Post-extrapolation for specified time-step results without interpolation in MOC-based 1D hydraulic transients and gas release computations

Abstract

The goal of the paper is to present a supplementary step called postextrapolation. When applied to the well-known method of characteristics (MOC), this assures the continuous use of the specified time steps or regular numerical grid without interpolations during computations of transients in 1D 2-phase flow in straight elastic pipes. The new method consists of two steps, the first being a typical MOC step, where the C− and C+ characteristics start from regular nodal points, allowing for the point of intersection to differ from a regular one. After defining the variables there the method transforms it corresponding to the near regular grid point, using the first derivatives contained in the original, nonlinear, governing equations, as evaluated numerically from the variables got earlier in the neighboring nodes. The procedure needs no interpolations; it deals with grid-point values only. Instead of the Courant-type stability conditions, shock-wave catching and smoothing techniques help to assure numerical stability between broad limits of parameters like the closing time of a valve and the initial gas content of the fluid. Comparison by runs with traditional codes under itemized boundary conditions and measurements on a simple TPV (tank-pipe-valve) setup show acceptable scatter.