Fundamental Research on Method of Characteristics Based on Cubic Interpolated Profile Scheme in Water Hammer Analysis

This paper introduces basic research conducted to develop a numerical analysis technique for water hammer analysis. The CIP (Cubic Interpolated Profile) scheme was applied to obtain more accurate results without greatly causing a spatial interpolation error depending on the Courant number in the method of characteristics. Regarding this technique, the authors derived a well-formed error formula by applying a linear stability analysis. Characteristics of the interpolation error were clarified by comparing existing interpolation schemes with the method of characteristics. The interpolation error of CIP scheme was superior to the Spatial Linear Interpolation Scheme, was approximately equal to the Time Linear Interpolation Scheme and the cubic spline interpolation scheme with sufficient number of computational grids. The calculation efficiency of the CIP scheme was superior to the other schemes excepting the Spatial Linear Interpolation Scheme.