulated using comparisons between numerical solutions, which are analytically derived, and exact solutions of standing waves in pipe networks. It will be useful tool for generating adequate grids for computations through accuracy control such as time-marching steady flow approach controlling the accuracy to be worst, leading to decaying fast the elementary mode of standing wave.